Thermoelectric Signatures of Time-Reversal Symmetry Breaking States in Multiband Superconductors

We show that superconductors with broken time-reversal symmetry have very specific magnetic and electric responses to inhomogeneous heating. A local heating of such superconductors induces a magnetic field with a profile that is sensitive to the presence of domain walls and crystalline anisotropy of superconducting states. A nonstationary heating process produces an electric field and a charge imbalance in different bands. These effects can be measured and used to distinguish s+is and s+id superconducting states in the candidate materials such as Ba_{1-x}K_{x}Fe_{2}As_{2}.