Probing Pair Density Waves with Twisted Josephson Junctions

Abstract

We show that twisted interfaces between superconductors can serve as a phase-sensitive platform for the detection and characterization of pair density waves (PDW). In the presence of an in-plane magnetic field, the critical Josephson current of a twisted PDW interface is maximal at a finite field value, determined by the twist angle and the PDW period -- an explicit signature of the PDW. The results are robust to variations in junction geometry and can be adapted to certain cases with strong disorder or fluctuations. Their temperature dependence allows to distinguish pure PDW from byproducts of coexistence of superconductivity and charge- or spin- density waves.

Figures (5)

• Figure 1: (a) Schematic of the proposed setup. We consider a Josephson junction formed at the interface of two identical bulk twisted pair density wave superconductors (gray/orange stripes) in the presence of an in-plane magnetic field $\vec{H}$. At the interface (b), the overlapping twisted PDWs form a moiré pattern with period $\lambda_m$ creating a quasiperiodic phase mismatch between the order parameters. (c) Normalized critical current $\overline{I}^{(1)}_c$, Eq. \ref{['rect_current']} of as a function of total magnetic flux $\Phi$ through the junction for field oriented as in (b). At a nonzero twist angle $\theta$, $\overline{I}^{(1)}_c$ shows a maximum at a finite $\Phi=\Phi_{max} \propto \lambda_m^{-1}$\ref{['eq:phimax']}, that provides a direct evidence of PDW. The junction width $L/\lambda_{\text{PDW}}\approx80$ was used in this plot.
• Figure 2: Density plot of the critical Josephson current, Eq. \ref{['field_orientation']}, for varied magnetic flux and field orientation. Dependence shown in Fig. \ref{['fig:cartoon']} (c) corresponds to a cut at $\Phi_y=0$. We take $L/\lambda_m=8.71$.
• Figure 3: Critical Josephson current of a twist PDW junction in presence of both first and second harmonic (Eq.\ref{['first_harmonic']} and Eq. \ref{['second_harm']}) for varied magnetic flux at two different temperatures. The critical currents are normalized by its value at $\Phi=0$ and $\theta=0^\circ$. To highlight the effects of temperature dependence $T_c$, we take dominant second harmonic $J_{c1}/J_{c2} (T=0)=1/6$ (possible in presence of disorder, see text) and $L/\lambda_m= 36.07$.
• Figure 4: The ratio of the finite field peak to the zero field peak close to $T_c$ for intrinsic PDW (red, see Fig. \ref{['fig:1st+2nd_harm']}) and ordinary superconductivity coexisting with CDW (blue, Eq. \ref{['cdw_op']}). Two scenarios show qualitatively different temperature dependence. We take $L/\lambda_m = 55.27$ , $J_{c1}/J_{c2}=1$ at $T=0$, $|\rho_k|^2=\beta=1$, and the field is along y as in Fig. \ref{['fig:cartoon']} (b).
• Figure S1: Critical Josephson current for a circular junction. We take $L/\lambda_{PDW}\approx 32$.