Effects of chirality in the electron transmission through step-like potential in zigzag, armchair, and (2m,m) carbon nanotubes

We report the one-electron spectrum and eigenstates of infinite achiral and chiral $(2m,m)$ carbon nanotubes found by using the analytic solution to the Schr\"odinger equation for the tight-binding H\"uckel-type Hamiltonian. With the help of matching the wave functions on the interfaces between the regions, where electrons have different site energies, we find and compare the transmission coefficients for zigzag, armchair and chiral nanotubes subjected to the action of an applied step-like potential. The correspondence between the nanotube band structure and the energy dependence of the transmission coefficient is demonstrated. It is shown that the $(2m,m)$ nanotubes with a medium chiral angle reveal intermediate transport properties as compared with the achiral armchair, and zigzag nanotubes.