Topological superconductivity and superconducting diode effect mediated via unconventional magnet and Ising spin-orbit coupling

TL;DR

The paper proposes a 1D tight-binding framework that combines unconventional magnetic order with Rashba and Ising spin-orbit coupling to realize topological insulating and superconducting phases, plus a field-free superconducting diode effect. A self-consistent mean-field analysis with an onsite attractive interaction yields topological superconductivity in both the BCS ($q=0$) and FFLO ($q\neq 0$) channels, with a winding number $\mathcal{N}_x=2$ and four Majorana end modes in the BCS case and persistent topological order in the FFLO case when Ising SOC is present. The FFLO state, stabilized by Ising SOC and unconventional magnetism, exhibits intrinsic nonreciprocal superconductivity characterized by a diode efficiency $\eta$, achieving values up to around $65\%$ in optimized parameter regimes. Overall, the work provides a unified, field-free platform for engineering topological superconductivity and large-strength superconducting diodes in 1D by tuning $J_A$, $J_I$, and SOC strengths, with potential implications for Majorana devices and low-dissipation superconducting electronics.

Abstract

We propose a theoretical framework in which a one-dimensional (1D) tight-binding model incorporating unconventional magnetic order together with Rashba and Ising spin-orbit couplings are considered to realize two key phenomena in condensed matter systems: topological superconductivity and the superconducting diode effect (SDE). We first elucidate the underlying band topology of the normal-state Hamiltonian and subsequently introduce an on-site attractive Hubbard interaction. Performing a a self-consistent mean-field analysis, we establish superconducting order parameters in both the conventional Bardeen-Cooper-Schrieffer (BCS) and finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing channels. Intriguingly, both pairing states can support topological superconductivity, characterized by a nontrivial winding number, and lead to the emergence of four zero-energy Majorana modes localized at the ends of the 1D chain. The FFLO state further gives rise to an intrinsic field-free SDE, manifested as a nonreciprocal supercurrent and quantified by the diode efficiency $η$. Notably, our model yields a large diode efficiency $η\sim 65\%$, highlighting its potential for realising topological superconductivity and highly efficient superconducting devices.

Figures (6)

• Figure 1: Band topology of the normal state Hamiltonian: (a) Bulk spectrum $E_k$ as a function of $k$ is depicted with $(m_0,\lambda_R,J_I)=(0.2t,0.5t,0)$, $J_A=0$ (orange) and $J_A=0.6t$ (blue). (b) Winding number $\mathcal{N}_x$ is shown in the ($m_0-J_A$) plane with $(\lambda_R,J_I)=(0.5t,0)$. (c) Bulk spectrum $E_k$ with respect to $k$ is shown with $(m_0,\lambda_R,J_A)=(0.5t,0.5t,0.4t)$, $J_I=0$ (orange) and $J_I=0.25t$ (blue). (d) Winding number $\mathcal{N}_x$ is displayed in the $(J_I-J_A)$ plane choosing $(m_0,\lambda_R)=(0.5t,0.5t)$.
• Figure 2: Topological superconductivity in the $s$-wave channel: (a) Self-consistently obtained superconducting pairing amplitude, $\Delta_{0}$ (left axis) and winding number $\mathcal{N}_x$ (right axis) are depicted as a function of $J_A/t$. (b) Real space energy eigenvalues $E_{n}$ (left axis) of $\mathcal{H}_{\rm BdG}$ (Eq. \ref{['Eq.H_BdG']}) is shown with respect to $J_A/t$ with the self-consistently obtained $\Delta_{0}$ values presented in panel (a). The same winding number $\mathcal{N}_x$ (right axis) is shown to support the topological regime indicated in $E_{n}$. Other model parameters are chosen as $(m_0,\lambda_R,J_I,\mu)=(0.5t,0.5t,0,0)$.
• Figure 3: Topological superconductivity in the FFLO channel: In panels (a) and (b), we showcase self-consistently obtained true FFLO order parameters $\Delta_{0}$ and $q_0$, respectively, as a function of $J_A/t$ for various values of $J_I/t$. (c) Winding number $\mathcal{N}_x$ is depicted with respect to $J_A/t$ for the same set of $J_I/t$ values mentioned in panel (a). (d) Variation of $\Delta_{0}$ in the FFLO channel is shown in the $J_A/t-J_I/t$ plane, and the region covered by the yellow dashed line highlight the TSC phase in $J_A/t-J_I/t$ plane. Other model paramaters are chosen as $(m_0,\lambda_R,\mu)=(0.5t,0.5t,0)$.
• Figure 4: Non-reciprocal supercurrent and SDE efficiency: Panel (a) depicts the variation of $q_0$ in the $J_I/t-J_A/t$ plane. The TSC phase in the FFLO pairing state is highlighted by the yellow dashed line. (b) The nonreciprocal nature of the supercurrent $J(q)$, normalized by $J_0\equiv J_c^+(J_I=0)$ is shown as a function of $q$ in the presence of Ising SOC, $J_I$. Panels (c) and (d) highlight the diode efficiency $\eta$ in the $J_I/t-J_A/t$ plane with $(m_0,\lambda_R,\mu)=(0.5t,0.5t,0)$ in panel (c) and $(m_0,\lambda_R,\mu)=(0.15t,0.15t,0.7t)$ in panel (d) respectively.
• Figure 5: Panel (a): Variation of winding number, $\mathcal{N}_x$, is depicted in the $\Delta/t-J_A/t$ plane. The variation of true superconducting order $\Delta_0$, obtained self-consistently, is hightlighted by yellow line, while the green dashed line represents the same without (w/o) self-consistent solution. Panel (b): Behavior of bulk gap, $G$ of the BdG Hamiltonian is illustrated, and the dependence of $\Delta_0$ for both self-consistent and w/o self-consistent cases are also highlighted. We choose the other model parameters as $m_0=\lambda_{R}=0.5t, \mu=J_I=0,U=1.5t,t=1$.