Omri Golan (Weizmann Institute of Science)

Effective action for the px +i*py superconductor from an analogy to gravity

The low energy limit of the px +i*py superconductor lattice model is shown to be a relativistic Majorana fermion coupled to gravity with both curvature and torsion (Riemann-Cartan space-time), where the order parameter and electromagnetic potential take the role of geometric fields known as the vielbein and the spin connection. Known results on Dirac fermions coupled to curvature and torsion are then applied to obtain the low energy effective action for the electromagnetic potential and for both the Higgs and Goldstone modes of the order parameter. This effective action contains a gravitational Chern-Simons term which describes in this context a U(1) anomaly relating the bulk Chern number and the boundary central charge, and is intimately related to the electronic energy and momentum densities, and to the dynamics of the Higgs mode.