Anomalous Hall Effects in Chiral Superconductors

Abstract

We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E${}_1$ and E${}_2$ representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and -- as we highlight -- the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, $\nu$, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for $\nu =\pm 1$, but vanishes for $|\nu |>1$. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, $R\ge \hslash /p_f$, the thermal Hall conductivity is finite for chiral order with $|\nu |\ge 2$, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.

arXiv comment29 pages, 11 figures

References in corpus (49)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Time-Reversal Symmetry Breaking Superconductivity in Sr2RuO4
• Chiral superconductivity from repulsive interactions in doped graphene
• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Evaluation of Spin-Triplet Superconductivity in Sr2RuO4
• Pronounced drop of ${}^{17}$O NMR Knight shift in superconducting state of Sr${}_2$RuO${}_4$
• The Order Parameter for the Superconducting Phases of UPt${}_3$
• The spin quantum Hall effect in unconventional superconductors
• Chiral P-Wave Order in Sr_2RuO_4
• Quasiparticle States near the Surface and the Domain Wall in a p_x\pm i p_y-Wave Superconductor
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Electronic thermal conductivity and the Wiedemann-Franz law for unconventional superconductors
• Observation of broken time-reversal symmetry in the heavy fermion superconductor UPt${}_3$
• Energy Magnetization and Thermal Hall Effect
• Three-band superconductivity and the order parameter that breaks time-reversal symmetry
• Upper limit on spontaneous supercurrents in Sr${}_2$RuO${}_4$
• Evidence for Time-Reversal-Symmetry-Broken Superconductivity in Locally Noncentrosymmetric SrPtAs
• Models for Superfluid ${}^3$He in Aerogel
• Topological surface states in nodal superconductors
• Possible Topological Superconducting Phases of MoS${}_2$
• Limits on Superconductivity-Related Magnetization in Sr${}_2$RuO${}_4$ and PrOs${}_4$Sb${}_{12}$ from Scanning SQUID Microscopy
• Chiral $d$-wave Superconductivity in SrPtAs
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Quantum Thermal Hall Effect in a Time-Reversal-Symmetry-Broken Topological Superconductor in Two Dimensions : Approach From Bulk Calculations
• Identifying the pairing symmetry in the Sr2RuO4 superconductor
• Momentum Resolved Superconducting Energy Gaps of Sr${}_2$RuO${}_4$ from Quasiparticle Interference Imaging
• Vertical line nodes in the superconducting gap structure of Sr2RuO4
• Evidence for even parity unconventional superconductivity in Sr${}_2$RuO${}_4$
• Large Chern Number and Edge Currents in Sr2RuO4
• Vortex lattices and broken time reversal symmetry in the topological superconductor UPt3
• Topological Weyl Superconductor to Diffusive Thermal Hall Metal Crossover in the B-Phase of UPt${}_3$
• Time-Reversal Invariant Superconductivity of Sr${}_2$RuO${}_4$ Revealed by Josephson Effects
• New Chiral Phases of Superfluid 3He Stabilized by Anisotropic Silica Aerogel
• Identification of the Orbital Pairing Symmetry in UPt_3
• Infrared Conductivity in Layered $d$-wave Superconductors
• Thermal Conductivity of Superconducting UPt${}_3$ at Low Temperatures
• Suppression of Superconductivity in UPt_3 Single Crystals
• Chiral singlet superconductivity in the weakly correlated metal LaPt3P
• Chiral Phases of Superfluid 3He in an Anisotropic Medium
• Edge mass current and roles of Majorana Fermions in superfluid 3He A-phase
• Anomalous Transport Phenomena in $p_x+i{p}_y$ Superconductors
• Electron bubbles and Weyl Fermions in chiral superfluid ${}^3$He-A
• Large Thermoelectric Effects in Unconventional Superconductors
• Topological Superconductivity in Two Dimensions with Mixed Chirality
• Thermal Conductivity of the Accidental Degeneracy and Enlarged Symmetry Group Models for Superconducting UPt₃
• Low Temperature Thermal Hall Conductivity of a Nodal Chiral Superconductor
• Anomalous Thermal Hall Effect in Chiral Phases of ${}^3$He-Aerogel
• Disorder Induced Anomalous Thermal Hall Effect in Chiral Phases of Superfluid ${}^3$He
• Impurity-Induced Anomalous Thermal Hall Effect in Chiral Superconductors

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