The two classes of low energy spectra in finite carbon nanotubes

TL;DR

This paper reveals that boundary effects, rather than disorder, can cause valley mixing in ultraclean armchair carbon nanotubes, leading to distinct low-energy spectral features compared to zigzag nanotubes, due to their different symmetries.

Contribution

It demonstrates that boundary-induced valley mixing occurs in clean armchair CNTs and explains the spectral differences between armchair and zigzag classes based on symmetry.

Findings

Boundary effects cause valley mixing in armchair CNTs.

Zigzag CNTs do not exhibit boundary-induced valley mixing.

Spectral level splitting varies nonmonotonically with energy level distance.

Abstract

Electrons in carbon nanotubes (CNTs) possess spin and orbital degrees of freedom. The latter is inherited from the bipartite graphene lattice with two inequivalent Dirac points. The electronic spectra obtained in several transport experiments on CNT quantum dots in parallel magnetic field often show an anticrossing of spectral lines assigned to the opposite Dirac valleys. So far this valley mixing has been attributed to the disorder, with impurity induced scattering. We show that this effect can arise also in ultraclean CNTs of the armchair class and it can be caused solely by the presence of the boundaries. In contrast, in CNTs of the zigzag class it does not occur. These two fundamentally different classes of spectra arise because of different symmetries of the low energy eigenstates of the two types of CNTs. The magnitude of the level splitting depends in a nonmonotonous way on the distance of the involved energy levels from the charge neutrality point.