Magnetic field-bias current interplay in HgTe-based three-terminal Josephson junctions

TL;DR

This work investigates HgTe/Nb three-terminal Josephson junctions in T- and X-shaped geometries to map how bias currents and magnetic flux control the collective Josephson response. Using CCCs and a multiterminal RSJ model, the authors show that the effective critical current $I^{\text{comb}}_{c,13}$ is not simply additive, e.g. $I^{\text{comb}}_{c,13}(I_1,I_2=0)\approx I_{c,13}+\min\{I_{c,12},I_{c,23}\}$, and demonstrate a bias-driven crossover from SQUID-like to Fraunhofer-like interference. Magnetic flux deforms the CCCs in the $(I_1,I_2)$-plane, with $\\pi\frac{\Phi}{\Phi_0}$-dependent phase relations that yield symmetric or asymmetric patterns; these effects can boost superconducting diode efficiency up to $\eta\approx0.8$ in the low-bias regime. RSJ simulations reproduce the experimental patterns and diode behavior, establishing a predictive framework for designing phase-coherent multiterminal superconducting circuits with potential uses in metrology, magnetometry, and scalable quantum architectures.

Abstract

We investigate HgTe/Nb-based three-terminal Josephson junctions in T-shaped and X-shaped geometries and their critical current contours (CCCs). By decomposing the CCCs into the contributions from individual junctions, we uncover how bias current and magnetic field jointly determine the collective Josephson behavior. A perpendicular magnetic field induces a tunable crossover between SQUID-like and Fraunhofer-like interference patterns, controlled by the applied bias. Moreover, magnetic flux produces pronounced deformations of the CCC, enabling symmetry control in the $(I_1,I_2)$ plane. Remarkably, we identify a regime of strongly enhanced Josephson diode efficiency, reaching values up to $η\approx 0.8$ at low bias and magnetic field. The experimental results are quantitatively reproduced by resistively shunted junction (RSJ) simulations, which capture the coupled dynamics of current and flux in these multi-terminal superconducting systems.

Figures (12)

• Figure 1: Overview of the T-device. (a): Schematic of the measured T-device. The superconducting Nb shown in yellow and HgTe in blue. Red numbers indicate the terminals and junctions, along with the corresponding voltages. The current sources are shown in black. Panels (b)-(d) show the differential resistances $dU_{13}/dI_{1}$, $dU_{12}/dI_{1}$ and $dU_{23}/dI_{1}$ of the corresponding junctions JJ$_{13}$, JJ$_{12}$ and JJ$_{23}$ as a function of the bias currents $I_1$ and $I_2$. The currents $I^{\text{comb}}_\text{c,13}(I_1,I_2=0)$ and $I^{\text{comb}}_\text{c,13}(I_1=0,I_2)$ (see section D in the main text) are highlighted in orange. The vertical red dashed lines in panel (b) indicate line cuts at $I_2=0,\, 1.0\,\mu \text{A},$ and $2\,\mu$A studied below as a function of an external magnetic field.
• Figure 2: Influence of a bias current and magnetic field on the T-MTJJ. (a)-(c): Differential resistance $dU_{13}/dI_1$ as a function of $I_1$ and in-plane magnetic field $B$ for $I_2=0,~1,~1.9\,\mu$A, respectively. (d)-(f) Differential resistance $dU_{13}/dI_1$ as a function of $I_1$ and in-plane magnetic field $B$, with the sample slightly rotated giving rise an out-of plane component, for $I_2=0,0.4,-0.4\,\mu$A.
• Figure 3: $dU_{13}/dI_1$ vs $I_1$ and $I_2$ for different magnetic fields in the X-junction: Experimental and theoretical results. (a): False-colored SEM schematic of the four terminal JJ. Yellow indicates the Nb leads, with two contacts shorted. (b): Differential resistance $dU_{13}/dI_1$ as a function of the magnetic field $B$, showing in a SQUID-like pattern. (c): $dU_{13}/dI_1$ as a function of $I_1$ and $I_2$ for four different magnetic fields $B_0,B_1,B_2,B_3$, indicated by colored arrows in panel (b). (d): Corresponding theoretical results, from the RSJ model, using $I_\text{c,13}=0.55\,\mu$A, $I_\text{c,12}=0.27\,\mu$A, $I_\text{c,23}=0.2\,\mu$A and $R_{13}=25.0\,\Omega$, $R_{12}=53.7\,\Omega$, $R_{23}=40.9\,\Omega$.
• Figure 4: Superconducting diode effect in the X-junction--- (a)-(b): Differential resistance $dR_{13}/dI_1$ as a function of the bias current $I_1$, for $B=0$ (a) and $B=2.3\,\text{mT}$ (b). Blue curves correspond to $I_2=0$ and red curves to $I_2\neq 0$. (c): Diode efficiency $\eta$ extracted from the experimental results for the three-terminal Josephson junction with X-shaped geometry shown in Fig. \ref{['fig3']}. The efficiency is plotted as a function of the bias current $I_2$ and magnetic field $B$.
• Figure 5: Results of permuting the current contacts. (a) Shows the same plot as in Figure \ref{['fig1']} (b), with all contacts connected as introduced before. In (b), the current contacts are permutated, so that $I_1$ is applied at contact 2 and $I_2$ at contact 3. This has an impact on the CCC and the junction in the zero resistance state. For (c) the current contacts are shifted once more from $2\rightarrow3, 3\rightarrow1$.