Odd-frequency Cooper pairs and zero-energy surface bound states in superfluid3He

Abstract

We study the odd-frequency Cooper pairs formed near the surface of superfluid 3 He. The oddfrequency pair amplitude is closely related to the local density of states in the low energy limit. We derive a formula relating explicitly the two quantities. This formula holds for arbitrary boundary condition at the surface. We also present some numerical results on the surface odd-frequency pair amplitude in superfluid 3 He-B. Those analytical and numerical results allow one to interpret the midgap surface density of states, observed recently by transverse acoustic impedance measurements on superfluid 3 He-B, as the manifestation of the surface odd-frequency state.

Theory of the proximity effect in two-dimensional unconventional superconductors with Rashba spin-orbit interaction

“…The anomalous proximity effect can occur in a DN/noncentrosymmetric superconductor junction when the spin-triplet pair potential is dominant [32]. The anomalous proximity effect, triggered by an oddfrequency spin-triplet s-wave pairing, shows several interesting physical properties: i) ZEP of the LDOS in the DN [26,27,33,34], ii) ZEP of the LDOS at rough surface [35], iii) zero bias conductance peak in quasiparticle transport in the DN/spin-triplet p-wave superconductor junctions [26,27,31], iv) significant enhancement of the Josephson current at low temperatures in the DN/spintriplet p-wave superconductor junctions [28] v) paramagnetic Meissner response [36][37][38][39][40][41][42][43], and vi) anomalous surface impedance [44,45]. It has been also shown that the anomalous proximity effect can occur in topologically designed hybrid systems based on conventional spin-singlet s-wave superconductor systems with spin-orbit coupling and Zeeman effect [31,46,47] and the anomalous proximity effect has been studied considering the classifica-tion of the topological nature of the Hamiltonian [48].…”

Odd-frequency pairing in topological superconductivity in a one-dimensional magnetic chain

“…The concept of the odd-frequency pairing naturally arises on introducing the frequency dependence of the pairing function. The odd-frequency pair ubiquitously exists in inhomogeneous superconducting systems with broken symmetries in, for instance, spin rotation [57][58][59][60][61][62][63] or translation [54,55,[64][65][66][67][68][69][70][71], In these systems, the odd-frequency pairings are prominent in the presence of the surface ABS [72][73][74][75][76], Since the MF is a type of ABS, it is expected to be related to odd-frequency pairing. It is elucidated that the odd-frequency pair becomes prominent at the edge of the nanowire/5 -wave superconductor junction described above [77,78].…”

Multifaceted properties of Andreev bound states: interplay of symmetry and topology

“…Using the quasi-classical approximation reliable for T c /T F 1, Higashitani et al [158] and Tsutsumi & Machida [159] demonstrated that in 3 for |E| < B . The OTE pairing amplitude, f OF z , is defined by the quasi-classical approximation of the anomalous Green's function, f ab (k, z; ω n ), as f OF μ = tr[−iσ y σ μ (f (ω n ) − f (ω n ))]/4.…”