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We study the quantum anomalous thermal Hall effect in a topologicalsuperconductor which possesses an integer bulk topological number, and supportsMajorana excitations on the surface. To realize the quantum thermal Halleffect, a finite gap at the surface is induced by applying an external magneticfield or by the proximity effects with magnetic materials or $s$-wavesuperconductors with complex pair-potentials. Basing on the lattice modelHamiltonian for superconducting states in Cu-doped Bi$_2$Se$_3$, we compute thethermal Hall conductivity as a function of various parameters such as thechemical potential, the pair-potential, and the spin-orbit coupling inducedband gap. It is argued that the bulk topological invariant corresponds to thequantization rule of the thermal Hall conductivity induced by complex $s$-wavepair-potentials.

Quantum thermal Hall effect of Majorana fermions on the surface of superconducting topoloigcal insulators