Theory of Surface Andreev Bound States and Odd-Frequency Pairing in Superconductor Junctions
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REVIEW
Theory of Surface Andreev Bound States and Odd-Frequency Pairing in Superconductor Junctions Yukio Tanaka1 · Shun Tamura1 Received: 24 August 2020 / Accepted: 3 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this review, we mention about the theoretical achievement of physics of surface Andreev bound state (SABS) and oddfrequency pairing during this quarter century based on our research. Currently, topological superconductors with Majorana edge state have become a central issue in condensed matter physics. It is noted that Majorana edge state is nothing but a zero energy surface Andreev bound state (ZESABS) and the study of ZESABS has started in the context of the pairing symmetry of high Tc cuprate. We mention our obtained conductance formula of quasiparticle tunneling and Josephson current in unconventional superconductor junctions through ZESABS have already captured the essence of the charge transport profile via the Majorana fermion. We also mention that in the presence of ZESABS, odd-frequency pairing like spin-triplet swave or spin-singlet p-wave is hugely enhanced near the surface or interface. We further analyze the spectroscopy of the induced odd-frequency pairings by extending bulk-boundary correspondence in ZESABS. If we consider a semi-infinite superconductor with ZESABS, the induced odd-frequency pair amplitude can be expressed by a c-number defined in bulk, which we call spectral bulk-boundary correspondence. The odd-frequency pair amplitude is classified into singular part and regular one, the former part is proportional to ∼ 1/z (z is a complex frequency) reflecting the presence of ZESABS, and the latter one is proportional to ∼ z. The coefficient of the latter one diverges at the topological phase transition point. Analyzing the spectral behavior of the odd-frequency pairing is useful to understand the critical phenomena near topological transition points. Keywords Andreev bound state · Odd-frequency pairing
1 Introduction In inhomogeneous superconducting systems, an electron is reflected as a hole by pair potential and this process has been known as Andreev reflection which is one of the fundamental phenomena in superconductivity [1]. The presence of Andreev reflection generates ingap states, so-called Andreev bound states in inhomogeneous superconductors. Andreev bound states have been known since the 1960s in a normal metal (N)/ superconductor (S) junction with finite thickness of N (S) [2], vortex Yukio Tanaka
[email protected] Shun Tamura [email protected] 1
Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan
core [3], and around magnetic impurity [4–6]. In 1982, Blonder Tinkham and Klapwijk have derived a tunneling conductance formula of a N/S junction taking into account the Andreev reflection where pairing symmetry of the superconductor is a conventional spin-singlet swave one [7]. The line shape of conductance reflects the bulk density of states in the low transparent limit. It h
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