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Massless Dirac fermions on a space-time lattice with a topologically protected Dirac cone

by A. Donís Vela, M. J. Pacholski, G. Lemut, J. Tworzydło, C. W. J. Beenakker

Submission summary

As Contributors: Alvaro Donís Vela
Arxiv Link: https://arxiv.org/abs/2201.02235v2 (pdf)
Date submitted: 2022-01-12 16:35
Submitted by: Donís Vela, Alvaro
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational

Abstract

The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here we introduce an implementation of Dirac fermions on a space-time lattice that removes both obstructions. The quasi-energy band structure has a single Dirac cone which cannot be removed without breaking both time-reversal and chiral symmetries. We show that this topological protection is absent in the familiar split-operator discretization, because there the time-evolution operator is discontinuous at Brillouin zone boundaries.

Current status:
Editor-in-charge assigned


Submission & Refereeing History

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Submission 2201.02235v2 on 12 January 2022

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