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

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.

13 pages, 3 figures

References in corpus (10)

• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Epitaxy of Semiconductor-Superconductor nanowires
• Hard gap in epitaxial semiconductor-superconductor nanowires
• Spectral properties of locally correlated electrons in a BCS superconductor
• Topological Superconductivity induced by Ferromagnetic Metal Chains
• Orbital Picture of Yu-Shiba-Rusinov Multiplets
• Microscopic resolution of the interplay of Kondo screening and superconducting pairing: Mn-phthalocyanine molecules adsorbed on superconducting Pb(111)
• Majorana Fermions in Magnetic Chains
• Electronic properties of InAs/EuS/Al hybrid nanowires
• Evidence for spin-polarized bound states in semiconductor-superconductor-ferromagnetic insulator islands