Spin-Hall effect in triplet chiral superconductors and graphene

Abstract

We study spin-Hall effects in time-reversal symmetry (TRS) broken systems such as triplet chiral superconductors and TRS preserved ones such as graphene. For chiral triplet superconductors, we show that the edge states carry a quantized spin-Hall current in response to an applied Zeeman magnetic field $B$ along the $\mathbf{d}$ vector \cite{leggett1}, whereas the edge spin-current for $\mathbf{B}\perp \mathbf{d}$ is screened by the condensate. We also derive the bulk spin-Hall current for chiral triplet superconductors for arbitrary relative orientation of $\mathbf{B}$ and $\mathbf{d}$ and discuss its relation with the edge spin-current. For TRS invariant system graphene, we show that the bulk effective action, unlike its TRS broken counterparts, does not support a SU(2) Hopf term but allows a crossed Hopf term in the presence of an external electromagnetic field, which yields a quantized bulk spin-Hall current in response to an electric field. We also present an analytical solution of the edge problem for armchair edges of graphene and contrast the properties of these edge states with their time reversal symmetry broken counterparts in chiral superconductors. We propose possible experiments to test our results.

v2; minor changes, additional refs

References in corpus (4)

• Dissipationless Quantum Spin Current at Room Temperature
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Edge States and the Quantized Hall Effect in Graphene
• Charge and spin Hall conductivity in metallic graphene

Cited by in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological surface states in nodal superconductors
• Collective modes and electromagnetic response of a chiral superconductor
• Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
• Pure spin current and perfect valley filter by designed separation of the chiral states in two-dimensional honeycomb lattices
• Unscreened Coulomb interactions and quantum spin Hall phase in neutral zigzag graphene ribbons
• Direct and inverse superspin Hall effect in two-dimensional systems: Electrical detection of spin supercurrents
• Multi-locational Majorana Zero Modes