fermi velocity of graphene from bandstructure

[nus11]

Hi, I am wondering to extract fermi velocity of single-layer graphene from vasp calculation and following the procedures below:

I have a basic hexagonal unit cell of two carbon atoms.
1 C
2 1.000000
3 2.460000 0.000000 0.000000
4 -1.230000 2.130422 0.000000
5 0.000000 0.000000 6.800000
6 2
7 Direct
8 0.000000 0.000000 0.500000
9 0.333333 0.666666 0.500000

I first do SCF relaxation with

Automatic Mesh
2 0
3 Monkhorst-Pack
4 64 64 1
5 0 0 0
or
Automatic Mesh
2 0
3 Gamma
4 64 64 1
5 0 0 0
the number of Kmesh has been tried with some other numbers like 32, 97,..

My Incar set as following

NSW = 100
2 PREC = ACU
3 # NELECT = 8.0784
4 NELMIN = 5
5 IBRION = 2
6 ISIF = 1
7 NBANDS = 14
I have also played with smearing ( using gaussian) and sigma

the POTCAR i have tried are PAW-PBE for carbon , with ENCUT = 400eV and 700 eV

after SCF, I choose the following Kpath to do band calcualtion .

K points along high symmetry line
2 60 ! 60 intersections
3 line mode
4 rec
5 -0.33333 0.66667 0.000 ! K
6 0.000 0.000 0.000 ! G
7 0.000 0 0 ! G
8 0 0.5 0 ! M
9 0 0.5 0 ! M
10 -0.33333 0.66667 0 ! K

with all the above calculation finished, I did the following:

Vf = dE/(h*dK), h is the reduced plank constant, to get the approximation of dE/dK, I go to the EIGENVAl file of band calculation.

Since I start with K point so I catch

-0.3333300E+00 0.6666700E+00 0.0000000E+00
12 4 1.1135
13 5 1.1137
-0.3276803E+00 0.6553705E+00 0.0000000E+00
28 4 0.9514
29 5 1.2745
I calculate the distance between the above two kpoint with the known reciprocal lattice vector in OUTCAR( I have times 2Pi for the original reciprocal lattice from OUTCAR) as dK
and the dE = 1.1135- 0.9514 , reduced plank constant is 6.582*10^-16 eV .s

I do the math as Vf = 1/ (6.582*10^-16) * dE/dK , however after I played around with different K mesh , smearing , I always get Vf around 3*10^5 m/s about 1/3 of the 10^6 m/s people talk about. Is the procedure I did above appropriate ? Any ideas about the discrepency?

thanks for your attention

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