Field-free Josephson diode and tunable $φ_0$-junction in chiral kagome antiferromagnets

TL;DR

This work identifies symmetry-breaking criteria for field-free Josephson diodes and tunable φ0-junctions in junctions formed by s-wave superconductors and kagome chiral antiferromagnets. By combining a microscopic kagome tight-binding model with symmetry analysis, it shows that breaking inversion, time-reversal, and the combined mirror–time-reversal symmetry TMz is essential for nonreciprocal transport, and demonstrates control over diode effects and φ0 shifts via spin–orbit coupling or Zeeman fields. Two experimentally feasible setups are proposed: (i) an SC/cAFM/SC junction with SOC yielding a field-free diode and tunable φ0, and (ii) an SC/cAFM/cAFM′/SC stack where relative cAFM orientation plus out-of-plane Zeeman field produces sizable diode response and tunable φ0. These results connect TMz-symmetry breaking to nonreciprocal superconductivity in kagome cAFMs, suggesting these materials as versatile platforms for symmetry-engineered Josephson diodes and tunable φ0-junctions with potential applications in superconducting spintronics and quantum information.

Abstract

The recent realization of superconducting proximity effect in chiral antiferromagnets (cAFMs) opens a new route to nonreciprocal superconducting transport of fundamental interest and practical importance. Using microscopic modeling and symmetry analysis, we show that Josephson junctions formed by conventional $s$-wave superconductors (SCs) and cAFMs on the kagome lattice exhibit Josephson diode effects and anomalous phase shifts ($φ_0$-junction state) when space inversion $\mathcal{I}$, time-reversal $\mathcal{T}$, and combined mirror-time-reversal $\mathcal{TM}_z$ symmetries are simultaneously broken. We propose two setups to realize these phenomena and achieve high diode efficiency. (i) An SC/cAFM/SC junction with spin-orbit coupling, which enables a field-free diode effect with a robust tunable $φ_0$-junction state. (ii) An SC/cAFM/cAFM$^\prime$/SC junction, where two cAFM layers with different in-plane order orientations, under an out-of-plane Zeeman exchange field, produces significant diode effect and anomalous phase shifts. These results establish a direct link between $\mathcal{TM}_z$ symmetry breaking and nonreciprocal superconductivity, suggesting cAFMs as versatile platforms for symmetry-engineered Josephson diodes and tunable $φ_0$-junctions.

Figures (5)

• Figure 1: Schematic of two Josephson setups based on cAFM on the kagome lattice. (a) The SC/cAFM/SC junction with SOC: the site arrows show the local magnetic moments, and the bond arrows mark the coplanar unit vectors $\bm{n}_{\mu\nu}$ associated with SOC in the cAFM. (b) The SC/cAFM/cAFM$'$/SC junction with two cAFM layers in middle: the two noncollinear orders differ by a relative angle $\theta^r$ and an out-of-plane Zeeman field $B_z$ is applied there.
• Figure 2: Josephson diode effect in the SC/cAFM/SC junction with SOC. (a) Current-phase relations for cAFM strength $J=t$, junction length is $N_L=40$ and different SOC strengths $t_{so}=0$, $0.1t$ and $0.2t$. (b) Diode efficiency $\eta$ as a function of $J$ and $t_{so}$ for $N_L=40$. (c) $\eta$ as a function of $J$ for $t_{so}=0.1t$ and $N_L=40$, 60 and $80$. (d) $\eta$ as a function of $t_{so}$ for $J=t$, $N_L=40$, $60$ and $80$. Other parameters are $\mu_{\text{AFM}}=0.2t$, $\mu_S=0.2t$, $\Delta=0.02t$ and temperature $k_BT = 0.02\Delta$.
• Figure 3: $\phi_0$-junction state in the SC/cAFM/SC junction with SOC. (a) Phase position $\phi_F^*$ of the lowest free energy $F_0\equiv\min_\phi[{F(\phi)}]$ as a function of SOC strength $t_{so}$ for $J=t$, $\mu_S=0.2t$ (blue) and $\mu_S=0.6t$ (orange). Inset: free energy $F$ measured relative to $F_0$ as a function of the superconducting phase difference $\phi$ for $J=t$ and $t_{so}=0$, $0.1t$, $0.2t$. (b) $\phi_F^*$ of $F_0$ as a function of $J$ for $t_{so}=0.1t$ and $\mu_S=0.2t$. Phase diagram of (c) the phase position $\phi_F^*$ and (d) the phase position $\phi_I^{*}$ as functions of $J$ and $t_{so}$ for $\mu_S=0.2t$. Other parameters are $\mu_{\text{AFM}}=0.2t$, $\Delta=0.02t$, $N_L=40$, and $k_BT = 0.02\Delta$.
• Figure 4: Josephson diode effect in the SC/cAFM/cAFM$^\prime$/SC junction. (a) Current-phase relations for $J=0.4t$, under an out-of-plane Zeeman field $B_z=0.1t$ and for relative cAFM angles $\theta^r=0,\;0.25\pi,\;0.5\pi$ and $0.75\pi$. The corresponding diode efficiencies are $\eta=0$, $0.018$, $0.067$ and $0.173$, respectively. (b) Same as panel (a) but for an in-plane Zeeman field applied along the $x$-direction ($B_x=0.1t$, solid line) and the $y$-direction ($B_y=0.1t$, dashed line). No diode effect is observed for either in-plane field. (c) Diode efficiency $\eta$ as a function of the relative cAFM angle $\theta^r$ for $J=0.4t$ with Zeeman fields ${\bf B}= (0.1t,0,0)$, $(0,0.1t,0)$, and $(0,0,0.1t)$ in the $x$-, $y$-, and $z$-directions, respectively. (d) $\eta$ as a function of $J$ for $\theta^r = 0.5\pi$, with Zeeman fields ${\bf B}= (0.1t,0,0)$, $(0,0.1t,0)$, and $(0,0,0.1t)$ applied along the $x$-, $y$-, and $z$-directions, respectively. Other parameters are $\mu_{\text{AFM}}=0.2t$, $\mu_S=0.2t$, $\Delta=0.02t$, $N_{L_1}=N_{L_2}=20$, and $k_B T= 0.02\Delta$.
• Figure 5: $\phi_0$-junction state in the SC/cAFM/cAFM$^\prime$/SC junction. (a) Phase position $\phi_F^*$ of lowest free energy $F_0$ as a function of the relative angle $\theta^r$ between the two cAFM orders for $J=0.4t$ with ($B_z=0.3t$) and without ($B_z=0$) Zeeman field along $z$-direction. (b) Phase position $\phi_I^*$ of the forward critical current as a function of $\theta^r$ for $J=0.4t$ with ($B_z=0.3t$) and without ($B_z=0$) Zeeman field along $z$-direction. Phase diagram of (c) $\phi_F^*$ and (d) $\phi_I^*$ as functions of $J$ and $\theta^r$ for $B_z=0.3$. Other parameters are $\mu_{\text{AFM}}=0.2t$, $\mu_S=2t$, $\Delta=0.02t$, $N_{L_1}=N_{L_2}=20$, and $k_B T = 0.02\Delta$.