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

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.

6 pages, 4 figures. In the second version some references were added and minor changes were made in the introduction

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Control of graphene's properties by reversible hydrogenation
• Chiral tunneling and the Klein paradox in graphene
• Fluorographene: Two Dimensional Counterpart of Teflon
• Topological confinement in bilayer graphene
• Single valley Dirac fermions in zero-gap HgTe quantum wells
• Tunneling between edge states in a quantum spin Hall system
• Chiral states in bilayer graphene: magnetic field dependence and gap opening

Cited by in corpus (8)

• Helical networks in twisted bilayer graphene under interlayer bias
• Current partition at topological zero-line intersections
• Spin-helical transport in normal and superconducting topological insulators
• Metal-Insulator Transition in Graphene on Boron Nitride
• Dynamics of domain-wall Dirac fermions on a topological insulator: a chiral fermion beam splitter
• Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection
• Chiral properties of topological-state loops
• Spectral flow for Aharonov--Bohm rings generated by zero-mass lines