Superconductors with broken time-reversal symmetry: Spontaneous magnetization and quantum Hall effects

TL;DR

This paper investigates how broken time-reversal symmetry in certain superconductors leads to surface states that produce spontaneous magnetization and unusual quantum Hall effects for spin and heat transport.

Contribution

It provides a detailed analysis of surface states in BTRS superconductors and derives the Hall conductance behavior, highlighting novel quantum Hall effects.

Findings

Surface states carry current and induce magnetization.

Hall conductance vanishes at zero wavevector but shows unusual structure at finite values.

Chirality of surface states causes quantum Hall effects in spin and heat transport.

Abstract

Broken time reversal symmetry (BTRS) in d+id' as well as in d+is superconductors is studied and is shown to yield current carrying surface states. We evaluate the temperature and thickness dependence of the resulting spontaneous magnetization and show a marked difference between weak and strong BTRS. We also derive the Hall conductance which vanishes at zero wavevector q and finite frequency w, however at finite q,w it has an unusual structure. The chirality of the surface states leads to quantum Hall effects for spin and heat transport in d+id' superconductors.