Responses and anomalies in a topological superconductor from emergent gravity | Israel Physical Society

IPS Conference 2017

Responses and anomalies in a topological superconductor from emergent gravity

Omri Golan , Ady Stern
Weizmann Institute of Science

We study the interplay of two phenomena that occur in 2+1 dimensional p-wave superconductors. The first is emergent gravity, where interacting fermions behave effectively as fermions interacting with a form of gravity, which is described by the superconducting order parameter. The second is topological superconductivity, the existence of nontrivial topological phases of the effectively free fermions in the gravitational, or order parameter, background. We show that an energy-momentum response of the fermions to the emergent gravitational background reveals their topological phase, via a gravitational Chern-Simons (gCS) term. This response is intimately related to the existence of chiral Majorana fermions on domain walls between different topological phases, via energy-momentum conservation, or gravitational anomaly inflow. Thus we provide a possible probe for topological phases of superconductors, and obtain a physical interpretation for the boundary gravitational anomaly and bulk gCS term in this context, which has so far been laking. We also set up the problem in curved space, and comment on the the interplay of the real and emergent geometries, which is similar to recent bi-metric descriptions of anisotropic quantum Hall states, and to the theory of massive gravity.