Peculiarities of dynamics of Dirac fermions associated with zero-mass lines

TL;DR

This paper investigates the behavior of Dirac fermions near zero-mass lines, analyzing how tunneling and bending affect their dispersion, mass acquisition, and geometric phases, with implications for various physical systems.

Contribution

It provides a detailed calculation of the energy gap due to tunneling between zero-mass lines and introduces a new geometric phase related to mass asymmetry.

Findings

Tunneling between zero-mass lines opens an energy gap and causes delocalization.

Adiabatic bending induces Berry and new geometric phases.

Mass asymmetry near zero-mass lines affects phase accumulation.

Abstract

Zero-mass lines result in appearance of linear dispersion modes for Dirac fermions. These modes play an important role in various physical systems. However, a Dirac fermion may not precisely follow a single zero-mass line, due to either tunneling between different lines or centrifugal forces. Being shifted from a zero-mass line the Dirac fermion acquires mass which can substantially influence its expected "massless" behavior. In the paper we calculate the energy gap caused by the tunneling between two zero-mass lines and show that its opening leads to the delocalization of linear dispersion modes. The adiabatic bending of a zero-mass line gives rise to geometric phases. These are the Berry phase, locally associated with a curvature, and a new phase resulting from the mass square asymmetry in the vicinity of a zero-mass line.