Electron properties of carbon nanotubes in a periodic potential

TL;DR

This paper explores how a periodic potential influences electron states in carbon nanotubes, revealing incompressible states, spectral gaps at rational densities, and potential for electron pumping, with implications for quantum transport.

Contribution

It introduces a comprehensive analysis of electron behavior in nanotubes under periodic potentials, highlighting the role of interactions and different binding regimes in forming incompressible states.

Findings

Spectral gaps occur at rational electron densities per potential period.

Incompressible states arise from Bragg diffraction in the Luttinger liquid regime.

Electron interactions enable fractional electron pumping in adiabatic transport.

Abstract

A periodic potential applied to a nanotube is shown to lock electrons into incompressible states that can form a devil's staircase. Electron interactions result in spectral gaps when the electron density (relative to a half-filled Carbon pi-band) is a rational number per potential period, in contrast to the single-particle case where only the integer-density gaps are allowed. When electrons are weakly bound to the potential, incompressible states arise due to Bragg diffraction in the Luttinger liquid. Charge gaps are enhanced due to quantum fluctuations, whereas neutral excitations are governed by an effective SU(4)~O(6) Gross-Neveu Lagrangian. In the opposite limit of the tightly bound electrons, effects of exchange are unimportant, and the system behaves as a single fermion mode that represents a Wigner crystal pinned by the external potential, with the gaps dominated by the Coulomb repulsion. The phase diagram is drawn using the effective spinless Dirac Hamiltonian derived in this limit. Incompressible states can be detected in the adiabatic transport setup realized by a slowly moving potential wave, with electron interactions providing the possibility of pumping of a fraction of an electron per cycle (equivalently, in pumping at a fraction of the base frequency).