Enhancement of Josephson Supercurrent in a $π$-Junction state by Chiral Antiferromagnetism

Abstract

Magnetic order typically disrupts superconductivity, reducing the supercurrent. Here, we show that chiral antiferromagnetism, with non-relativistic spin-split bands and distinctive valley-locked spin texture, can instead significantly enhance Josephson supercurrents. This enhancement stems from the emergence of dominant equal-spin triplet pairing and strong fluctuations of singlet pairing in momentum space, both induced by chiral antiferromagnetism. We demonstrate these results in Josephson junctions composed of chiral antiferromagnetic metals and conventional superconductors on kagome lattices. Furthermore, we show that the enhanced Josephson supercurrent is stabilized in a $π$-junction state. These phenomena persist across a broad energy range and remain stable for different temperatures and junction lengths. Our results unveil a previously unexplored mechanism for enhancing supercurrent by strong magnetic order and provide crucial insights into the large Josephson currents observed in Mn$_3$Ge.

Figures (14)

• Figure 1: (a) Left: cAFM on kagome lattices, where the arrows indicate the local magnetic moments. Right: Fermi surfaces at valleys $K$ and $K'$ with valley-dependent spin textures for $|\mu_{\text{AFM}}|<|J|$. (b) Schematic of the Josephson junction, where the yellow regions represent the superconducting leads, while the cyan region is the cAFM with $N_L$ layers (in units of $\sqrt{3}a$). (c) Net spin-singlet $|\mathcal{F}_s|$ (blue) and spin-triplet $|\mathcal{F}_{\uparrow\uparrow(\downarrow\downarrow)}|$ (purple) pairing amplitudes (in units of $\mathcal{F}_{s0}$) at the junction center ($y=N_L/2$) as functions of $J$. Here, $\mathcal{F}_{s0}$ is the singlet pairing amplitude in the bulk superconductor. For illustration, $\omega_0=0.1 k_B T_c$ is used. (d) $k_x$-resolved singlet and triplet pairing amplitudes, $i\tilde{f}_{\uparrow\uparrow}$ and $\tilde{f}_s$, at the junction center. (e) Maximum supercurrent $I_c$ (in units of $e\Delta/\hbar$) as a function of $J$ for temperature $T=0.02T_c$. Insets show the current-phase relations at $J=0$ (blue) and $0.4t$ (purple), respectively. (f) Phase position $\phi^*_{I}$ (purple, in units of $\pi$) for $I_c$ and $\phi^*_{F}$ (blue, in units of $\pi$) for the lowest free energy as functions of $J$. (c)-(f) are calculated with the self-consistently determined superconducting order parameter. Other parameters: $\mu_S=2t$, $\mu_{\text{AFM}}=0.2t$, $N_L=60$, and $U=0.65t$ which yields $\Delta=0.023t$ and $k_BT_c = 0.013t$.
• Figure 2: (a) Singlet $|\mathcal{F}_s|$ (blue) and equal-spin triplet $|\mathcal{F}_{\uparrow\uparrow(\downarrow\downarrow)}|$ (red) pairing amplitudes in the junction without cAFM order ($J=0$) for $\mu_{\text{AFM}}=0.2t$. (b) Same as (a) but in presence of cAFM ($J=0.4t$). (c) $|\mathcal{F}_s|$ at the junction center ($y=N_L/2$) as a function of $J$ and $\mu_{\text{AFM}}$. (d) $|\mathcal{F}_{\uparrow\uparrow(\downarrow\downarrow)}|$ at the junction center as a function of $J$ and $\mu_{\text{AFM}}$. (e, f) $k_x$ and sublattice-resolved singlet and triplet pairing amplitudes at the junction center for $J=0.4t$ and $\mu_{\text{AFM}}=0.2t$. Other parameters: $\Delta_0 = 0.02t$, $\omega_0=0.1\Delta_0$, $N_L=60$, and $\mu_S=2t$.
• Figure 3: (a) Maximum supercurrent $I_c$ (in units of $e\Delta/\hbar$) as a function of $J$ and $\mu_{\text{AFM}}$ for $N_L=60$. (b) $I_c$ as a function of $J$ and $N_L$ for $\mu_{\text{AFM}}=0.2t$. (c) Enhancement ratio $\eta=I_c/I_c(J=0)$ as a function of $J$ for $N_L=50$, $\mu_{\text{AFM}}=0.1t$ and increasing $T$ (i.e., $T=0.03T_c$, $0.1T_c$, $\cdots$, $0.9T_c$, and $0.95T_c$, where $T_c=0.57\Delta$). (d) $I_c$ as a function of $N_L$ for $\mu_{\text{AFM}}=0.2t$ and various $J$. $k_BT=0.02\Delta$ in (a,b,d), $\Delta=0.02t$ and $\mu_S=2t$ for all panels.
• Figure 4: (a) Free energy $\delta F(\phi)= F(\phi)-F(\phi=0)$, measured relative to the value at $\phi=0$, as a function of phase difference $\phi$ for various $J$. (b) CPR $I_s(\phi)$ for various $J$, corresponding to (a). (c) Phase position $\phi^*_I$ (in units of $\pi$) of $I_c$ as a function of $J$ and $\mu_{\text{AFM}}$. (d) $\phi^*_I$ as a function of $J$ and $N_L$ for $\mu_{\text{AFM}}=0.2t$. Other parameters are the same as Fig. \ref{['fig:PairingCorrelation']}.
• Figure 5: (a) Singlet $|\mathcal{F}_s|$ (blue) and equal-spin triplet $|\mathcal{F}_{\uparrow\uparrow}|=|\mathcal{F}_{\downarrow\downarrow}|$ (orange) pairing amplitudes in the junction without cAFM order ($J=0$). $\mathcal{F}_{s0}$ is the singlet pairing amplitude in the bulk of the superconductor. (b) Same as (a) but in the presence of cAFM ($J=0.4t$). The results are calculated using self-consistently determined superconducting order parameters. Parameters: $U=0.65t$ (yielding $\Delta=0.023t$ and $k_BT_c = 0.013t$), $T=0.1T_c$, $N_S=N_L=60$, and other parameters are the same Figs. 2(a)-(b) of the main text.