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arXiv · 1206.2244

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

Timur Tudorovskiy·Mikhail I. Katsnelson
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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.

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Timur Tudorovskiy, Mikhail I. Katsnelson. 2012-06-11. Peculiarities of dynamics of Dirac fermions associated with zero-mass lines. https://doi.org/10.1103/physrevb.86.045419

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