Calculate fermi velocity

[huckelbuckel]

Lines from A review on silicene—New candidate for electronics

The Fermi velocity calculated by Lew Yan Voon et al.  in graphene, silicene and
germacene are 6.3×10⁵   5.1×10⁵   and  3.8×10⁵ m/s,respectively

Another paper Two- and one-dimensional honeycomb structures of silicon and germanium  S. Cahangirov et. al,

says that Low buckled Si and Ge structures all have Vf of the order of 10⁶ m/sec  very close to graphene!!!

[Anders Blom]

Then you have to see what is different in their calculation - electronic structure method, GGA/LDA, etc. Maybe they even use tight-binding? All details must be considered.

[huckelbuckel]

Repetaed with GGA-PBE, 41X41X1 k points and DZDP basis

Graphene:   1.785 X 10⁶ m/sec
Germanene :8.7786 X 10⁵ m/sec
Silicene     : 4.1896 X 10⁵ m/sec

slowest in silicene?

[Anders Blom]

Obviously the values are quite sensitive to details - and perhaps also to how the Fermi velocity is computed, which value of epsilon you use. You need to make real sure there is no spurious band gap (because of too small unit cell in C, for instance, or too small k-point sampling). I also know it can be hard to get the exact right buckling in silicene, so this may have an influence.

[huckelbuckel]

i used eps = 0.0001. the 'c' parameter of the hex crystal was kept very large 42.32 Angstroms to avoid inter layer periodic interactions.

[Anders Blom]

It would be a good idea to try esp=0.001 as well, even 0.01 and 0.1, to see how linear the dispersion actually is. Also, if you rely upon very small eps, you will want to make sure that the energies are very accurate, which may mean you need to reduce the tolerance of the self-consistent loop.

[sonal AGRAWAL]

It's easy

K = (1/3,1/3,0) in units of the inverse lattice vectors GA=2pi/a*(1,1/sqrt(3),0) and GB=2pi/a*(1,-1/sqrt(3),0). Hence, K=4pi/3a*(1,1,0) in reciprocal Cartesian.
(We had LaTeX support on the Forum before, I lost it in an update... should bring it back.)

So, K-eps*(1,1,0)=(4pi/3a)*eps*(-1,0,0) and hence dK = 4pi/3a*eps.

Dear sir,
The method given in the above-quoted post  Is the same method i.e. used in the calculate velocity function given in the tutorials of calculation of Fermi velocity in ATK-VNL.
From the tutorial, I am getting the Fermi velocity of silicene and graphene in the 10^5 and 10^6 which is in good agreement in literature but in case of germanene, I am getting only 10^2 m/s. 
Thanks in advance