Abstract
We analyze the subgap excitations and phase diagram of a quantum dot (QD) coupled to a semiconducting nanowire fully wrapped by a superconducting (S) shell. We take into account how a Little-Parks (LP) pairing fluxoid (a winding in the S phase around the shell) influences the proximity effect on the dot. We find that under axially symmetric QD-S coupling, shell fluxoids cause the induced pairing to vanish, producing instead a level renormalization that pushes subgap levels closer to zero energy and flattens fermionic parity crossings as the coupling strength increases. This fluxoid-induced stabilization mechanism has analoges in symmetric S-QD-S Josephson junctions at phase $\pi$, and can naturally lead to patterns of near-zero modes weakly dispersing with parameters in all but the zero-th lobe of the LP spectrum.
Highlights
Introduction.—In the quest to create the necessary conditions for topological superconductivity and Majorana bound states (MBSs)[1,2,3,4,5,6,7,8] in hybrid semiconducting nanowires[9,10,11], researchers have explored new architectures that aim to overcome various limitations in the original nanowire designs
Subsequent experiments reproduced zero bias anomalies in similar devices that were instead explained in terms of quantum dot (QD) Yu-Shiba-Rusinov states[33,34,35] localized at the end of the full-shell nanowires[26], which are by nature non-topological
We study it in the spirit of the superconducting impurity Anderson (SIA) model[36], extended to explicitly include the cylindrical geometry of the S shell and its pairing winding within n = 0 lobes, see Fig. 1, an aspect of these devices not yet analyzed
Summary
The presence of an axial external magnetic field, or alternatively a magnetic flux penetrating a thin-walled S cylinder, Φ = πR2B, leads to three effects that need to be considered in the S-shell Hamiltonian: orbital effects, that are taking into account with a standard Peierls substitution, a winding of the superconducting pairing phase θ of the S order parameter ∆ = ∆e−inθ, where n is the quantized fluxoid or fluxon[32], i.e., n = Φ/Φ0 , with Φ0 = h/2e the S magnetic flux quantum, and a modulation of the S gap with the flux ∆(Φ), explained All these ingredients lead to a generalized superconducting impurity Anderson (SIA) model of the. In the limit of d → 0, though, an approximated solution exists[22]
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