Quantum-geometric spin and charge Josephson diode effects

Abstract

We present a general mechanism for large charge and spin Josephson diode effects in strongly spin-polarized superconductor-ferromagnet hybrid structures with a noncoplanar spin texture, formulated in terms of quantum-geometric phases. We present necessary conditions for this effect to occur, and show numerical results for disordered materials, relevant for applications. We calculate Josephson diode efficiencies for both charge- and spin-diodes and show that a spin-diode efficiency of 100% can be reached. Finally, we present a SQUID device that can switch between nearly pure spin-up and spin-down equal-spin supercurrents across the ferromagnet by reversing the flux. These findings establish functionalities that are absent for coplanar spin textures.

Figures (4)

• Figure 1: (a) Superconducting hybrid structure consisting of a strongly spin-polarized metallic ferromagnet (sFM) coupled to singlet superconductors (SC) by thin ferromagnetic insulating layers (FI1/2). At the outer interfaces the system is connected to superconducting reservoirs each characterized by $\Delta_{1/2} e^{i\chi_{1/2}}$(Left: 1, Right: 2). (b) Relative orientation of the FI magnetic moments $m_{1/2}$ with respect to the sFM magnetization $M$, defining a quantum-geometric phase $\Delta \varphi$. (c) Fermi surface mismatch between SC and sFM, shown for the case $k_{F,\downarrow}^\mathrm{sFM} < k_F^{\mathrm{SC}} < k_{F,\uparrow}^\mathrm{sFM}$. (d) Sketch of phases acquired by the transmission of $\mu$${\uparrow\uparrow}$-pairs and $\nu$${\downarrow\downarrow}$-pairs.$^1$
• Figure 2: The functional dependence of (a) the charge current $I_\mathrm{ch}$ and (b) the spin current $I_\mathrm{sp}$ on the quantum-geometric phase difference $\Delta\varphi = \varphi_2 - \varphi_1$ and the superconducting phase difference $\Delta\chi = \chi_2 - \chi_1$ normalised to their overall maximum value reached. The thick grey lines denote zero current. In both panels the black solid and dashed lines show $\Delta\chi^+(\Delta\varphi)$ and $\Delta\chi^-(\Delta\varphi)$ for the positive and negative critical charge current at given $\Delta\varphi$, respectively.
• Figure 3: The functional dependence of (a) the charge diode efficiency $\eta_\mathrm{ch}$ (green) and (b) the spin diode efficiency $\eta_\mathrm{sp}$ (violet) on the quantum-geometric phase difference $\Delta\varphi$ for the currents shown in Fig. \ref{['fig:colormap_all_curr']}.
• Figure 4: (a) The spin-resolved currents in the metallic ferromagnet as functions of $\Delta\chi$ [see Fig. \ref{['fig:colormap_all_curr']}] for $\Delta\varphi = 0.31 \pi$. (b) The corresponding spin-polarization $\mathcal{P}(\Delta\chi)$ for the Josephson currents shown in (a). $\Phi$ denotes the flux through a SQUID geometry and the arrows denote the change of the current in response to a nonzero flux.