Subgap states and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures

TL;DR

This paper theoretically investigates the spectral properties and quantum phase transitions in a one-dimensional superconductor-ferromagnetic insulator hybrid nanostructure, revealing tunable subgap states and phase transitions driven by device parameters.

Contribution

It introduces a detailed theoretical model of a 1D semiconductor-superconductor-ferromagnetic insulator system, classifies Andreev bound states, and analyzes their evolution and quantum phase transitions as a function of device parameters.

Findings

ABS can cross below Fermi energy at critical lengths

Quantum phase transitions are induced by ABS crossings

Device parameters allow tunable subgap states

Abstract

We theoretically study the spectral properties of a one dimensional semiconductor-superconductor-ferromagnetic insulator (SE-SU-FMI) hybrid nanostructure, motivated by recents experiments where such devices have been fabricated using epitaxial growing techniques. We model the hybrid structure as a one-dimensional single-channel semiconductor nanowire under the simultaneous effect of two proximity-induced interactions: superconducting pairing and a (spatially inhomogeneous) Zeeman exchange field. The coexistence of these competing interactions generates a rich quantum phase diagram and a complex subgap Andreev bound state (ABS) spectrum. By exploiting the symmetries of the problem, we classify the solutions of the Bogoliubov-de Gennes equations into even and odd ABS with respect to the spatial inversion symmetry $x\to -x$. We find the ABS spectrum of the device as a function of the different parameters of the model: the length $L$ of the coexisting SU-FMI region, the induced Zeeman exchange field $h_0$, and the induced superconducting coherence length $\xi$. In particular we analyze the evolution of the subgap spectrum as a function of the length $L$. Interestingly, we have found that depending on the ratio $h_0/\Delta$, the emerging ABS can eventually cross below the Fermi energy at certain critical values $L_c$, and induce spin-and fermion parity-changing quantum phase transitions. We argue that this type of device constitute a promising highly-tunable platform to engineer subgap ABS.