## Cross-Correlated Responses of Topological Superconductors and Superfluids

We study nontrivial responses of topological superconductors and superfluids to the temperature gradient and rotation of the system. In two-dimensional gapped systems, the Str\v{e}da formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the orbital angular momentum and thermal polarization (entropy polarization). These results can be naturally related to the gravitoelectromagnetism description of three-dimensional topological superconductors and superfluids, analogous to the topological magnetoelectric effect in ${\mathbb{Z}}_2$ topological insulators.

### References

Cross-Correlated Responses of Topological Superconductors and Superfluids
*Kentaro Nomura, Shinsei Ryu, Akira Furusaki, and N. Nagaosa*

## Surface-Quantized Anomalous Hall Current and the Magnetoelectric Effect
in Magnetically Disordered Topological Insulators

We study theoretically the role of quenched magnetic disorder at the surface of a topological insulator by numerical simulation and scaling analysis. It is found that all the surface states are localized while the transverse conductivity is quantized to be $\pm {{e^2} \over {2 h}}$ as long as the Fermi energy is within the bulk gap. This greatly facilitates the realization of the topological magnetoelectric effect proposed by Qi {\it et al.} (Phys. Rev. B\textbf{78}, 195424 (2008)) with the surface magnetization direction being controlled by the simultaneous application of magnetic and electric fields .

### References

Surface-Quantized Anomalous Hall Current and the Magnetoelectric Effect
in Magnetically Disordered Topological Insulators
*K. Nomura and N. Nagaosa*
Phys. Rev. Lett. 106, 166802 (2011) pdf

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