Where are the high symmetry points on a graphene band structure?

[gwr]

Hi!

Is anyone familiar with generating band structures from DFT simulations? I am using graphene, and am trying to plot the electronic structure at the high symmetry points (K, M, and gamma). Grappling to understand this theory, my questions are:

1. Is the location of the high symmetry points dependent upon the choice of the reciprocal lattice vectors, or only the geometry of the first Brillouin zone? For example, in my DFT simulation, I am using a supercell, so not the primitive cell. Hence my lattice vectors and thus reciprocal vectors are not primitive. Does this affect the whereabouts of the high symmetry points in my case?

2. Do any of the high symmetry points, as defined in reciprocal space, coincide with any physical features of the crystal lattice in real space? For example, I initially thought that the K and K' points coincided with the C-atom sites, but now think that this is incorrect.

3. In light of the above, is there a particularly easy way to calculate what lines I should plot the band structure along in order to map out the gamma-M-K-gamma path?

Any assistance would be greatly appreciated!

Thanks,
gwr

 

[saroj]

if u r doing dft in quantum espresso, then just open input scf file with xcrysden, then go to tool and then select the k path selection. u can select any path u desire. then choose number of k points. use them in input scf file for band replacing k points by the .pwscf file u obtained from xcrysden. then u can calculate bands.x for band structure.

 

[t!m]

1. The location of high-symmetry points very much depends on the choice of the unit cell. A larger real-space unit cell (like a supercell) will have a different Brillouin zone, and therefore different high-symmetry points. In certain reduced units (i.e. in units of the real-space unit cell lattice vector), the expressions for the high-symmetry points may look the same.

2. The points in reciprocal space don't so much correspond to points in real space, but rather to the wavelength or periodicity of extended states in real space.

3. The method suggested by saroj, using xcrysden, is one simple way. Alternatively, you can just look at the documentation (e.g. for quantum espresso), which gives the implied reciprocal lattice vectors. Then you can compare to a diagram of the Brillouin zone for your unit cell, to figure out where your high-symmetry points are (just a little bit of geometry ).

 

[DrDu]

I would recommend you to try to solve a Hückel model for graphene first by hand before using quantum chemical software. This reduces to solving a 2x2 matrix eigenvalue problem and you can sketch the eigenfunctions for the high symmetry points to get a feeling for what all is about.