Spin-polarized transport and quantum phase transitions in one-dimensional superconductor-ferromagnetic insulator heterostructures

TL;DR

This work investigates spin-polarized transport and quantum phase transitions in one-dimensional SE-SC-FMI hybrids by constructing a discrete BdG model of a central SE-SC-FMI region coupled to semi-infinite leads. The FMI layer is kept shorter than the SE-SC region to create an inhomogeneous Zeeman profile, and the semiconductor nanowire is assumed to have weak Rashba SOC, enabling spin-polarized Andreev bound states (ABS) with well-defined S^z. Transport is computed with non-equilibrium Keldysh Green's functions, embedding the finite device in semi-infinite leads to access subgap spectra via local and non-local conductances; ABS appear as subgap poles, and zero-energy crossings of ABS as a function of the backgate chemical potential μ_BG signal spin- and parity-changing quantum phase transitions (QPTs). By tuning the FMI length $L_M$ and the backgate $V_{BG}$ (through μ_BG), the device exhibits QPTs evidenced by ABS crossing $ε_{ ext{ABS}}=0$, with distinct ground-state spins S^z changing in steps as $N_M$ increases. The results imply a robust, experimentally accessible platform for exploring QPTs in hybrid nanowires, with moderate disorder and finite-temperature effects discussed as caveats to be addressed in real devices.

Abstract

We theoretically propose a one-dimensional electronic nanodevice inspired in recently fabricated semiconductor-superconductor-ferromagnetic insulator (SE-SC-FMI) hybrid heterostructures, and investigate its zero-temperature transport properties. While previous related studies have primarily focused on the potential for generating topological superconductors hosting Majorana fermions, we propose an alternative application: using these hybrids to explore controllable quantum phase transitions (QPTs) detectable through transport measurements. Our study highlights two key differences from existing devices: first, the length of the FMI layer is shorter than that of the SE-SC heterostructure, introducing an inhomogeneous Zeeman interaction with significant effects on the induced Andreev bound states (ABS). Second, we focus on semiconductor nanowires with minimal or no Rashba spin-orbit interaction, allowing for the induction of spin-polarized ABS and high-spin quantum ground states. We show that the device can be tuned across spin- and fermion parity-changing QPTs by adjusting the FMI layer length orange and/or by applying a global backgate voltage, with zero-energy crossings of subgap ABS as signatures of these transitions. Our findings suggest that these effects are experimentally accessible and offer a robust platform for studying quantum phase transitions in hybrid nanowires.

Figures (5)

• Figure 1: (color online) Schematic representation of the SC-SE-FMI heterostructure. The contact leads (denoted in red) are coupled to the SE nanowire, at each side of the FMI region at a distance $\Delta L$, and are connected to bias voltages $V_L$ and $V_R$. The backgate voltage $V_\text{BG}$ controls the chemical potential of the system.
• Figure 2: (color online) Local and nonlocal conductances (in units of $G_0=4e^2/h$) versus frequency $\omega$ and background chemical potential $\mu_\text{BG}$. (a) Spectral density (blue curves at basal plane) and local conductance maxima, with quantum phase transitions occurring at $\mu_\text{BG}$ values where Andreev bound states (ABS) cross $E_F$ (red curves). (b,c) High-resolution plots of local and non-local conductance, respectively, showing clearer zero-energy crossings ($\omega = 0$) of ABS in the local conductance.
• Figure 3: (color online) Colormaps of (a-d) local and (e-h) nonlocal conductance (units of $G_0$) versus chemical potential $\mu_\text{BG}/\Delta$ and frequency $\omega/\Delta$, calculated for $h_0/\Delta=1.5$. (i-l) Corresponding ground state total spin $S_z$. Each column shows different ferromagnetic insulator (FMI) lengths $N_M$. Increasing $N_M$ generates spin-polarized ABS pairs from gap edges (yellow arrows), with zero-energy crossings (white arrows) appearing at $N_M=38$ ($S_z=1$) and $N_M=82$ ($S_z=2$). (i) $N_M=30$: No crossings ($S_z=0$); (j) $N_M=38$: Crossings at $\mu_\text{BG}\approx\pm8\Delta$; (k) $N_M=56$: Universal crossings (orange arrows) and new ABS group; (l) $N_M=82$: Second crossing ($S_z=2$).
• Figure 4: (color online) Colormaps of the local conductance (in units of $G_0$) in terms of the chemical potential $\mu_\text{BG}/\Delta$ and $\omega/\Delta$, calculated for $h_0/\Delta=1.5$ and $N_M=38$. Each column (a-d) represents different disorder strength $v_0 = \left\{ 0,0.2,0.4,0.6\right\}$ respectively, corresponding to a weak disorder regime.
• Figure 5: (color online). Local conductance $\mathsf{G}_{LL}$ as a function of $\omega/\Delta$ for a system with $N_\text{M}=38$, computed for two different parameters $\mu_\text{BG}/\Delta=-2$ and $\mu_\text{BG}/\Delta=-8$, and different temperatures, as given by Eq. (\ref{['eq:G_LL_final3']}).