Torsion, parity-odd response, and anomalies in topological states

2014/07/25 by Onkar Parrikar, Taylor L. Hughes, Robert G. Leigh · 81 citations
Materials Science · Mathematics · Physics and Astronomy · #Covariant transformation #Curvature #Geometry #Graphene research and applications #Hamiltonian (control theory) #Mathematical physics #Mathematics #Parity (physics) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #Torsion (gastropod) #cond-mat.mes-hall #hep-th

paper · pdf · doi:10.1103/physrevd.90.105004

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 90(10) (American Physical Society) · 70 pages, single column

arxiv created 2014/07/25 · openalex publication_date 2014/11/06 · arxiv updated 2014/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We study the response of a class of topological systems to electromagnetic and gravitational sources, including torsion and curvature. By using the technology of anomaly polynomials, we derive the parity-odd response of a massive Dirac fermion in d=2+1 and d=4+1, which provides a simple model for a topological insulator. We discuss the covariant anomalies of the corresponding edge states, from a Callan-Harvey anomaly inflow, as well as a Hamiltonian spectral flow point of view. We also discuss the applicability of our results to other systems such as Weyl semimetals. Finally, using dimensional reduction from d=4+1, we derive the effective action for a d=3+1 time-reversal invariant topological insulator in the presence of torsion and curvature, and discuss its various physical consequences.

Citations

• Attachment of Surface "Fermi Arcs" to the Bulk Fermi Surface: "Fermi-Level Plumbing" in Topological Metals
• Topological field theory of time-reversal invariant insulators
• Topological phases and the quantum spin Hall effect in three dimensions
• Weak indices and dislocations in general topological band structures
• Inversion-symmetric topological insulators
• Time-reversal invariant realization of the Weyl semimetal phase
• A no-go theorem for regularizing chiral fermions
• Quantum Spin Hall Effect in Graphene
• Topological Insulators with Inversion Symmetry
• Topological Crystalline Insulators
• Experimental Demonstration of Topological Surface States Protected by Time-Reversal Symmetry
• Hall viscosity from effective field theory
• Topological Insulators
• The Quantum Spin Hall Effect: Theory and Experiment
• "Hall viscosity" and intrinsic metric of incompressible fractional Hall fluids
• Chern-Simons modification of general relativity

Cited by

• Emergent gravity in the cubic tight-binding model of Weyl semimetal in the presence of elastic deformations
• Cubic Hall viscosity in three-dimensional topological semimetals
• Scale magnetic effect in quantum electrodynamics and the Wigner-Weyl formalism
• Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations