[Pw_forum] Band Structure/graphene

[Giovanni Cantele]

nazari at iasbs.ac.ir wrote:
>
>  Dear All,
>
>  I wish to get the band structure and band gap for graphene nanoribbon.
>  In the following you can find the input for 2*2 graphene nanoribbon.
>  In litrature the reported band gap for such  structure is in the range
>   of 0.5-0.6. I get such value for small  number  of k-point but by
>  increasing the number of kpoint the band gap  decrases  and this not
> compatible with litratue. Is there probelm in the input.
>
>  regards
>  Fariba nazari
>  IASBS
>
> Input for small band gap:
>
> &control
>     calculation='nscf'
>     prefix='graphene'
>     pseudo_dir = '/lhome/aa/espresso-4.0.2/pseudo/',
>     outdir='/lhome/aa/tmp/'
>  /
>  &system
>    ibrav= 8, celldm(1)=9.302, celldm(2)=3.864, celldm(3)=2.844, nat=12,
> ntyp=2,
>    occupations='smearing', degauss=0.02, ecutwfc =30.0, ecutrho
> =300.0,nbnd=28,
> /
>  &electrons
>     conv_thr =  1.0d-6
>     mixing_beta = 0.7
>  /
> &IONS
>   ion_dynamics = 'bfgs'
> /
> ATOMIC_SPECIES
> C 12.0107 C.pbe-van_bm.UPF
> H 1.00794 H.pbe-van_ak.UPF
> ATOMIC_POSITIONS {angstrom}
> C        1.769889031   1.322946944  -0.012817900
> C        1.770489086   4.159733324  -0.022135401
> C        0.539682313   3.462493413  -0.021948354
> C        0.539180075   2.020040405  -0.016808553
> H        1.769947891   0.229915494  -0.001367763
> H        1.774772992   5.252856855  -0.017605292
> C        4.231096346   1.322960286  -0.012817558
> C        4.231696827   4.159712177  -0.022136595
> C        3.000909807   3.462494493  -0.021949575
> C        3.000394654   2.020036555  -0.016806896
> H        4.231213438   0.229870885  -0.001367555
> H        4.236032200   5.252906248  -0.017606218
> K_POINTS
>  15
>  0.00 0.00 0.00 1
>  0.0173 0.0 0.00 1
>  0.0273 0.0 0.0 1
>  0.0373  0.0 0.0 1
>  0.0473  0.0 0.0 1
>  0.0573  0.0 0.0 1
>  0.0673  0.0 0.0 1
>  0.0773  0.0 0.0 1
>  0.0873  0.0 0.0 1
>  0.0973  0.0 0.0 1
>  0.137  0.0 0.0  1
>  0.173  0.0 0.00 1
>  0.2754 0.0 0.0 1
>  0.334  0.0 0.0 1
>  0.50 0.00 0.00 1
> Input for  band gap in the range of 0.5-0.6:
>
>
>  &control
>     calculation='nscf'
>     prefix='graphene'
>     pseudo_dir = '/lhome/aa/espresso-4.0.2/pseudo/',
>     outdir='/lhome/aa/tmp/'
>  /
>  &system
>    ibrav= 8, celldm(1)=9.302, celldm(2)=3.864, celldm(3)=2.844, nat=12,
> ntyp=2,
>    occupations='smearing', degauss=0.02, ecutwfc =30.0, ecutrho
> =300.0,nbnd=28,
> /
>  &electrons
>     conv_thr =  1.0d-6
>     mixing_beta = 0.7
>  /
> &IONS
>   ion_dynamics = 'bfgs'
> /
> ATOMIC_SPECIES
> C 12.0107 C.pbe-van_bm.UPF
> H 1.00794 H.pbe-van_ak.UPF
> ATOMIC_POSITIONS {angstrom}
> C        1.769889031   1.322946944  -0.012817900
> C        1.770489086   4.159733324  -0.022135401
> C        0.539682313   3.462493413  -0.021948354
> C        0.539180075   2.020040405  -0.016808553
> H        1.769947891   0.229915494  -0.001367763
> H        1.774772992   5.252856855  -0.017605292
> C        4.231096346   1.322960286  -0.012817558
> C        4.231696827   4.159712177  -0.022136595
> C        3.000909807   3.462494493  -0.021949575
> C        3.000394654   2.020036555  -0.016806896
> H        4.231213438   0.229870885  -0.001367555
> H        4.236032200   5.252906248  -0.017606218
> K_POINTS
> 5
>  0.00 0.00 0.00 1
>  0.137  0.0 0.0  1
>  0.173  0.0 0.00 1
>  0.2754 0.0 0.0 1
>  0.50 0.00 0.00 1
>   

Hi,
are you sure that the literature results you mention are just referred 
to this ribbon?

As far as I understand, you are considering a graphene nanoribbon with 
zigzag edge.
The literature results (e.g. Son, PRL (2006)) report that (not very 
aware about what happens
for the width of your ribbon, but for sure this holds for a larger width):
i) the spin unpolarized calculation gives a semimetal, so no gap at all 
(bands around the Fermi
level merge from about (2/3) pi/a to pi/a, this is consistent with what 
you're finding!)
ii) the lowest-energy configuration is spin polarized, with 
antiferromagnetic ordering between the
two ribbon edges. Such configuration has a gap, of the order of 0.1-0.3 
eV (if I well remember),
but this is not the "gap" you are speaking about, being (as far as I see 
from your input)
your calc. spin unpolarized.

Therefore, it seems that your results are reasonable, the "0.5-0.6 eV 
gap" calc. gives a different result
just because you are not considering enough k points in your path (also 
consider that your unit cell seems to
be doubled, so the band structure is folded with respect to the ones you 
may found in the literature).


Among the possible solutions:
i) there is something "peculiar" with the zigzag-edge nanoribbon with 
minimum width like the
one you are studying, in this case can you please also give a reference 
about the papers reporting
the results disagreeing with yours?

ii) the all-semiconducting ribbons reported in the literature are  with 
armchair edge, are you
maybe trying to reproduce results for these ribbons? In this case it 
seems that your unit cell
reproduces the "wrong" edge.

iii) did you check convergence of your scf or relax calc. with respect 
to parameters like: k-point grid,
degauss (maybe 0.02 too large??), etc.? actually, I think that, unless 
one uses very unreasonable parameters,
this should not change, at least qualitatively, the results.

Giovanni

-- 



Dr. Giovanni Cantele
Coherentia CNR-INFM and Dipartimento di Scienze Fisiche
Universita' di Napoli "Federico II"
Complesso Universitario di Monte S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
Phone: +39 081 676910
Fax:   +39 081 676346
E-mail: giovanni.cantele at cnr.it
        giovanni.cantele at na.infn.it
Web: http://people.na.infn.it/~cantele
Research Group: http://www.nanomat.unina.it