Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions

Abstract

The doubling of massless Dirac fermions on two-dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broken chiral symmetry is topologically protected even when the Dirac cone is tilted. This is due to the generalized chiral symmetry defined for lattice systems, where such models can be generated by a deformation of the chiral-symmetric lattice models. The present paper shows for two-band lattice models that this is a general way to produce systems with the generalized chiral symmetry in that such systems can always be transformed back to a lattice model with the conventional chiral symmetry. We specifically show that the number of zero modes is an invariant of the transformation, leading to the topological protection à la Nielsen-Ninomiya of the doubling of tilted and massless Dirac fermions in two dimensions.

arXiv comment5 pages, 3 figures, ICPS 2018

References in corpus (19)

• The electronic properties of graphene
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Electronic transport in two dimensional graphene
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Type-II Weyl Semimetals
• Dirac semimetal in three dimensions
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Spawning rings of exceptional points out of Dirac cones
• Dirac Semimetals in Two Dimensions
• Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe${}_2$
• Double Dirac Semimetals in Three Dimensions
• Generalized Chiral Symmetry and Stability of Zero Modes for Tilted Dirac Cones
• Topological aspect of graphene physics
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
• Lattice realization of the generalized chiral symmetry in two dimensions

Cited by in corpus (2)

• Electric field assisted amplification of magnetic fields in tilted Dirac cone systems
• Bulk-edge correspondence with generalized chiral symmetry