## 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 

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

 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]

### Zipped files

 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

### Examples 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.