## Abstract

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.

Original language | English (US) |
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Article number | 184503 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 85 |

Issue number | 18 |

DOIs | |

State | Published - May 3 2012 |

## ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics