Quantum confinement, energy spectra and backscattering of Dirac fermions in quantum wire in magnetic field

TL;DR

This paper investigates the energy spectra, backscattering, and conductance of Dirac fermions in a quantum wire under magnetic fields, revealing conditions for suppressed backscattering and the formation of massless surface subbands.

Contribution

It introduces a detailed analysis of Dirac fermions in cylindrical quantum wires with boundary conditions, magnetic field effects, and backscattering suppression mechanisms.

Findings

Surface states depend on boundary parameter a0 even without magnetic field.

Magnetic field induces massless surface subbands at half-integer flux quanta.

Backscattering can be suppressed under specific conditions.

Abstract

We address the problems of an energy spectrum and backscattering of massive Dirac fermions confined in a cylindrical quantum wire. The Dirac fermions are described by the 3D Dirac equation supplemented by time-reversal-invariant boundary conditions at a surface of the wire. Even in zero magnetic field, spectra quantum-confined and surface states substantially depend on a boundary parameter a0. At the wire surface with a0 > 0 (a0 < 0) the surface states form 1D massive subbands inside (outside) the bulk gap. The longitudinal magnetic field transforms the energy spectra. In the limit of the thick wires and the weak magnetic fields, the 1D massless surface subbands arise at half- integer number of magnetic flux quanta passing through the wire cross section. We reveal conditions when backscattering of the surface Dirac fermions by a non-magnetic impurity is suppressed. In addition, we calculate a conductance formed by the massless surface Dirac fermions in the magnetic field in collisional and ballistic regimes.