Density of states (DOS) for SWCNT's

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.

Definitions and Relations

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)

Filenames 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]

Zipped files 0.5 MB
0.4 <= D < 1.0 nm 1.6 MB
1.0 <= D < 2.0 nm 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 was used in both figures.