Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model

Abstract

Hybrid semiconductor-superconductor systems are interesting melting pots where various fundamental effects in condensed matter physics coexist. For example, when a quantum dot is coupled to a superconducting electrode two very distinct phenomena, superconductivity and the Kondo effect, compete. As a result of this competition, the system undergoes a quantum phase transition when the superconducting gap ∆ is of the order of the Kondo temperature TK . The underlying physics behind such transition ultimately relies on the physics of the Anderson model where the standard metallic host is replaced by a superconducting one, namely the physics of a (quantum) magnetic impurity in a superconductor. A characteristic feature of this hybrid system is the emergence of subgap bound states, the so-called Yu-Shiba-Rusinov (YSR) states, which cross zero energy across the quantum phase transition, signaling a switching of the fermion parity and spin (doublet or singlet) of the ground state. Interestingly, similar hybrid devices based on semiconducting nanowires with spin-orbit coupling may host exotic zero-energy bound states with Majorana character. Both, parity crossings and Majorana bound states (MBS)s, are experimentally marked by zero bias anomalies in transport, which are detected by coupling the hybrid device with an extra normal contact. We here demonstrate theoretically that this extra contact, usually considered as a non-perturbing tunneling weak probe, leads to nontrivial effects. This conclusion is supported by numerical renormalization group calculations of the phase diagram of an Anderson impurity coupled to both superconducting and normal-state leads. We obtain this phase diagram for an arbitrary ratio ∆ T K for the first time, which allows us to analyze relevant experimental scenarios, such as parity crossings as well as novel Kondo features induced by the normal lead, as this ratio changes. Spectral functions at finite temperatures and magnetic fields, which can be directly linked to experimental tunneling transport characteristics, show zero-energy anomalies irrespective of whether the system is in the doublet or singlet regime. We also derive the analytical condition for the occurrence of Zeeman-induced fermion-parity switches in the presence of interactions which bears unexpected similarities with the condition for emergent MBSs in nanowires.

SNS junctions in nanowires with spin-orbit coupling: Role of confinement and helicity on the subgap spectrum

“…Unfortunately, the outcome of the simplest detection protocol for MBSs in NW devices [20][21][22], detection of subgap zero modes through zero-bias anomalies in transport [23][24][25][26][27][28], can be obscured, or even mimicked, by other effects [29][30][31][32][33][34][35][36]. As a result, there is no clear consensus yet on whether MBSs have been observed or not in NWs.…”

Nonlinear electric and thermoelectric Andreev transport through a hybrid quantum dot coupled to ferromagnetic and superconducting leads

“…Whereas Coulomb interaction favors transport of single carriers, superconducting proximity effect leads to transport of electrons as Cooper pairs. The competition between these two interactions yields a variety of phenomena such as the occurrence of Kondo zero-bias anomalies [7] or the formation of Yu-Shiba-Rusinov states [8] and their connection to Majorana quasiparticles [9,10]. Furthermore, N-QD-S systems might be relevant in certain quantum information processing setups [11].…”

Enhancements of the Andreev conductance due to emission/absorption of bosonic quanta

“…For this reason, in the subgap Andreev spectroscopy the correlations hardly contributed any Coulomb blockade. Instead of it, they can eventually induce the singlet-doublet quantum phase transition [35] and/or the Kondo physics [34]. In this paper we consider the strongly asymmetric coupling Γ N ≪ Γ S and focus on the deep subgap regime Γ N,S ≪ ∆, therefore the Kondo-type effects [30][31][32][33][34] would be rather negligible.…”