Existence of bulk chiral fermions and crystal symmetry

By J. Mañes. 2011

135 citations recorded by the source corpus.

We consider the existence of bulk chiral fermions around points of symmetry in the Brillouin zone of nonmagnetic three-dimensional (3D) crystals with negligible spin-orbit interactions. We use group theory to show that this is possible, but only for a reduced number of space groups and points of symmetry that we tabulate. Moreover, we show that for a handful of space groups the existence of bulk chiral fermions is not only possible but unavoidable, irrespective of the concrete crystal structure. Thus our tables can be used to look for bulk chiral fermions in a specific class of systems, namely, that of nonmagnetic $3\text{D}$ crystals with sufficiently weak spin-orbit coupling. We also discuss the effects of spin-orbit interactions and possible extensions of our approach to Weyl semimetals, crystals with magnetic order, and systems with Dirac points with pseudospin 1 and $3/2$. A simple tight-binding model is used to illustrate some of the issues.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/20b211a2f8048edc835cbdf4558dc885cb0968e3

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

Topological Semimetals from First Principles (2018, background): “Note that when spin-orbit coupling is vanishingly small, threefold band crossings can also occur for symmorphic space groups (153).”
Classification of stable three-dimensional Dirac semimetals with nontrivial topology (2014, methodology): “solving the lattice Hamiltonians in equations (16) and (19), both of which lead to the same phase diagram.”
Weyl and Dirac semimetals in three-dimensional solids (2017, background): “…such point degeneracies have been studied (Michel and Zak, 1999) and identified for specific crystal structures both with and without spin-orbit coupling in two (Damljanovic and Gajic, 2016; Young and Kane, 2015) and in three dimensions (Mañes, 2012; Steinberg et al., 2014; Young et al., 2012).”
Probing the chiral anomaly with nonlocal transport in three dimensional topological semimetals (2013, background): “[44] J.”