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Bulletin of the American Physical Society

Dirac Fermion Renormalization near Topological Lifshitz Transitions

Valeri N. Kotov, Bruno Uchoa, Oleg P. Sushkov

Published Mar 17, 2021• 0 citations
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Type-II Weyl fermions may emerge behind the event horizon of black holes. We employ the Painlevé-Gullstrand metric to study the surface of the Lifshitz transition at the horizon, equivalent to the interface separating the type-I and type-II Weyl states. We find several analogies between the black hole horizon and the transformation of type-I to type-II Weyl fermions through the Dirac line. We analyze the symmetry-protected topological order at the Lifshitz transition originating in semimetals. The emergence of Hawking radiation in Weyl semimetals is discussed. We show that the transition state from type-I to type-II Dirac fermions can be viewed as a black-hole horizon, which exhibits unique characteristics, including a Dirac-line Fermi surface with a nontrivial topological invariant and a critical chiral anomaly effect.
Near the critical point of a phase transition, physical observables are characterized by a set of pure numbers -- the critical exponents -- which are identical for a whole class of transitions defining a ``universality class''. Novel Dirac materials exhibit quantum critical points, which are not captured by conventional universality classes and their description defines new challenges for theory. The authors present here a comprehensive renormalization group study and give quantitative predictions for universality classes of Dirac fermions, as relevant to semimetal-insulator transitions in graphene and emergent supersymmetry in topological insulators. The authors also compare to independent conformal bootstrap results and quantum Monte Carlo estimates.
We discuss the emergence of rings of zero-energy excitations in momentum space for superfluid phases of ultracold fermions when spin-orbit effects, Zeeman fields, and interactions are varied. We show that phases containing rings of nodes possess nontrivial topological invariants, and that phase transitions between distinct topological phases belong to the Lifshitz class. Upon crossing phase boundaries, existing massless Dirac fermions in the gapless phase annihilate to produce bulk zero-mode Majorana fermions at phase boundaries, and then become massive Dirac fermions in the gapped phase. We characterize these tunable topological phase transitions via several spectroscopic properties, including excitation spectrum, spectral function, and momentum distribution.