Resistance in Superconductors

Abstract

In this pedagogical review, we discuss how electrical resistance can arise in superconductors. Starting with the idea of the superconducting order parameter as a condensate wave function, we introduce vortices as topological excitations with quantized phase winding, and we show how phase slips occur when vortices cross the sample. Superconductors exhibit non-zero electrical resistance under circumstances where phase slips occur at a finite rate. For one-dimensional superconductors or Josephson junctions, phase slips can occur at isolated points in space-time. Phase slip rates may be controlled by thermal activation over a free-energy barrier, or in some circumstances, at low temperatures, by quantum tunneling through a barrier. We present an overview of several phenomena involving vortices that have direct implications for the electrical resistance of superconductors, including the Berezinskii-Kosterlitz-Thouless transition for vortex-proliferation in thin films, and the effects of vortex pinning in bulk type II superconductors on the non-linear resistivity of these materials in an applied magnetic field. We discuss how quantum fluctuations can cause phase slips and review the non-trivial role of dissipation on such fluctuations. We present a basic picture of the superconductor-to-insulator quantum phase transitions in films, wires, and Josephson junctions. We point out related problems in superfluid helium films and systems of ultra-cold trapped atoms. While our emphasis is on theoretical concepts, we also briefly describe experimental results, and we underline some of the open questions.

Chapter to appear in "Bardeen, Cooper and Schrieffer: 50 Years," edited by Leon N. Cooper and Dmitri Feldman, to be published by World Scientific Press

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Suppressing Charge Noise Decoherence in Superconducting Charge Qubits
• Disorder-Induced Inhomogeneities of the Superconducting State Close to the Superconductor-Insulator Transition
• Superconductivity in one dimension
• Critical velocity for superfluid flow across the BEC-BCS crossover
• Phase diagram for a Bose-Einstein condensate moving in an optical lattice
• The approach to a superconductor-to-Bose-insulator transition in disordered films
• Magnetically Induced Metallic Phase in Superconducting Tantalum Films
• Decay of a superfluid currents in a moving system of strongly interacting bosons
• Infinite-randomness quantum critical points induced by dissipation
• Phase-slip induced dissipation in an atomic Bose-Hubbard system
• Sharp Superconductor-Insulator Transition in Short Wires
• The Effect of Quantum Phase Slip Interactions on the Transport of Thin Superconducting Wires
• Quantum dynamics in a camel-back potential of a dc SQUID
• Superconductor-to-normal transition in finite nanowires

Cited by in corpus (40)

• Quantised supercurrent decay in an annular Bose-Einstein condensate
• Anomalous metals -- failed superconductors
• Motion of a Solitonic Vortex in the BEC-BCS Crossover
• Connecting dissipation and phase slips in a Josephson junction between fermionic superfluids
• Superinsulator-Superconductor Duality in Two Dimensions
• Tunneling transport of unitary fermions across the superfluid transition
• Vacuum as a hyperbolic metamaterial
• Evidence for charge-vortex duality at the LaAlO${}_3$/SrTiO${}_3$ interface
• The dynamics of bimeron skyrmions in easy-plane magnets induced by a spin supercurrent
• Deterministic phase slips in mesoscopic superconducting rings
• Absence versus Presence of Dissipative Quantum Phase Transition in Josephson Junctions
• Thermally-Activated Phase Slips in Superfluid Spin Transport in Magnetic Wires
• Magnetic Domain Walls as Hosts of Spin Superfluids and Generators of Skyrmions
• Energy Storage via Topological Spin Textures
• Decay mechanisms of superflow of Bose-Einstein condensates in ring traps
• Perspective: (Beyond) spin transport in insulators
• Nonlocal Spin Transport Mediated by a Vortex Liquid in Superconductors
• Topological Effects on Quantum Phase Slips in Superfluid Spin Transport
• Quantum Hydrodynamics of Vorticity
• Entropy generation and momentum transfer in the superconductor-normal and normal-superconductor phase transformations and the consistency of the conventional theory of superconductivity
• Quantum hydrodynamics of spin winding
• Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition
• Quantum phase slips in a resonant Josephson junction
• Energy storage in magnetic textures driven by vorticity flow
• Transverse instability and universal decay of spin spiral order in the Heisenberg model
• Superconducting materials: the w$hole$ story
• The Josephson junction as a quantum engine
• Dissipation in a Finite Temperature Atomic Josephson Junction
• Berezinskii-Kosterlitz-Thouless transition transport in spin-triplet superconductor
• Evidence of Josephson coupling in a few-layer black phosphorus planar Josephson junction
• Functional Renormalization Group Approach to Circuit Quantum Electrodynamics
• Irreversible entropy transport enhanced by fermionic superfluidity
• Superconducting Vortices in Half-Metals
• Superfluid Spin Transistor
• Signatures in the conductance for phase transitions in excitonic systems
• Mutual friction and vortex Hall angle in a strongly interacting Fermi superfluid
• Sn2Pd: a possible superconducting material with topological surface states
• Spin Hall effect of vorticity
• Persistent current noise in narrow Josephson junctions
• Thin amorphous molybdenum silicide superconducting shells around individual nanowires deposited via magnetron co-sputtering