Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor

TL;DR

This paper explores how coupling a superconductor to a minimal Kitaev chain with quantum dots introduces complex Majorana and Yu-Shiba-Rusinov states, affecting their detection and properties.

Contribution

It reveals the emergence of non-local Majorana effects and YSR states due to superconductor coupling, altering the chain's low-energy excitations and Majorana signatures.

Findings

Coupling to a superconductor induces non-local Majorana effects.

Emergence of YSR states coexisting with MZMs.

Hybridization of YSR and MZMs spoils Majorana quantization.

Abstract

Two semiconducting quantum dots (QDs) coupled through a superconductor constitute a minimal realisation of a Kitaev chain with Majorana zero modes (MZMs). Such MZMs can be detected by e.g., tunneling conductance between each QD and normal leads [Dvir et al, Nature 614, 445 (2023)]. We here discuss how the seemingly trivial substitution of one of the normal leads by a superconducting (SC) one gives rise to a plethora of new effects. In particular, the coupling to the SC lead induces non-local Majorana effects upon variations of the QDs' energies. Furthermore, the lowest excitation of the chain is no longer determined by the bulk gap but rather by the energy of an emergent subgap Yu-Shiba-Rusinov (YSR) state coexisting with the MZMs. The YSR state hybridizes with the MZMs when the coupling between the SC and the QD is larger than the spin splitting, spoiling the Majorana properties, including the quantized conductance.