Odd-frequency superconductivity induced by nonmagnetic impurities

Abstract

A growing body of literature suggests that odd-frequency superconducting pair amplitudes can be generated in normal metal-superconductor junctions. The emergence of odd-frequency pairing in these systems is often attributed to the breaking of translation invariance. In this work, we study the pair symmetry of a one-dimensional s-wave superconductor in the presence of a single non-magnetic impurity and demonstrate that translation symmetry breaking is not sufficient for inducing odd-frequency pairing. We consider three kinds of impurities: a local perturbation of the chemical potential, an impurity possessing a quantum energy level, and a local perturbation of the superconducting gap. Surprisingly, we find local perturbations of the chemical potential do not induce any odd-frequency pairing, despite the fact that they break translation invariance. Moreover, although odd-frequency can be induced by both the quantum impurity and the perturbation of the gap, we find these odd-frequency amplitudes emerge from entirely different kinds of scattering processes. The quantum impurity generates odd-frequency pairs by allowing one of the quasiparticles belonging to an equal-time Cooper pair to tunnel onto the impurity state and then back to the superconductor, giving rise to odd-frequency amplitudes with a temporal broadening inversely proportional to the energy level of the impurity. In contrast to this, the perturbation of the gap leads to odd-frequency pairing by "gluing-together" normal state quasiparticles from different points in space and time, leading to odd-frequency amplitudes which are very localized in the time domain.

The Role of Odd‐Frequency Pairing in Multiband Superconductors

“…For example, if describes a generic real‐space tight‐binding Hamiltonian then, if is an inhomogeneous on‐site order parameter, then the inequality in Equation is generically satisfied and we expect to find odd‐ω pairing. Note that this is entirely consistent with previous results studying the emergence of odd‐ω pairing in inhomogeneous systems, including at SN interfaces . In contrast, if is a spatially homogeneous on‐site order parameter and is trivial in spin space and has only real elements, no odd‐ω pairing is possible.…”

“…Still, while the existence of such intrinsic odd‐ω order parameters remains an intriguing theoretical question, a great deal of progress has been made studying the emergence of odd‐ω pair correlations in systems with conventional equal‐time order parameters . This latter possibility relies on the conversion of intrinsic even‐ω superconducting correlations to odd‐ω correlations, with a number of proposals in the literature realizing such symmetry conversion through a variety of different mechanisms …”

“…Since this interband hybridization is generally uniform throughout the bulk of a multiband superconductor, this establishes the existence of a class of systems that should host bulk odd‐ω pairing. Since the original proposal, multiple additional works have built on this concept generalizing the original idea to related systems, focusing on specific physical examples, or studying the experimental consequences of odd‐ω pairing in these multiband systems. With many known multiband superconductors with highly unconventional features, such as Sr 2 RuO 4 , iron‐based superconductors, MgB 2 , and UPt 3 it remains a very interesting question how much odd‐ω superconductivity contributes to the physical properties of these and related systems.…”

Van Der Waals Heterostructures with Spin‐Orbit Coupling

“…Interestingly, the authors found that, in general, because tunneling between adjacent layers dominates, an asymmetry emerges between the induced gaps on the two layers. This asymmetry leads directly to odd‐frequency interlayer pairing in such vdW heterostructures, similar to phenomena studied in multiband superconductors, double quantum dots, and double nanowires …”

Odd-frequency superconducting pairing in one-dimensional systems

“…In this regime Majorana Kramers pairs, or even parafermions if the system is interacting, can be induced. The generation of odd-ω correlations are allowed due to the additional degree of freedom offered by the wire index [116,141]. The authors of Ref.…”