Andreev bound states and their signatures

J. A. Sauls*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


Many of the properties of superconductors related to quantum coherence are revealed when the superconducting state is forced to vary in space-in response to an external magnetic field, a proximity contact, an interface to a ferromagnet or to impurities embedded in the superconductor. Among the earliest examples is Andreev reflection of an electron into a retro-reflected hole at a normal-superconducting interface. In regions of strong inhomogeneity, multiple Andreev reflection leads to the formation of sub-gap states, Andreev bound states, with excitation energies below the superconducting gap. These states play a central role in our understanding of inhomogeneous superconductors. The discoveries of unconventional superconductivity in many classes of materials, advances in fabrication of superconducting/ferromagnetic hybrids and nanostructures for confining superfluid3He, combined with theoretical developments in topological quantum matter have dramatically expanded the significance of branch conversion scattering and Andreev bound state formation. This collection of articles highlights developments in inhomogeneous superconductivity, unconventional superconductivity and topological phases of superfluid3He, in which Andreev scattering and bound states underpin much of the physics of these systems. This article provides an introduction to the basic physics of Andreev scattering, bound-state formation and their signatures. The goal is both an introduction for interested readers who are not already experts in the field, and to highlight examples in which branch conversion scattering and Andreev bound states provide unique signatures in the transport properties of superconductors.

Original languageEnglish (US)
Article number20180140
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2125
StatePublished - Aug 6 2018


  • Andreev reflection
  • Andreev scattering
  • Andreev spectroscopy
  • Josephson junctions
  • Unconventional superconductivity

ASJC Scopus subject areas

  • Engineering(all)
  • Physics and Astronomy(all)
  • Mathematics(all)


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