Wiki Max - User contributions [en]

Solution LAB3 CNT

2021-04-01T18:05:13Z

Daniele Varsano: /* Step 2 */

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 3: A small Carbon nanotube (CNT)]]
In order to build the cell we can use a CNT generator, several options available:

==Step 1==
*go to CNT generator http://turin.nss.udel.edu/research/tubegenonline.html
*For simplicity set the crystal cell as cubic
*Choose a format with PBC (e.g. PDB with PBC). Note that the units are in Angstrom.
*In building the input file: Note the tube axis is along z.
Suggestions: (Use ibrav=8, set an arbitrary amount of vacuum, and set cilldm(3)=c/a)
*Visualize the structure using xcrysden

==Step 2==
*You can use cell_dofree='z' to relax the cell parameter along the tube axis
*Set a value of k-points (along z) not tool large (12 should be enough)
*Set forc_conv_thr = 1.0d-2/1de-3 otherwise the relaxation process it too long (celldm(1)=20 ~15 min)
*Visualize the relaxation output in xcrysden (curvature effects wrt ideal graphene structure)

Solution LAB3 CNT

2021-04-01T17:48:28Z

Daniele Varsano: /* Step 2 */

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 3: A small Carbon nanotube (CNT)]]
In order to build the cell we can use a CNT generator, several options available:

==Step 1==
*go to CNT generator http://turin.nss.udel.edu/research/tubegenonline.html
*For simplicity set the crystal cell as cubic
*Choose a format with PBC (e.g. PDB with PBC). Note that the units are in Angstrom.
*In building the input file: Note the tube axis is along z.
Suggestions: (Use ibrav=8, set an arbitrary amount of vacuum, and set cilldm(3)=c/a)
*Visualize the structure using xcrysden

==Step 2==
*You can use cell_dofree='z' to relax the cell parameter along the tube axis
*Set a value of k-points (along z) not tool large (12 should be enough)
*Set forc_conv_thr = 1.0d-2/1de-3 otherwise the relaxation process it too long (cilldm(1)=20 ~15 min)
*Visualize the relaxation output in xcrysden (curvature effects wrt ideal graphene structure)

Solution LAB3 CNT

2021-04-01T17:23:31Z

Daniele Varsano: /* Step 2 */

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 3: A small Carbon nanotube (CNT)]]
In order to build the cell we can use a CNT generator, several options available:

==Step 1==
*go to CNT generator http://turin.nss.udel.edu/research/tubegenonline.html
*For simplicity set the crystal cell as cubic
*Choose a format with PBC (e.g. PDB with PBC). Note that the units are in Angstrom.
*In building the input file: Note the tube axis is along z.
Suggestions: (Use ibrav=8, set an arbitrary amount of vacuum, and set cilldm(3)=c/a)
*Visualize the structure using xcrysden

==Step 2==
*You can use cell_dofree='z' to relax the cell parameter along the tube axis
*Set a value of k-points (along z) not tool large (12 should be enough)
*Set forc_conv_thr = 1.0d-2/1de-3 otherwise the relaxation process it too long
*Visualize the relaxation output in xcrysden (curvature effects wrt ideal graphene structure)

Solution LAB3 CNT

2021-04-01T17:23:06Z

Daniele Varsano: /* Step 2 */

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 3: A small Carbon nanotube (CNT)]]
In order to build the cell we can use a CNT generator, several options available:

==Step 1==
*go to CNT generator http://turin.nss.udel.edu/research/tubegenonline.html
*For simplicity set the crystal cell as cubic
*Choose a format with PBC (e.g. PDB with PBC). Note that the units are in Angstrom.
*In building the input file: Note the tube axis is along z.
Suggestions: (Use ibrav=8, set an arbitrary amount of vacuum, and set cilldm(3)=c/a)
*Visualize the structure using xcrysden

==Step 2==
*You can use cell_dofree='z' to relax the cell parameter along the tube axis
*Set a value of k-points (along z) not tool large (12 should be enough)
*Set forc_conv_thr = 1.0d-2 otherwise the relaxation process it too long
*Visualize the relaxation output in xcrysden (curvature effects wrt ideal graphene structure)

Solution LAB3 CNT

2021-04-01T17:22:48Z

Daniele Varsano: /* Step 2 */

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 3: A small Carbon nanotube (CNT)]]
In order to build the cell we can use a CNT generator, several options available:

==Step 1==
*go to CNT generator http://turin.nss.udel.edu/research/tubegenonline.html
*For simplicity set the crystal cell as cubic
*Choose a format with PBC (e.g. PDB with PBC). Note that the units are in Angstrom.
*In building the input file: Note the tube axis is along z.
Suggestions: (Use ibrav=8, set an arbitrary amount of vacuum, and set cilldm(3)=c/a)
*Visualize the structure using xcrysden

==Step 2==
*You can use cell_dofree='z' to relax the cell parameter along the tube axis
*Set a value of k-points (along z) not tool large (12 should be enough)
*Set forc_conv_thr = 1.0d-2 otherwise the relaxation process it too long
*Visualize the relaxation output in xcrysden

Solution LAB3 CNT

2021-04-01T17:04:13Z

Daniele Varsano:

Solution LAB3 CNT

2021-04-01T16:58:37Z

Daniele Varsano:

Solution LAB3 CNT

2021-04-01T16:57:59Z

Daniele Varsano:

Solution LAB3 CNT

2021-04-01T16:28:05Z

Daniele Varsano:

Solution LAB3 CNT

2021-04-01T16:27:45Z

Daniele Varsano:

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 3: Carbon (hBN) ]]
In order to build the cell we can use a CNT generator, several options available:

*go to http://turin.nss.udel.edu/research/tubegenonline.html

Solution LAB3 CNT

2021-04-01T16:26:27Z

Daniele Varsano: Created page with "In order to build the cell we can use a CNT generator, several options available: *go to http://turin.nss.udel.edu/research/tubegenonline.html"

In order to build the cell we can use a CNT generator, several options available:

*go to http://turin.nss.udel.edu/research/tubegenonline.html

Electronic properties of 2D and 1D systems

2021-04-01T16:20:49Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png | Sketch of Carbon nanotube band structure depending on the rolling direction
File:cnt_chirality.jpg | Carbon nanotube configurations with the chiral vector C and unit vectors a and b. From: R. Mishra et al. Textile Progress 46(2) (2014)
</gallery>

* Create the quantum espresso input file for the smaller CNT (3,3)
* Relax the structure
* Calculate the band structure
* Calculate the density of states (Van Hove singularity)

[[Solution_LAB3_CNT | Hints]]

Electronic properties of 2D and 1D systems

2021-04-01T16:14:13Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Electronic properties of 2D and 1D systems

2021-04-01T16:11:42Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png | Sketch of Carbon nanotube band structure depending on the rolling direction
File:cnt_chirality.jpg | Carbon nanotube configurations with the chiral vector C and unit vectors a and b. From: R. Mishra et al. Textile Progress 46(2) (2014)
</gallery>
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T16:10:11Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png
File:cnt_chirality.jpg | Carbon nanotube configurations with the chiral vector C and unit vectors a and b. From: R. Mishra et al. Textile Progress 46(2) (2014)
</gallery>
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T16:09:01Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png
File:cnt_chirality.jpg
</gallery>
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

File:Cnt chirality.jpg

2021-04-01T16:08:18Z

Daniele Varsano:

Electronic properties of 2D and 1D systems

2021-04-01T16:08:04Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png
File:cnt_chirality.jpg
</gallery>
Memo

[[File:Cnt chirality.jpg|thumb]]
* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T16:07:29Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png
File:cnt_chirality.jpg
</gallery>
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T16:07:14Z

Daniele Varsano:

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png]
File:cnt_chirality.jpg|
</gallery>
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T16:07:06Z

Daniele Varsano:

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.
<gallery widths=300px heights=200px>
File:Cnt_bs.png]
File:cnt_chirality.jpg|
</gallery>
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T16:00:10Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

[[File:Cnt_bs.png|border|300px]]
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:59:59Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

[[File:Cnt_bs.png|border]]
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:59:34Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

[[File:Cnt_bs.png|border|thumb]]
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

File:Cnt bs.png

2021-04-01T15:58:20Z

Daniele Varsano:

Electronic properties of 2D and 1D systems

2021-04-01T15:58:03Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

[[File:Cnt bs.png|border|thumb]]
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:57:40Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

[[File:Cnt bs.png|thumb]]
Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:57:02Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

[[File:cnt_bs.png| border|400px]]

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:56:51Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

[[File: cnt_bs.png| border |400px]]

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:55:49Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled. We can start from the graphene band structure considering the boundary condition along the circumference.

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:49:42Z

Daniele Varsano: /* Exercise 3: A small Carbon nanotube (CNT) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Here we want to study te electronic structure of a small carbon nanotube, obtained rolling up a graphene sheet. Interestingly the electronic structure will change drastically depending on how the rube is rolled.

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:48:51Z

Daniele Varsano: /* Exercise 3: A small CNT */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small Carbon nanotube (CNT)===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:47:18Z

Daniele Varsano: /* Exercise 2: 2D Hexagonal Boron Nitride (hBN) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb | Hexagonal Boron Nitride sheet]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:46:56Z

Daniele Varsano: /* Exercise 2: 2D Hexagonal Boron Nitride (hBN) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn.png|200px|thumb]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

File:Hbn.png

2021-04-01T15:46:25Z

Daniele Varsano: hbn picture

== Summary ==
hbn picture

Electronic properties of 2D and 1D systems

2021-04-01T15:45:24Z

Daniele Varsano:

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===
[[File:hbn|200px|thumb]]
*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Solution LAB3 hBN

2021-04-01T15:43:24Z

Daniele Varsano:

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 2: Hexagonal Boron Nitrite (hBN) ]]
Now we do have two non-equivalent atoms
*If you do not have already done, git pull the LabQSM repository to get the Boron pseudo-potential
*Use the same input used for graphene inserting the two non-equivalent atoms
*Relax the cell as done before
*For the bulk structure the c/a cell parameter is 2.582 bohr

Electronic properties of 2D and 1D systems

2021-04-01T15:41:33Z

Daniele Varsano: /* Exercise 2: 2D Hexagonal Boron Nitride (hBN) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===

*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference wrt the 2D structure?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:41:12Z

Daniele Varsano: /* Exercise 2: Hexagonal Boron Nitride (hBN) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: 2D Hexagonal Boron Nitride (hBN)===

*build a supercell for 2D hBN
*calculate the DOS and band structure
*Calculate the electronic structure for bulk hBN, what is the main difference?

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:39:58Z

Daniele Varsano: /* Exercise 2: Hexagonal Boron Nitrite (hBN) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: Hexagonal Boron Nitride (hBN)===

*build a supercell for hBN
*calculate the DOS and band structure

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Solution LAB3 hBN

2021-04-01T15:39:33Z

Daniele Varsano:

Solution LAB3 hBN

2021-04-01T15:39:25Z

Daniele Varsano:

Solution LAB3 hBN

2021-04-01T15:38:47Z

Daniele Varsano:

Solution LAB3 hBN

2021-04-01T15:38:00Z

Daniele Varsano:

* Back to the previous page: [[Exercise 2: Hexagonal Boron Nitrite (hBN)]]
Now we do have two non-equivalent atoms
*If you do not have already done, git pull the LabQSM repository to get the Boron pseudo-potential
*Use the same input used for graphene replacing the

Solution LAB3 hBN

2021-04-01T15:37:38Z

Daniele Varsano:

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 2: hBN]]
Now we do have two non-equivalent atoms
*If you do not have already done, git pull the LabQSM repository to get the Boron pseudo-potential
*Use the same input used for graphene replacing the

Solution LAB3 hBN

2021-04-01T15:36:43Z

Daniele Varsano:

Now we do have two non-equivalent atoms
*If you do not have already done, git pull the LabQSM repository to get the Boron pseudo-potential
*Use the same input used for graphene replacing the

Solution LAB3 hBN

2021-04-01T15:35:38Z

Daniele Varsano: Created page with "Now we do have two non-equivalent atoms *If you do not have already done, git pull the Labreporisot *Use the same input used for graphene replacing the"

Now we do have two non-equivalent atoms
*If you do not have already done, git pull the Labreporisot
*Use the same input used for graphene replacing the

Electronic properties of 2D and 1D systems

2021-04-01T15:34:39Z

Daniele Varsano: /* Exercise 2: Hexagonal Boron Nitrite (hBN) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: Hexagonal Boron Nitrite (hBN)===

*build a supercell for hBN
*calculate the DOS and band structure

[[Solution_LAB3_hBN | Hints]]

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Electronic properties of 2D and 1D systems

2021-04-01T15:27:09Z

Daniele Varsano: /* Exercise 2: Hexagonal Boron Nitrite (hBN) */

Prev:[[LabQSM#Module 3: Low dimensional structures (6h)]]

<gallery widths=300px heights=200px>
File:Graphen.jpg| Graphene sheet: Picture by AlexanderAlUS]
File:cnt.png| Rolling graphene sheets: Carbon Nanotubes
</gallery>

==Input set-up for a low dimensional system:==
Now we want to deal with systems of reduced dimensionality, e.g. periodic in one or two dimension but isolated in the other directions. This is accomplished by:

* Isolating the system in the non-periodic dimension as seen in [[Electronic properties of isolated molecules]], so inserting an amount of vacuum in the supercell.
* Sampling the Brillouin zone that now has reduced dimension:

In Quantum ESPRESSO one needs to set the following:
K_POINTS automatic
nk nk 1 0 0 0
this will generate a 2D sampling.
In brief: you will need large supercells because of the present of vacuum which reflects in a large number of plane waves and a converged sampling of the BZ. The combination of this two issues makes the calculations of 2D system rather cumbersome.

==Exercises:==
===Exercise 1: Graphene===
[[File:honeycomb.png|200px|thumb| Honeycomb lattice structure of graphene.Picture from: J. Fuchs and M. Goerbig: [https://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Introduction to the Physical Properties of Graphene]]]
*build a supercell for an ideal graphene structure
*relax the supercell
*calculate the graphene band structure
*calculate the density of states projected on π and σ states

[[Solution_LAB3_graphene | Hints]]

===Exercise 2: Hexagonal Boron Nitrite (hBN)===

*build a supercell for hBN
*calculate the DOS and band structure

===Exercise 3: A small CNT===

Memo

* Picture of the rolling sheet
* Picture of the Dirac cone slice
* Link to the tube generator

Solution LAB3 graphene

2021-04-01T15:24:23Z

Daniele Varsano: /* Step 4 */

* Back to the previous page: [[Electronic properties of 2D and 1D systems#Exercise 1: Graphene]]

==Step 1 ==

[[File:Gr unit.png| border |400px |Picture from [https://aip.scitation.org/doi/10.1063/1.4951692 G. Yang at al. AIP Advances 6, 055115 (2016)]]]

* Graphene has an honeycomb lattice and we can define the unit cell by considering an hexagonal lattice and two atoms per cell. The CC distance is 0.142nm. An input file can be set using an hexagonal bravais lattice as:

&system
ibrav= 4, celldm(1) =4.6542890, celldm(3)=something appropriate, nat= 2, ntyp= 1, [...]
/
ATOMIC_POSITIONS {crystal}
C 0.0000000 0.0000000 0.000000
C 0.3333333 0.6666666 0.000000

* Graphene is a quasi-metal, pay attention to the smearing
* K point sampling on the plane. If multiple of 3 you can include the high symmetry point K in your sampling
* You may want visualise your input using xcrysden and measure the CC distance

==Step 2 ==

*When relaxing the system you may want to keep fixed the direction orthogonal to the graphene sheet. This is done by inserting in your input the CELL namelist

&CELL
cell_dofree='2Dxy'
...
/

==Step 3 ==
[[File:gr_bz.jpg|200px|thumb| Graphene Brillouin Zone]]

*Let's consider the path Γ-M-K-Γ
*We can get the high symmetry k-point path using xcrysden:
xcrysden --pwi scf_graphene.in

Tools->K-path selection:

[[File:kpath.png|200px|Xcrysden K-path selection]]

Notice that the k points showed in xcrysden are in crystal_b unit.

*Perform a "bands" calculation using pw.x assigning the path e.g:

K_POINTS {crystal_b}
4
0.0 0.0 0.0 20
0.0 0.5 0.0 20
0.33333333 0.333333333 0. 20
0.0 0.0 0.0 20

*Finally we can post-process the result using bands.x

==Step 4 ==

*Calculate the electronic structure with a fine mesh of k-points (at least 48x48x1 better larger)
*Use projwfc.x to project onto the s and p orbitals. (Note the file containing the p projections show the x,y,z component in 3 columns)