Geometric dependence of critical current magnitude and nonreciprocity in planar Josephson junctions

TL;DR

The paper investigates how the critical current and superconducting diode effect in symmetric planar Josephson junctions with semiconducting weak links depend on geometry and gate tuning under an in-plane magnetic field. By varying the longitudinal contact width $W_\text{sc}$ and gate voltage $V_g$, they show that $I_c$ approaches a width-independent limit exponentially with a characteristic coherence length $\xi \approx 0.586\,\mu\text{m}$, linking geometry to Andreev bound state coherence. The diode efficiency $\eta$ exhibits width-dependent maxima at finite fields, with the field of maximum nonreciprocity $B_\eta$ saturating for large $W_\text{sc}$, and the smaller-field extremum $B_*$ increasing with gate voltage, suggesting a coexistence of orbital effects and spin--orbit/Zeeman-induced finite momentum pairing. Overall, the study highlights geometry as a tunable knob for probing SDE mechanisms and informs design strategies to optimize diode functionality in planar JJs.

Abstract

Planar Josephson junctions in a magnetic field exhibit the superconducting diode effect, by which the critical current magnitude depends on the polarity of the transport current. A number of different mechanisms for the effect have been proposed.Here, we study symmetric, T-shaped planar Josephson junctions with semiconducting weak links in an in-plane magnetic field perpendicular to an applied current bias. In particular, we vary the longitudinal width (i.e.\ parallel to the current) of the superconducting contacts and the voltage of an electrostatic gate. We observe an increase in both critical current and diode efficiency with increasing contact width and relate the critical current behavior to the induced coherence length of the Andreev bound states that mediate the supercurrent flow through the junction. We further observe a linear trend, with respect to inverse contact width, of the field at which the diode efficiency is maximized, which saturates as the contact width becomes large compared to the coherence length. The smaller field at which the critical current is maximized additionally exhibits a strong gate dependence. We interpret these observations in the context of multiple underlying mechanisms, including spin--orbit coupling and orbital effects.

Figures (4)

• Figure 1: Symmetric T-shaped planar Josephson junctions and diode effect mechanisms.(a) Scanning electron micrograph of a representative planar Josephson junction co-fabricated on the same chip as the devices presented here. The superconductor (blue) and semiconductor (green) are falsely colored. The gate (yellow) is shown schematically. All devices are 4µm wide with 80nm separating the superconducting contacts. Each device has a different superconducting contact width $W_\text{sc}$. A current bias $I$ and gate voltage $V_\text{g}$ are applied. The in-plane magnetic field $B_\parallel$ is perpendicular to the current. The dashed red line indicates the cross section shown schematically in (b). (b) Schematic of the device cross section indicated by the dashed red line in (a). The magnitude of the Andreev bound state wave function $\abs{\psi}$ decays with characteristic length $\xi$ into the superconductor. A magnetic flux $\Phi$ threads the area $W_\text{sc}d$ between the superconducting contacts (blue) and the proximitized 2DEG (dark green). A Meissner current flows in the superconducting contacts of thickness $d_\text{sc}$. In the 2DEG, the Rashba spin--orbit split Fermi surface (grey) is Zeeman-shifted by the in-plane magnetic field, yielding Cooper pairs of electrons with wavevectors $\bf{q}\pm\bf{k}$ (black). (The inner Fermi surface is not shown.)
• Figure 2: Critical current and coherence length.(a) Critical current $I_{\text{c}\pm}$ versus in-plane magnetic field $B_\parallel$ perpendicular to the current, for five devices with different contact widths $W_\text{sc}$, at gate voltage $V_\text{g}=0$ (see Section S.IV for similar field traces at positive and negative gate voltages). Markers identify the extrema plotted in (b,c). (b) Extrema of $I_{\text{c}\pm}$ versus inverse superconducting contact width $W_\text{sc}^{-1}$, fit to \ref{['eq:ic-vs-wsc']}. The markers correspond to the legend in (a). (c) In-plane magnetic field $B_*=\mathop{\mathrm{arg\,max}}\limits_{B_\parallel}I_{\text{c}+}=-\mathop{\mathrm{arg\,min}}\limits_{B_\parallel}I_{\text{c}-}$ at which $I_{\text{c}\pm}$ are extremized. Black dots correspond to the $V_\text{g}=0$ extrema marked in (a); blue (red) upward-pointing (downward-pointing) triangles correspond to the extrema at positive (negative) gate voltage; see Section S.IV.
• Figure 3: Gate dependence and spin--orbit coupling. In-plane magnetic field $B_*=\mathop{\mathrm{arg\,max}}\limits_{B_\parallel}I_{\text{c}+}=-\mathop{\mathrm{arg\,min}}\limits_{B_\parallel}I_{\text{c}-}$ at which $I_{\text{c}\pm}$ is extremized, for five devices with different $W_\text{sc}$. This is the same data as in \ref{['fig:critical-current']}(c) plotted here as a function of gate voltage $V_\text{g}$. The right-hand axis indicates the directions of increasing Rashba spin--orbit coupling strength $\alpha$ and junction transparency $\tau$ according to \ref{['eq:bstar']}.
• Figure 4: Diode efficiency and orbital effect.(a) Diode efficiency $\eta$, as defined in \ref{['eq:diode-efficiency']}, determined from the data in \ref{['fig:critical-current']}(a) (see Section S.IV for similar field traces at positive and negative gate voltages). Markers identify the extrema plotted in (b,c). (b) Extrema $\max\eta=-\min\eta$ versus inverse superconducting contact width $W_\text{sc}^{-1}$. The markers correspond to the legend in (a). (c) In-plane magnetic field $B_\eta=\mathop{\mathrm{arg\,max}}\limits_{B_\parallel}\eta=-\mathop{\mathrm{arg\,min}}\limits_{B_\parallel}\eta$ at which $\eta$ is extremized. Black dots correspond to the extrema marked in (a); blue (red) upward-pointing (downward-pointing) triangles correspond to the extrema at positive (negative) gate voltage. The solid black line is a fit to \ref{['eq:flux']} of the $V_\text{g}=0$ series, excluding the point at $W_\text{sc}^{-1}=0$.