Giant and robust Josephson diode effect in multiband topological nanowires

TL;DR

This work analyzes giant, robust Josephson diode effects in multiband topological nanowires hosting Majorana bound states. By coupling Majorana and conventional Andreev bound states in a quasi-1D, multiband setting and using a recursive Green's function framework, the authors show that a large, long-lived diode efficiency arises from the balance between fractional $I_{4\pi}$ and conventional $I_{2\pi}$ currents deep in the topological phase. A novel spin-parity exchange mechanism between subbands in the multiband regime creates a robust high-efficiency plateau, tunable via external fields and subband engineering. The results provide practical routes to optimize the Josephson diode effect and offer new topological-phase signatures in superconducting nanowires.

Abstract

We theoretically predict the giant and robust Josephson diode effect in quasi-one-dimensional topological Majorana nanowires in the regime with multiple subbands, which is expected to be relevant for the real experiment. In the multiband regime, the Majorana bound states and conventional Andreev bound states can naturally coexist, and respectively contribute to the fractional and conventional parts in the Josephson effect, with the former/latter having 4$π$/2$π$-periodicity. We show that the interplay between the two types of bound modes can produce a robust and giant diode effect in the deep topological phase regime. Notably, we unveil a novel spin parity exchange mechanism, occurring only in the multiband regime, which leads to a robust high efficiency plateau of the giant diode effect. This effect is a nontrivial consequence of the balanced Fermi moment shifts of the multiple subbands in tuning the external magnetic field. Our finding highlights the subband engineering as a powerful tool to optimize the Josephson diode effect realistically and provides a new feasible signature to identify topological phase regime in superconducting nanowires.

Figures (8)

• Figure 1: (a) Schematic plot of the quasi-1D Josephson junction nanowire proximity-coupled to an $s$-wave superconductor. MBSs are shown with blue and red curves. (b) The lowest energy subbands of particle states in the Rashba nanowire. Spinful subbands with $(i_y,i_z)$ = (1,1) and (2,1) are shown. (c) The energy spectrum of Majonara and continuum modes of the quasi-1D junction in deep topological region. The blue, red, and black lines denote isolated MZMs, coupled MZMs, and bulk states, respectively. (d) Interplay between 2$\pi$-periodic and 4$\pi$-periodic currents. The blue curve represents current caused by occupied MBS for ground state. The discontinuity in the total current $I_{\mathrm{tot}}$ arises from an abrupt parity switch at the crossing point of the $4\pi$-periodic current $I_{4\pi}$.
• Figure 2: Relatively high and stable efficiency $\eta$ of the system populating 3 spinful subbands in the region of strong $h_x$ under various parameters. (a) $\eta$ vs $h_x$ for typical $\alpha_x$'s when 1 subband (calculated with $N_y=1$, ideal 1D model) or 3 subbands (evaluated with $N_y=2$) are occupied. (b) $\eta$ vs $h_x$ for realistic $L_y$'s. (c) $\eta$ vs $h_y$ for different $h_x$'s. (d) $\eta$ vs $\mu_{0}$ when other parameters are fixed. "Tri", "Topo", "Gapl" and "Vac" stand for "Trivial", "Topological", "Gapless" and "Vacuum", respectively. Parameters: $\alpha_x$ is set to be 30 in panel (b)-(c), and $h_y=0.8$ in panel (a)-(c). In panel (d), $\alpha_x=10,\,h_x=5,\, h_y=0.7$.
• Figure 3: High diode efficiency plateau by spin-parity subband exchanges mechanism. (a) Energy bands before, during, and after the spin-parity band exchange in the 2-orbit ($N_y=2$) model with 3 occupied subbands. Colored bands denote different spin-parity subbands, and colored arrows mark the Fermi point shifts induced by the inversion-symmetry-breaking field $h_y$. (b) Diode efficiency $\eta$ as a function of $h_x$, where the background colors correspond to the band structures shown in (a). (c) Energy bands showing the spin-parity band exchange in the three-orbital ($N_y=3$) model with five occupied subbands. (d) $\eta$ versus $h_x$, with color segments matching the band structures in (c). Parameters: $\alpha_x=10,\, h_y=0.8$.
• Figure 4: Underlying mechanism of high diode efficiency plateau after the spin-parity subband exchange. (a) Dependence of Fermi momenta $(k_\textrm{F})_{i_y}^{\pm}a_x$ on field strength $h_x$ for $N_y=2$ with three occupied subbands and the same parameters as Fig. \ref{['Fig3']}(a). (b) Fermi momentum shifts $\Delta k_\textrm{F}=k_\textrm{F}(h_y)-k_\textrm{F}(h_y=0)$. The yellow line denotes a dimensionless ratio $\xi$ that quantifies the competition between left- and right-shifted Fermi points. Parameters: $\alpha_x=10$, $h_y=0.8$.
• Figure S1: The tight binding model for the multiband nanowire. Here $N_y$ denotes the number of orbital channels included in the system. Each orbital is treated as a chain along the $x$-direction. The coordinate origin in the $x$-direction is defined at the interface between the left lead and the normal region.