TY - JOUR

T1 - Gravitational anomalies and thermal Hall effect in topological insulators

AU - Stone, Michael

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2012/5/3

Y1 - 2012/5/3

N2 - It has been suggested that after being gapped by a small symmetry-breaking field, the Majorana quasiparticles localized on the surface of a class DIII topological insulator will exhibit a thermal Hall effect that arises from a gravitational Chern-Simons term. We critically examine this idea, and argue that the thermogravitational Hall effect is more complicated than its familiar analog. A conventional Hall current is generated by a uniform electric field, but computing the flux from the gravitational Chern-Simons functional shows that gravitational field gradients-i.e., tidal forces-are needed to induce an energy-momentum flow. We relate the resulting surface energy-momentum flux to a domain-wall gravitational anomaly via the Callan-Harvey inflow mechanism. We stress that the gauge invariance of the combined bulk-plus-boundary theory ensures that the current in the domain wall always experiences a "covariant" rather than "consistent" anomaly. We use this observation to confirm that the tidally induced energy-momentum current exactly accounts for the covariant gravitational anomaly in (1+1)-dimensional domain-wall fermions. The same anomaly arises whether we write the Chern-Simons functional in terms of the Christoffel symbol or in terms of the spin connection.

AB - It has been suggested that after being gapped by a small symmetry-breaking field, the Majorana quasiparticles localized on the surface of a class DIII topological insulator will exhibit a thermal Hall effect that arises from a gravitational Chern-Simons term. We critically examine this idea, and argue that the thermogravitational Hall effect is more complicated than its familiar analog. A conventional Hall current is generated by a uniform electric field, but computing the flux from the gravitational Chern-Simons functional shows that gravitational field gradients-i.e., tidal forces-are needed to induce an energy-momentum flow. We relate the resulting surface energy-momentum flux to a domain-wall gravitational anomaly via the Callan-Harvey inflow mechanism. We stress that the gauge invariance of the combined bulk-plus-boundary theory ensures that the current in the domain wall always experiences a "covariant" rather than "consistent" anomaly. We use this observation to confirm that the tidally induced energy-momentum current exactly accounts for the covariant gravitational anomaly in (1+1)-dimensional domain-wall fermions. The same anomaly arises whether we write the Chern-Simons functional in terms of the Christoffel symbol or in terms of the spin connection.

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U2 - 10.1103/PhysRevB.85.184503

DO - 10.1103/PhysRevB.85.184503

M3 - Article

AN - SCOPUS:84861150682

VL - 85

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 18

M1 - 184503

ER -