Abstract
We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curved-\emph{spacetime} geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can also account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials.
Highlights
Semimetals and quantum liquids with linear dispersion near degeneracy points exhibit emergent relativistic physics at low energies
We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curvedspacetime geometry and synthetic gauge fields
By employing Clifford representations and Schrieffer-Wolff transformations, we carried out a controlled derivation of quantum-mechanical low-energy theory for chiral fermions in Weyl semimetals with smooth TRand I-breaking textures
Summary
Long Liang and Teemu Ojanen2 1Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland 2Computational Physics Laboratory, Physics Unit, Faculty of Engineering and Natural Sciences, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland (Received 19 June 2019; published 16 October 2019). We show how the universal low-energy properties of Weyl semimetals with spatially varying time-reversal (TR) or inversion (I) symmetry breaking are described in terms of chiral fermions experiencing curvedspacetime geometry and synthetic gauge fields. By employing Clifford representations and Schrieffer-Wolff transformations, we present a systematic derivation of an effective curved-space Weyl theory with rich geometric and gauge structure. To illustrate the utility of the formalism, we give a concrete prescription of how to fabricate nontrivial curved spacetimes and event horizons in topological insulators with magnetic textures. Our theory can account for strain-induced effects, providing a powerful unified framework for studying and designing inhomogeneous Weyl materials
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