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.

arXiv commentv2; minor changes, additional refs

References in corpus (23)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Universal Intrinsic Spin-Hall Effect
• Dissipationless Quantum Spin Current at Room Temperature
• Electronic Properties of Disordered Two-Dimensional Carbon
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• The spin quantum Hall effect in unconventional superconductors
• Edge States and the Quantized Hall Effect in Graphene
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Nondissipative Spin Hall Effect via Quantized Edge Transport
• Superconducting Gap Structure of Spin-Triplet Superconductor Sr_2RuO_4 Studied by Thermal Conductivity
• Charge and spin Hall conductivity in metallic graphene
• Spin-triplet superconductivity in Sr${}_2$RuO${}_4$ probed by Andreev reflection
• Spontaneous Hall effect in chiral p-wave superconductor
• Observation of Andreev Surface Bound States in the 3-K phase Region of Sr_2RuO_4
• The role of spin-orbit coupling for the superconducting state in Sr_2RuO_4
• Anisotropy of magnetothermal conductivity in Sr2RuO4
• Vortex Charging Effect in a Chiral $p_x\pm i{p}_y$-Wave Superconductor
• Edge states and determination of pairing symmetry in superconducting Sr2RuO4
• How to detect edge electron states in (TMTSF)2X and Sr2RuO4 experimentally
• Spin waves in a two dimensional p-wave superconductor: Sr${}_2$RuO${}_4$
• Hopf invariant for long-wavelength skyrmions in quantum Hall systems for integer and fractional fillings
• Axial Anomaly Effect in Chiral p-wave Superconductor

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