Odd-frequency superconductivity near a magnetic impurity in a conventional superconductor

Abstract

Superconductor-ferromagnetic heterostructures have been suggested as one of the most promising alternatives of realizing odd-frequency superconductivity. In this work we consider the limit of shrinking the ferromagnetic region to the limit of a single impurity embedded in a conventional superconductor, which gives raise to localized Yu-Shiba-Rusinov (YSR) bound states with energies inside the superconducting gap. We demonstrate that all the sufficient ingredients for generating odd-frequency pairing are present at the vicinity of these impurities. We investigate the appearance of all possible pair amplitudes in accordance with the Berezinskii SP * OT * = −1 rule, being the symmetry under the exchange of spin, spatial, orbital (in our case O = +1) and time index, respectively. We study the spatial and frequency dependence of of the possible pairing amplitudes, analyzing their evolution with impurity strength and identifying a reciprocity between different symmetries related through impurity scattering. We show that the odd-frequency spin-triplet pairing amplitude dominates at the critical impurity strength, where the YSR states merge at the middle of the gap, while the even components cancel out close to the impurity. We also show that the spin-polarized local density of states exhibits the same spatial and frequency behavior as the odd-ω spin-triplet component at the critical impurity strength.

Odd-frequency superconductivity in dilute magnetic superconductors

“…We expect therefore superconductivity to be induced at the impurity site by the proximity effect. Because of the time-reversal symmetry breaking due to the magnetic field at the impurity, an odd-ω pair- ing component is expected to appear [4], similarly to the single-impurity case [31,32]. As the impurity electrons form the YSR bands, these should then display an odd-ω superconducting component in the superconducting function.…”

“…One recent study has reported odd-ω superconductivity at the interface of a topological insulator with a conventional superconductor [29]. In another recent development, which builds upon earlier theoretical work [30,31], the presence of an odd-ω component in scanning tunneling spectroscopy (STS) has finally been reported in a system of a magnetic impurity in contact with a conventional superconductor [32].…”

“…III, where we show the appearance of impurity bands inside the superconducting gap, the Yu-Shiba-Rusinov bands, which possess an odd-ω component. Differently from the single-impurity case [31,32], odd-ω superconducting pairing is present for the whole system, for both magnetic and nonmagnetic sites, making it eventually exploitable in transport and device making. In Sec.…”

Transient dynamics of a magnetic impurity coupled to superconducting electrodes: exact numerics versus perturbation theory

“…At the transition between the doublet and the singlet ground state, the subgap states (also known as Yu-Shiba-Rusinov states) cross the Fermi level [24][25][26] leading to a super-current sign reversal, the so-called 0 − π transition [27][28][29][30][31]. At the ground state transition, BCS pair correlations are suppressed and the electron pairing is predominantly spin-triplet close to the impurity [32,33].…”

Induced odd-frequency superconducting state in vertex-corrected Eliashberg theory

“…In this discussion it is important to distinguish between existence of a superconducting condensate with an odd-frequency order parameter, i.e., with nonzero gap function, and oddfrequency pair correlations. The latter can occur when a frequency-even superconductor is placed in close proximity to a magnetic layer or when a magnetic impurity is placed on a conventional superconductor [10][11][12][13][14][15][16][17][18]. The spins of the conventional Cooper-pair electrons become rotated in the exchange field, leading to a spin-triplet component with time-odd parity [10,19].…”