Discrete symmetries of low-dimensional Dirac models: A selective review with a focus on condensed-matter realisations
arXiv:1206.0355 · doi:10.1017/S1446181115000115
Abstract
The most fundamental characteristics of a physical system can often be deduced from its behaviour under discrete symmetry transformations such as time reversal, parity and chirality. Here we review basic symmetry properties of the relativistic quantum theories for free electrons in (2+1)- and (1+1)-dimensional spacetime. Additional flavour degrees of freedom are necessary to properly define symmetry operations in (2+1) dimensions and are generally present in physical realisations of such systems, e.g., in single sheets of graphite. We find that there exist two possibilities for defining any flavour-coupling discrete symmetry operation of the two-flavour (2+1)-dimensional Dirac theory. Physical implications of this previously unnoticed duplicity are discussed.
15 pages, 1 figure, accepted for ANZIAM Journal, Special Issue on Nanotechnology (invited contribution), v2: improved notation, expanded introduction & added references
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- Novel criticality of Dirac fermions in the presence of emergent gauge fields
- Novel criticality of Dirac fermions from lattice symmetry breaking
- Relative entanglement entropy for widely separated regions in curved spacetime
- Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
- Andreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling
- Triplet character of 2D-fermion dimers arising from -wave attraction via spin-orbit coupling and Zeeman splitting