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graphene obtains a "band gap" in the spectral function
http://epwforum.uk/viewtopic.php?f=6&t=736
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Author:  chrisewolf [ Mon Dec 10, 2018 1:32 pm ]
Post subject:  graphene obtains a "band gap" in the spectral function

Dear all,

I am facing a weird problem when calculating the spectral function for graphene.

I have first converged the line-width of the electrons which works fine at an nscf-mesh of 33x33x1 and a q-point mesh of 11x11x1. I interpolate at a fine q mesh of 500x500x1 which gives very nice smooth linewidth plots.

however when I calculate the spectral function the material suddenly has a sizable "gap" at the K point of ~0.250 eV. I am curious where this might arise?

I used a fine mesh in the "path.dat" file close to K

Code:
...
        0.3318285135    0.3318285135    0.0000000000  0.00
        0.3323290090    0.3323290090    0.0000000000  0.00
        0.3328295045    0.3328295045    0.0000000000  0.00
        0.3333300000    0.3333300000    0.0000000000  0.00
        0.3333333333    0.3333333333    0.0000000000  0.00
        0.3338305105    0.3323290090    0.0000000000  0.00
        0.3343310210    0.3313280180    0.0000000000  0.00
        0.3348315315    0.3303270270    0.0000000000  0.00
        0.3353320420    0.3293260360    0.0000000000  0.00
....


the interpolated bands and phonons look excellent (I use the common trick with two carbon atoms)

Code:
  proj(1)     = 'C1:sp2;pz'
  proj(2)     = 'C2:pz'



and I checked "by hand" that the Fermi level is properly located at the "Dirac point". Increasing the k and q grid did not change the situation so I think I am stuck at something else - does anyone know what it might be?

Thanks in advance for your help!

Chris

Author:  sponce [ Thu Dec 13, 2018 6:32 pm ]
Post subject:  Re: graphene obtains a "band gap" in the spectral function

Hello,

Well the underlying perturbation theory is by construction ill defined for metals/semi-metals.

The real part of the el-ph self energy corresponds to the quasi-particle shift with respect to KS. This is responsible for the zero-point motion.
By definition the spectral function contains the real-part of the self-energy (not only the imaginary part).

As a result this will open a gap.

See for example PRB 92, 085137 (2015) for more info on spectral functions.

An add-hoc "solution" is just to shift back the spectral function so that both end touch. This is off course a big approximation and one need to be careful.

Hope this helps.
Best,
Samuel

Author:  chrisewolf [ Mon Jan 07, 2019 1:33 pm ]
Post subject:  Re: graphene obtains a "band gap" in the spectral function

Hi Samuel,

thanks a lot for your reply! Interestingly it did eventually work out quite well by doubling the coarse k-mesh - the resulting spectral function has a nice Dirac-cone like shape. It also helped to determine the fermi level more precisely using tetrahedron method in a separate calculation and read it later in EPW. I am not sure if that is a "cancellation of error" kind of situation but the results look good and are comparable to literature!

Hope that helps the next guy who stumbles across graphene :)

Best,
Chris

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