Superconducting diode effect in multichannel Majorana wires

Abstract

The superconducting diode effect (SDE) enables nonreciprocal dissipationless transport when inversion and time-reversal symmetries are simultaneously broken. Rashba nanowires proximitized by conventional s-wave superconductors provide a minimal setting where spin-orbit coupling and Zeeman fields generate asymmetric finite-momentum pairing. While most studies focus on the single-channel limit, which typically yields small diode efficiencies and requires multiple Zeeman-field components, realistic devices generically host multiple transverse subbands (channels). Here, we investigate the SDE in multichannel Rashba nanowires with harmonic and rectangular quantum-well confinement using a self-consistent Bogoliubov-de Gennes formalism. Both geometries support asymmetric Fulde-Ferrell (FF) states driving pronounced nonreciprocal supercurrents. Crucially, this current-driven FF state stabilizes a topological phase with Majorana zero modes, where Cooper pair momentum is controlled by an externally injected supercurrent, enabling direct topological manipulation. Pairing susceptibility analysis reveals that field-induced asymmetries favor directional Cooper pairing, explaining the diode response's nonmonotonic Zeeman-field dependence. Harmonic confinement yields diode efficiencies of ~60% (interacting channels) and ~55% (independent channels). Notably, interchannel coupling enables a finite response from a transverse Zeeman field alone. Rectangular confinement achieves ~60% efficiency across both regimes, alongside a tunable sign reversal of efficiency when channels interact. These results establish the robustness of the SDE and FF states against transverse confinement variations, highlighting multichannel nanowires as powerful platforms for high-efficiency nonreciprocal transport and current-controlled topological superconductivity.

Figures (12)

• Figure 1: Electronic and Bogoliubov quasiparticle spectra of a multichannel nanowire under harmonic confinement:: Normal-state energy spectrum of the multichannel nanowire: (a) in the presence of an external magnetic field with $B_x \neq 0$ and $B_y = 0$, and (b) when both in-plane components are finite ($B_x \neq 0$, $B_y \neq 0$). Panels (c) and (d) show the corresponding Bogoliubov quasiparticle spectra. In (c), we consider $B_x \neq 0$, $B_y = 0$ with zero Cooper-pair momentum ($q = 0$), whereas in (d), both $B_x \neq 0$ and $B_y \neq 0$ are applied and a finite Cooper-pair momentum $q \neq 0$ is included.
• Figure 2: FF superconducting ground state in a harmonically confined nanowire: (a) The self-consistent superconducting gap $\Delta(q)$ is shown as a function of the finite Cooper-pair momentum $q$ for a fixed $B_x = 0.0$ and varying $B_y$. Here, $\Delta_0$ denotes the superconducting order parameter in the absence of any external magnetic field.(b) The finite momentum value of the FF ground state, $q_0$, is plotted as a function of $B_y$. A stable FF ground state with $q_0 \neq 0$ emerges even when only one magnetic field component is present $(B_x = 0)$. The model parameters used are $(B_z, \mu, U, \beta^{-1}) = (0.0, 0, {13.35} \, \text{meV}, 0.1 \, \text{meV})$.
• Figure 3: Topological signatures of the FF superconducting state for harmonic confinement case: (a) Low-energy spectrum as a function of the longitudinal magnetic field $B_x$, showing the emergence of zero-energy states associated with MZMs. (b) Evolution of the energy spectrum with Cooper-pair momentum for $B_x /\Delta_0 = 2$. (c) Phase diagram in the ($q, B_x$) plane, indicating the boundary between topologically trivial (black) and nontrivial (yellow) regions for a fixed pairing potential $\Delta = 0.5$. (d) Spatial probability density of a Majorana quasiparticle at $B_x / \Delta = 2$. The calculations were performed using $L = 4~\mu\text{m}$, $\Delta = 0.5~\text{meV}$, $\mu = 0.0~\text{meV}$, and $\alpha = 100~\text{meV·nm}$.
• Figure 4: Supercurrent density and diode efficiency in a harmonically confined nanowire with interacting channels ($\delta_{\rm HC} \neq 0$):(a) Supercurrent density $J(q)$ as a function of the Cooper-pair momentum $q$ for fixed $B_y / \Delta = 0.5$ and different values of $B_x$. A clear asymmetry appears between the positive and negative critical supercurrents, and importantly, nonreciprocity persists even when only the transverse magnetic field is present ($B_y \neq 0$, $B_x = 0$). (b,c) The corresponding diode efficiency $\eta$ as a function of $B_y / \Delta$ for several fixed values of $B_x$ (panel b) and as a function of $B_x / \Delta$ for several fixed values of $B_y$ (panel c). The model parameters are $(B_z, \alpha, \mu, U, \beta^{-1}) = (0.0, 100~\text{meV - nm}, 0.0, {13.35}~\text{meV}, 0.1~\text{meV})$.
• Figure 5: Effect of chemical potential and temperature on superconducting diode efficiency of a harmonically confined nanowire: (a) The plot shows how the superconducting diode efficiency varies with the chemical potential $\mu$ for a fixed $B_x/\Delta_0 = {0.5}$ and different values of $B_y$. (b) The second panel illustrates how the efficiency changes with temperature for a fixed $B_x/\Delta_0 ={0.5}$ while varying $B_y$. The calculations are performed using following model parameters $(B_z,\alpha, \mu, U) = (0.0, 100~\mathrm{meV-nm}, 0.0, {10.35}~\mathrm{meV})$.