Chern-Simons Theory and Wilson Loops in the Brillouin Zone

Understand

Berry connection is conventionally defined as a static gauge field in the Brillouin zone.

• Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a Chern-Simons gauge theory.
• The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle.
• This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow.