Origin of the anomalous Hall effect in two-band chiral superconductors

Abstract

We consider the origin of the anomalous Hall effect in a general model of a clean two-band chiral superconductor. Within the Kubo formalism we derive an analytic expression for the high-frequency ac Hall conductivity valid close to the critical temperature. This expression involves two distinct gauge-invariant time-reversal-odd bilinear (TROB) functions involving the pairing potential and its Hermitian conjugate. We argue that the existence of at least one of these TROBs generically implies a nonzero ac Hall conductivity. The TROBs allow us to clarify the roles of intra- and interband pairing, and provide a straightforward criterion for a superconducting state to exhibit the anomalous Hall effect. We briefly exemplify our results with model calculations for a chiral $p$-wave pairing state in strontium ruthenate and a chiral $d$-wave pairing state on the honeycomb lattice.

arXiv comment9 pages, 1 figure

References in corpus (37)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Quantum Spin Hall Effect in Graphene
• Time-Reversal Symmetry Breaking Superconductivity in Sr2RuO4
• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Pronounced drop of ${}^{17}$O NMR Knight shift in superconducting state of Sr${}_2$RuO${}_4$
• Chiral Superconductors
• Evidence for time-reversal symmetry breaking in the non-centrosymmetric superconductor LaNiC${}_2$
• Resonating valence bonds and mean-field d-wave superconductivity in graphite
• Observation of broken time-reversal symmetry in the heavy fermion superconductor UPt${}_3$
• Strong spin-orbit coupling effects on the Fermi surface of Sr2RuO4 and Sr2RhO4
• A polarized neutron-scattering study of the Cooper-pair moment in Sr2RuO4
• Exotic Superconducting Properties in the Electron-Hole Compensated Heavy Fermion `Semimetal' URu2Si2
• High-resolution photoemission on Sr2RuO4 reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies
• Polar Kerr Effect as Probe for Time-Reversal Symmetry Breaking in Unconventional Superconductors
• Reduction of the ${}^{17}$O Knight shift in the Superconducting State and the Heat-up Effect by NMR Pulses on Sr${}_2$RuO${}_4$
• Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
• Evidence for broken time-reversal symmetry in the superconducting phase of URu${}_2$Si${}_2$
• Stabilizing Even-Parity Chiral Superconductivity in Sr${}_2$RuO${}_4$
• Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node
• Time-Reversal-Symmetry-Breaking Superconductivity in Epitaxial Bismuth/Nickel Bilayers
• Intrinsic Hall effect in a multiband chiral superconductor in the absence of an external magnetic field
• Frequency and temperature dependence of the anomalous Hall conductivity in a chiral px+ipy superconductor with impurities
• Tailoring $T_c$ by symmetry principles: The concept of Superconducting Fitness
• Impurity Induced Polar Kerr Effect in A Chiral p-wave Superconductor
• Correlated Dirac Particles and Superconductivity on the Honeycomb Lattice
• Intrinsic optical dichroism in the chiral superconducting state of Sr${}_2$RuO${}_4$
• The Kerr rotation in the unconventional superconductor Sr${}_2$RuO${}_4$
• Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor UPt${}_3$
• Kerr effect from diffractive skew scattering in chiral $p_x\pm i{p}_y$ superconductors
• Time Reversal Symmetry Breaking in the B Phase of the Heavy Fermion Superconductor PrOs${}_4$Sb${}_{12}$
• Loop currents and anomalous Hall effect from time-reversal symmetry-breaking superconductivity on the honeycomb lattice
• Intrinsic ac anomalous Hall effect of nonsymmorphic chiral superconductors with an application to $\mathrm{UP}{\mathrm{t}}_3$
• Anomalous Transport Phenomena in $p_x+i{p}_y$ Superconductors
• Weyl Superconductivity in UTe2
• Hidden anomalous Hall effect in Sr${}_2$RuO${}_4$ with chiral superconductivity dominated by the Ru $d_{xy}$ orbital
• Anomalous Hall effect in single-band chiral superconductors from impurity superlattices
• Pseudospin bases for a model of Cu:Bi${}_2$Se${}_3$

Cited by in corpus (12)

• Doping a moiré Mott Insulator: A t-J model study of twisted cuprates
• Anapole superconductivity from $\mathcal{P}\mathcal{T}$-symmetric mixed-parity interband pairing
• Quantum-geometry-induced anapole superconductivity
• General theory of robustness against disorder in multi-band superconductors
• Intrinsic Anomalous Hall Effect in a Bosonic Chiral Superfluid
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Quantum-geometry-induced anomalous Hall effect in nonunitary superconductors and application to Sr${}_2$RuO${}_4$
• Pair-breaking in superconductors with strong spin-orbit coupling
• Polar Kerr Effect in Multiband Spin-Orbit Coupled Superconductors
• Circular-polarization-selective perfect reflection from chiral superconductors
• Sensitivity of superconducting states to the impurity location in layered materials
• Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr${}_2$RuO${}_4$