Hall conductivity as bulk signature of topological transitions in superconductors

Abstract

Topological superconductors may undergo transitions between phases with different topological numbers which, like the case of topological insulators, are related to the presence of gapless (Majorana) edge states. In $\mathbb{Z}$ topological insulators the charge Hall conductivity is quantized, being proportional to the number of gapless states running at the edge. In a superconductor, however, charge is not conserved and, therefore, ${\sigma }_{xy}$ is not quantized, even in the case of a $\mathbb{Z}$ topological superconductor. Here it is shown that while the ${\sigma }_{xy}$ evolves continuously between different topological phases of a $\mathbb{Z}$ topological superconductor, its derivatives display sharp features signaling the topological transitions. We consider in detail the case of a triplet superconductor with p-wave symmetry in the presence of Rashba spin-orbit (SO) coupling and externally applied Zeeman spin splitting. Generalization to the cases where the pairing vector is not aligned with that of the SO coupling is given. We generalize also to the cases where the normal system is already topologically non-trivial.

10 pages, 10 figures

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Cited by in corpus (10)

• Fate of Majorana fermions and Chern numbers after a quantum quench
• Winding numbers of phase transition points for one-dimensional topological systems
• Entanglement modes and topological phase transitions in superconductors
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Magnetic chains on a triplet superconductor
• Broken-symmetry phases of interacting nested Weyl and Dirac loops
• Duality in topological superconductors and topological ferromagnetic insulators in a honeycomb lattice
• Effect of hybridization symmetry on topological phases of odd-parity multiband superconductors
• Hall conductivity in the normal and superconducting phases of the Rashba system with Zeeman field
• Superconductivity in a Chern band: effect of time-reversal-symmetry breaking on superconductivity