Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling

TL;DR

This paper introduces tangent fermions on a lattice as a novel approach to simulate Dirac and Majorana fermions without fermion doubling, enabling new topological and quantum phenomena simulations.

Contribution

It proposes tangent dispersion as a new method to avoid fermion doubling and explores its applications in topological insulators, quantum Hall effects, and Majorana fermions.

Findings

Tangent dispersion successfully avoids fermion doubling.

Topologically protected Dirac cones are realizable with tangent fermions.

Majorana fermion phases are characterized using tangent lattice models.

Abstract

I. Introduction II. Two-dimensional lattice fermions III. Methods to avoid fermion doubling (sine dispersion, sine plus cosine dispersion, staggered lattice dispersion, linear sawtooth dispersion, tangent dispersion) IV. Topologically protected Dirac cone V. Application: Klein tunneling (tangent fermions on a space-time lattice, wave packet propagation) VI. Application: Strong antilocalization (transfer matrix of tangent fermions, topological insulator versus graphene) VII. Application: Anomalous quantum Hall effect (gauge invariant tangent fermions, topologically protected zeroth Landau level) VIII. Application: Majorana metal (Dirac versus Majorana fermions, phase diagram) IX. Outlook