TDOS1800.txt from TDOS1020.zip was used in both figures.
Ch. Kramberger and S. Bäs-Fischlmair
| g0 = 2.9 | Carbon interaction energy [eV] |
| a0 = 0.246 | lattice constant of graphene [nm] |
| dmp = 10-3 | damping of van Hove resonance [1] |
The DOS was calculated from the tight binding band
structure of graphene using the zone folding procedure for energys
between 0 and 3*g0.
The DOS is tabulated in units per eV and carbon (eV-1 C-1).
An algorithm was used, which allows dynamic steps on energy scale,
to guarantee full hight for all van Hove singularities. Eventually
the diverging singularities were cut off at 1 eV-1 C-1.
| Ch = (m,n) | Chiral vector |
| Dr = HCD(2*n+m,2*m+n) | Highest Common Divisor |
| range = Floor((n2+m2+n*m)/Dr) | Bandindexrange |
| j = -range, ..., +range-1 | Index of the band |
| D = 0.0783*(n2+m2+m*n)0.5 | Tube diameter [nm] |
| N = 4*(n2+m2+n*m)/Dr | Number of C atoms per unit cell |
| T = (3*(m2+n2+m*n))0.5*a0/Dr | Length of unit cell |
n2 = n2+m2+n*m
nen = n20.5
f1 = 30.5*a0*k/(2*nen)
f2 = g0*30.5*a0/(2*nen)
g1 = cos(p*(2*n+m)/Dr)*cos(f1*m+j*p*(2*n+m)/n2)
g2 = cos(p*(n+2*m)/Dr)*cos(-f1*n+j*p*(n+2*m)/n2)
g3 = cos(p*(n-m)/Dr)*cos(f1*(n+m)+j*p*(n-m)/n2)
E(n,m,k,j) = g0*(1+2*(g1+g2)+2*(1+g3))0.5
TDOS(n,m,E') = (Sum(Sum(1/(|dE/dk|+f2*dmp), j), E=E'))*T/(N*p)
| TDOSxy.zip | x and y are lower and upper diameter limits. |
| TDOSnm.txt | Filename for DOS of tube with chirality (m,n). |
| Each file contains two columns: | |
| Energy [eV], DOS [eV-1 C-1] |
| TDOS0410.zip | 0.5 MB | 0.4 <= D < 1.0 nm |
| TDOS1020.zip | 1.6 MB | 1.0 <= D < 2.0 nm |
| TDOS2030.zip | 4.1 MB | 2.0 <= D < 3.0 nm |
|
|
Density of states for the (18,0) tube. The lower figure exhibits the shift
of the Fermi level for filling the conduction band. TDOS1800.txt from TDOS1020.zip was used in both figures. |