Torsion, Parity-odd Response and Anomalies in Topological States

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 semi-metals. 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.

70 pages, single column

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Cited by in corpus (7)

• Emergent gravity and chiral anomaly in Dirac semimetals in the presence of dislocations
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Chiral torsional effect with finite temperature, density and curvature
• Symmetry breaking and lattice kirigami: finite temperature effects
• Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures
• Geometric and computational aspects of chiral topological quantum matter
• Quantum matter and gravitation: photons in a waveguide