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Abstract: In this pedagogical review, we discuss how electrical resistance can arise insuperconductors. Starting with the idea of the superconducting order parameteras a condensate wave function, we introduce vortices as topological excitationswith quantized phase winding, and we show how phase slips occur when vorticescross the sample. Superconductors exhibit non-zero electrical resistance undercircumstances where phase slips occur at a finite rate. For one-dimensionalsuperconductors or Josephson junctions, phase slips can occur at isolatedpoints in space-time. Phase slip rates may be controlled by thermal activationover a free-energy barrier, or in some circumstances, at low temperatures, byquantum tunneling through a barrier. We present an overview of severalphenomena involving vortices that have direct implications for the electricalresistance of superconductors, including the Berezinskii-Kosterlitz-Thoulesstransition for vortex-proliferation in thin films, and the effects of vortexpinning in bulk type II superconductors on the non-linear resistivity of thesematerials in an applied magnetic field. We discuss how quantum fluctuations cancause phase slips and review the non-trivial role of dissipation on suchfluctuations. We present a basic picture of the superconductor-to-insulatorquantum phase transitions in films, wires, and Josephson junctions. We pointout related problems in superfluid helium films and systems of ultra-coldtrapped atoms. While our emphasis is on theoretical concepts, we also brieflydescribe experimental results, and we underline some of the open questions.

Author: Bertrand I. Halperin, Gil Refael, Eugene Demler


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