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Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions
Author(s) -
Kawarabayashi Tohru,
Aoki Hideo,
Hatsugai Yasuhiro
Publication year - 2019
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201970025
Subject(s) - massless particle , dirac fermion , physics , fermion doubling , lattice (music) , fermion , invariant (physics) , theoretical physics , symmetry (geometry) , quantum mechanics , mathematical physics , geometry , mathematics , acoustics
The doubling of massless Dirac fermions on a lattice is topologically protected even when the Dirac cone is tilted with the usual chiral symmetry broken, which is shown to come from the generalized chiral symmetry. In article no. 1800524 , Kawarabayashi et al. show for two‐band lattice models that such systems can generally be produced by a deformation (as illustrated by the upper three panels) of the chiral‐symmetric models in that they can always be transformed back to a lattice model with the conventional chiral symmetry. Specifically, the number of zero modes is an invariant of the transformation, leading to the topological protection (as symbolized by the bottom left panel) à la Nielsen‐Ninomiya of the doubling of tilted and massless Dirac fermions in two dimensions.