# CNT: Tight-Binding Code for Graphene and SWCNTs

We calculate the electronic structure and dielectric response of a single graphene layer, and a single-wall carbon nanotube within the tight-binding approximation. For simplicity, we consider only $\pi$ orbitals and limit ourselves to nearest-neighbour interactions [1-5].

### List of Files

cnt.py Basic parameters for Graphene and a Single-Walled Carbon Nanotube. Zone-folding model for Single-Walled Carbon Nanotubes. Electronic structure and response of a single graphene layer, and a single wall carbon nanotube using a first-nearest-neighbour tight-binding model. Calculate AR-EELS of a tube by expanding the external plane-wave perturbation into Bessel functions.

### Examples

The following python script calculates the electron energy-loss function of a (9,3) single-wall carbon nanotube for a plane-wave perturbation with a momentum transfer perpendicular to the tube axis.

# example script to calculate the response of a (9,3) CNT
# to a plane-wave perturbation using tight-binding approx.

import numpy as np;
import matplotlib.pylab as plt;
import cnt;
import tight_binding as tb;
import ar_eels as ar;

CNT =cnt.CNT(9,3); # define tube
TB =tb.TB_CNT(CNT); # init tight-binding for this tube
E =np.arange(0,15,0.1); # energies in eV
qx = 0.4; # momentum perpendicular to tube [1/A]
qz = 0.0; # " parallel to tube [1/A]
q_cc=[qx*0.529177,0,qz*0.529177]; # conversion to [a.u.]

# define function that returns tube susceptibility
# which is calculated using the tight-binding method
def chi_CNT(qz,L):
eps = TB.eps((qz,L),E)
return (1./eps - 1) / cnt.coulCNT(TB.CNT,(qz,L));

# calculate response of CNT to plane wave perturbation
epsi=ar.plane_wave_epsi(CNT,q_cc,chi_CNT,lmax=20);

# plotting
plt.plot(E,-epsi.imag);
plt.show();

Further examples are included at the end of each file and can be executed using python <file>. A detailed documentation can be found in the code (use pydoc) and in appendix C of my PhD Thesis [5].

### References

1. Shung K. W. K., Phys. Rev. B (34) 979 (1986)
2. C. Zener, Phys. Rev. 36, 51 (1930)
3. M.F.Lin, C.S. Huang, D.S. Chuu, PRB (55) 13961 (1997)
4. M.F.Lin, D.S. Chuu, C.S. Huang, Y.K. Lin, K.W.K. Shung, PRB (53) 15493 (1996)
5. R. Hambach, PhD Thesis (2010), pdf
6. R.Saito, G.Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press (1998)