Distribution functions in non-equilibrium theory of superconductivity and Andreev spectroscopy in unconventional superconductors

Abstract

We present a new theoretical formulation of non-equilibrium superconducting phenomena, including singlet and triplet pairing. We start from the general Keldysh-Nambu-Gor'kov Green's functions in the quasiclassical approximation and represent them in terms of 2x2 spin-matrix coherence functions and distribution functions for particle-type and hole-type excitations. The resulting transport equations for the distribution functions may be interpreted as a generalization to the superconducting state of Landau's transport equation for the normal Fermi liquid of conduction electrons. The equations are well suited for numerical simulations of dynamical phenomena. Using our formulation we solve an open problem in quasiclassical theory of superconductivity, the derivation of an explicit representation of Zaitsev's nonlinear boundary conditions [A.V. Zaitsev, JETP 59, 1015 (1984)] at surfaces and interfaces. These boundary conditions include non-equilibrium phenomena and spin singlet and triplet unconventional pairing. We eliminate spurious solutions as well as numerical stability problems present in the original formulation. Finally, we formulate the Andreev scattering problem at interfaces in terms of the introduced distribution functions and present a theoretical analysis for the study of time reversal symmetry breaking states in unconventional superconductors via Andreev spectroscopy experiments at N-S interfaces with finite transmission. We include impurity scattering self consistently.

18 pages, 5 figures. This is a considerably extended version. It includes a new section about Andreev spectroscopy as an application of the theoretical formulation

References in corpus (4)

• Quasiclassical Green's function approach to mesoscopic superconductivity
• Electromagnetic Response of a Vortex in Layered Superconductors
• Diamagnetic Response of an N-S-Proximity System at Arbitrary Impurity Concentration
• Andreev Bound States, Surfaces and Subdominant Pairing in High Tc Superconductors

Cited by in corpus (169)

• Odd Triplet Superconductivity and Related Phenomena in Superconductor-Ferromagnet Structures
• Spin-polarized supercurrents for spintronics: a review of current progress
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Theory of Half Metal-Superconductor Heterostructures
• Topology of Andreev Bound States with Flat Dispersion
• Theory of the proximity effect in junctions with unconventional superconductors
• Odd-frequency pairing in normal metal/superconductor junctions
• Topological surface states in nodal superconductors
• Nonlocal Thermoelectric Effects and Nonlocal Onsager Relations in a Three-Terminal Proximity-Coupled Superconductor-Ferromagnet Device
• Josephson currents through spin-active interfaces
• Spin-dependent Cooper Pair Phase and Pure Spin Supercurrents in Strongly Polarized Ferromagnets
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Manifestation of the odd-frequency spin-triplet pairing state in diffusive ferromagnet / superconductor junctions
• General Boundary Conditions for Quasiclassical Theory of Superconductivity in the Diffusive Limit: Application to Strongly Spin-polarized Systems
• Surface bound states and spin currents in non-centrosymmetric superconductors
• Thermodynamic properties of thin films of superfluid 3He-A
• Andreev bound states and tunneling characteristics of a non-centrosymmetric superconductor
• Pairing symmetry conversion by spin-active interfaces in superconducting junctions
• The scattering problem in non-equilibrium quasiclassical theory of metals and superconductors: general boundary conditions and applications
• Andreev Bound States and Their Signatures
• Phase Diagram and Spectroscopy of FFLO states of two-dimensional d-wave superconductors
• Density of states and supercurrent in diffusive SNS junctions: role of nonideal interfaces and spin-flip scattering
• Interplay of spin-discriminated Andreev bound states forming the 0-$\pi$ transition in Superconductor-Ferromagnet-Superconductor Junctions
• Proximity Effect and Multiple Andreev Reflections in Diffusive SNS Junctions
• Quasiclassical description of transport through superconducting contacts
• Nonequilibrium Superconductivity near Spin Active Interfaces
• Signature of odd-frequency pairing correlations induced by a magnetic interface
• Vortices in chiral, spin-triplet superconductors and superfluids
• Proximity effect between two superconductors spatially resolved by scanning tunneling spectroscopy
• Electronic transport through ferromagnetic and superconducting junctions with spin-filter tunneling barriers
• Josephson Current in S-FIF-S Junctions: Nonmonotonic Dependence on Misorientation Angle
• Nonlocal Andreev reflection at high transmissions
• Transfer-matrix description of heterostructures involving superconductors and ferromagnets
• Phase Modulated Thermal Conductance of Josephson Weak Links
• Crossed Andreev reflection at spin-active interfaces
• Heat Transport Through Josephson Point Contacts
• Phase-Sensitive Impurity Effects in Vortex Core of Moderately Clean Chiral Superconductors
• Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of the spin-orbit coupling
• Theory of pairing symmetry inside the Abrikosov vortex core
• Tuning of Magnetic Activity in Spin-Filter Josephson Junctions Towards Spin-Triplet Transport
• Theory of Nonequilibrium Spin Transport and Spin Transfer Torque in Superconducting-Ferromagnetic Nanostructures
• Theory of superconductor-ferromagnet point contact spectra: the case of strong spin polarization
• Josephson current and Andreev states in superconductor-half metal-superconductor heterostructures
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Quasiparticle Decoherence in d-wave Superconducting Qubits
• Triplet Cooper pairs induced in diffusive s-wave superconductors interfaced with strongly spin-polarized magnetic insulators or half-metallic ferromagnets
• Quasiclassical theory of disordered multi-channel Majorana quantum wires
• Generation of pure superconducting spin current in magnetic heterostructures via non-locally induced magnetism due to Landau Fermi-liquid effects
• Inverse proximity effect and influence of disorder on triplet supercurrents in strongly spin-polarized ferromagnets
• Quasiclassical Theory of Spontaneous Currents at Surfaces and Interfaces of d-Wave Superconductors
• Observation of Andreev bound states in bicrystal grain-boundary Josephson junctions of the electron doped superconductor LaCeCuO
• Fractional flux quanta at intrinsic metallic interfaces of noncentrosymmetric superconductors
• Non-equilibrium effects in a Josephson junction coupled to a precessing spin
• Tuning odd triplet superconductivity by spin pumping
• Edge Current due to Majorana Fermions in Superfluid ${}^3$He A- and B-Phases
• Superconducting Proximity Effect through a Magnetic Domain Wall
• Superfluid 3He in a restricted geometry with a perpendicular magnetic field
• Odd-frequency Cooper pairs and zero-energy surface bound states in superfluid 3He
• Odd-frequency pairing and proximity effect in Kitaev chain systems including topological critical point
• Superconducting proximity effect and long-ranged triplets in dirty metallic antiferromagnets
• Effects of spin-orbit interaction on superconductor-ferromagnet heterostructures: spontaneous electric and spin surface currents
• Robustness of Spin-Triplet Pairing and Singlet-Triplet Pairing Crossover in Superconductor/Ferromagnet Hybrids
• Analytical Formulation of the Local Density of States around a Vortex Core in Unconventional Superconductors
• Theory of Andreev Bound States in S-F-S Junctions and S-F Proximity Devices
• Influence of the impurity scattering on charge transport in unconventional superconductor junctions
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• Current fluctuations in unconventional superconductor junctions with impurity scattering
• Spontaneously broken translational symmetry at edges of high-temperature superconductors: thermodynamics in magnetic field
• Relaxation of Nonequilibrium Quasiparticles in Mesoscopic Size Superconductors
• Normal metal tunnel junction-based superconducting quantum interference proximity transistor: the N-SQUIPT
• Negative thermal magnetoresistivity as a signature of chiral anomaly in Weyl superconductors
• Time-reversal symmetry breaking state near the surface of $s_{\pm }$-superconductor
• Large thermoelectric effect in ballistic Andreev interferometers
• Quasiclassical numerical method for mesoscopic superconductors: bound states in a circular d-wave island with a single vortex
• Theory of pairing symmetry in Fulde-Ferrell-Larkin-Ovchinnikov vortex state and vortex lattice
• Positions of Point-Nodes in Borocarbide Superconductor YNi2B2C
• Effect of Surface Andreev Bound States on the Bean-Livingston Barrier in d-Wave Superconductors
• Dynamics of spin transport in voltage-biased Josephson junctions
• Chirality sensitive effect on surface states in chiral p-wave superconductors
• Dynamics of two ferromagnetic insulators coupled by superconducting spin current
• Intrinsic spin-orbit interaction in diffusive normal wire Josephson weak links: supercurrent and density of states
• Thermally induced spin-transfer torques in superconductor/ferromagnet bilayers
• Quasiclassical expressions for the free energy of superconducting systems
• Enhancement of thermoelectric effect in diffusive superconducting bilayers with magnetic interfaces
• Quasiclassical theory of charge transport across mesoscopic normal metal-superconducting heterostructures with current conservation
• Andreev Bound States in Superconducting Films and Confined Superfluid He-3
• Nonlocal conductance via overlapping Andreev bound states in ferromagnet-superconductor heterostructures
• Proximity Effect in Normal Metal - High Tc Superconductor Contacts
• Phase Crystals
• The quasiclassical theory for interfaces with spin--orbit coupling
• Transfer-matrix approach to multiband Josephson junctions
• Destruction of surface states of ($d_{zx}+i{d}_{yz}$)-wave superconductor by surface roughness: application to Sr${}_2$RuO${}_4$
• Coreless vortices as direct signature of chiral $d$-wave superconductivity
• Analytical Result on Electronic States around a Vortex Core in a Noncentrosymmetric Superconductor
• Breaking time-reversal and translational symmetry at edges of $d$-wave superconductors: microscopic theory and comparison with quasiclassical theory
• Theory of vortices in hybridized ballistic/diffusive-band superconductors
• Quasiclassical theory for antiferromagnetic metals
• Charge Dynamics of Vortex Cores in Layered Chiral Triplet Superconductors
• Excess current in superconducting Sr${}_2$RuO${}_4$
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Quasiclassical theory of superconductivity: interfering paths
• Spontaneous symmetry-breaking at surfaces of $d$-wave superconductors: influence of geometry and surface ruggedness
• Nonlocal superconducting quantum interference device
• Thermopower and thermophase in a $d$-wave superconductor
• Spin-resolved crossed Andreev reflection in ballistic heterostructures
• Influence of interface transmissivity and inelastic scattering on the electronic entropy and specific heat of diffusive SNS Josephson junctions
• Phase-dependent dissipation and supercurrent of a graphene-superconductor ring under microwave irradiation
• Influence of diffuse surface scattering on the stability of superconducting phases with spontaneous surface current generated by Andreev bound states
• Two regimes for effects of surface disorder on the zero-bias conductance peak of tunnel junctions involving d-wave superconductors
• Thermally induced spin torque and domain wall motion in superconductor/antiferromagnetic insulator bilayers
• Bogoliubov - de Gennes versus Quasiclassical Description of Josephson Structures
• Anomalous inverse proximity effect in unconventional-superconductor junctions
• Nonlinear magnetic field dependence of the conductance in d-wave NIS tunnel junctions
• SuperConga: an open-source framework for mesoscopic superconductivity
• Shot noise in normal metal-d-wave superconducting junctions
• Thermodynamic properties of a superconductor interfaced with an altermagnet
• Ballistic and diffusive: theory of vortices in the two-band superconductor MgB2
• Disordered Josephson Junctions of d-Wave Superconductors
• A finite element method for the quasiclassical theory of superconductivity
• Theory of quantum-geometric charge and spin Josephson diode effects in strongly spin-polarized hybrid structures with noncoplanar spin textures
• Spin imbalance in hybrid superconducting structures with spin-active interfaces
• Cooper Pair Shape in Normal-metal/Superconductor Junctions
• Robustness of chiral surface current and subdominant $s$-wave Cooper pairs
• Nonequilibrium Transport in Superconductor/Ferromagnet/Superconductor Diffusive Junctions: Interplay between Proximity Effect and Ferromagnetism
• Tunnelling conductance of $d+ip$-wave superconductor
• Impurity Scattering Rate and Coherence factor in Vortex Core of Sign-reversing s-wave Superconductors
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Subharmonic Gap Structure in Superconductor/Ferromagnet/Superconductor Junctions
• Multiparticle tunneling in diffusive superconducting junctions
• Influence of spin filtering and spin mixing on the subgap structure of I-V characteristics in superconducting quantum point contact
• calcQPI: A versatile tool to simulate quasiparticle interference
• Interplay between single-particle and two-particle tunneling in normal metal-d-wave superconductor junctions probed by shot noise
• Signatures of spin-triplet Cooper pairing in the density of states of spin-textured superconductor-ferromagnet bilayers
• Tunable ground states in helical $p$-wave Josephson junctions
• The influence of spin-dependent phases of tunneling electrons on the conductance of a point ferromagnet/isolator/superconductor contact
• Heat transport in nonuniform superconductors
• Spin caloritronics as a probe of nonunitary superconductors
• Reconstruction of the DOS at the end of a S/F bilayer
• Spin-polarized currents and noise in NS junctions with Yu-Shiba-Rusinov impurities
• Theory of a Weak-Link Superconductor-Ferromagnet Josephson Structure
• Spin-resolved Josephson diode effect through strongly spin-polarized conical magnets
• Shaping graphene superconductivity with nanometer precision
• Quasiclassical circuit-theory of contiguous disordered multiband superconductors
• Theory of surface spectroscopy for noncentrosymmetric superconductors
• Anomalous acoustoelectric effect induced by clapping modes in chiral superconductors
• Josephson effect in spin-singlet superconductor/ferromagnetic insulator/spin-triplet superconductor junctions with helical $p$-wave states
• Giant thermopower in superconducting heterostructures with spin-active interfaces
• Dissipative Currents in Superfluid 3He Weak Links
• Probing the topological band structure of diffusive multiterminal Josephson junction devices with conductance measurements
• Abrikosov flux-lines in two-band superconductors with mixed dimensionality
• Order parameter sign-reversal near $s_{\pm }$-superconductor surface
• Subgap in the surface bound states spectrum of Superfluid ${}^3$He-B with Rough Surface
• Local density of states in clean two-dimensional superconductor--normal metal--superconductor heterostructures
• Sparse modeling approach for quasiclassical theory of superconductivity
• Spectral properties of superconductors with ferromagnetically ordered magnetic impurities
• Non-Equilibrium Quasiclassical Theory for Josephson Structures
• Spin polarized current and Andreev transmission in planar superconducting/ferromagnetic Nb/Ni junctions
• Multiple Andreev Reflections in Weak Links of Superfluid 3He-B
• Impurity Effect on the Local Density of States around a Vortex in Noncentrosymmetric Superconductors
• Absence of "fractional ac Josephson effect" in superconducting junctions
• Nonequilibrium and relaxation effects in tunnel superconducting junctions
• Fulde-Ferrell-Larkin-Ovchinnikov state in a superconducting thin film attached to a ferromagnetic cluster
• Crossed Andreev reflection and spin-resolved non-local electron transport
• Density of states near a vortex core in ferromagnetic superconductors: Application to STM measurements
• Self-consistent theory of current injection into $d$ and $d+is$ superconductors
• The influence of the spin-dependent phases of tunneling electrons on the conductance of a point ferromagnet/isolator/d-wave superconductor contact
• Proximity-driven source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor voltage-biased Josephson junction
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Chiral Current Inversion Induced by Flat-Band Andreev Bound States