Dynamical vortex transitions in a gate-tunable Josephson junction array

TL;DR

This study addresses how current-driven dynamical vortex transitions depend on magnetic frustration $f$ in a gate-tunable 2D JJA built from epitaxial Al/InAs. Using a square array of $1\,\mu$m islands with a top gate tuning $E_J$ and the vortex-pinning energy $E_B$, the authors map the transition by measuring differential resistance and its scaling against $I_{\rm dc}$ and $f$. Key findings include a split transition at $f=0$ in the superconducting phase, an unsplit transition in the anomalous metal, symmetry around $f=1/2$, and an even-odd skew pattern around integer $f$, with nonuniversal scaling exponents. The results challenge simple Mott-transition universality for vortex melting and highlight the role of lattice geometry and pinning strength, connecting the physics to Bose-Hubbard-type descriptions in gate-tunable superconducting-semiconductor architectures.

Abstract

We explore vortex dynamics in a two-dimensional Josephson junction array of micron-size superconducting islands fabricated from an epitaxial Al/InAs superconductor-semiconductor heterostructure, with a global top gate controlling Josephson coupling and vortex pinning strength. With applied dc current, minima of differential resistance undergo a transition, becoming local maxima at integer and half-integer flux quanta per plaquette, $f$. The zero-field transition from the superconducting phase is split, but unsplit for the anomalous metal phase, suggesting that pinned vortices are absent or sparse in the superconducting phase, and abundant but frozen in the anomalous metal. The onset of the transition is symmetric around $f=1/2$ but skewed around $f=1$, consistent with a picture of dilute vortices/antivortices on top of a checkerboard ($f = 1/2$) or uniform array of vortices ($f = 1$). Transitions show good scaling but with exponents that differ from Mott values obtained earlier. Besides the skewing at $f=1$, transitions show an overall even-odd pattern of skewing around integer $f$ values, which we attribute to vortex commensuration in the square array leading to symmetries around half-integer $f$.

Figures (5)

• Figure 1: Hybrid array and frustration-dependent dynamical vortex transitions. a,b) Schematic of device with $W=100$ by $L=400$ epitaxial $a = 1\, \mu$m Al squares (gray), separated by $b=350$ nm strips (blue) of exposed InAs heterostructure, with ac + dc current bias, $I$, and voltage $V$ measured using side probes. False-color micrograph taken before top gate was deposited. Gate voltage, $V_g$, controls carrier density in InAs strips between Al squares Boettcher2018. c) Sheet resistance, $R_s \equiv (W/L) V/I$, as a function of dc current, $I_{\rm dc}$, and perpendicular magnetic field, $B_\perp$, shows $R_{s}=0$ for small $I_{\rm dc}$ with enhanced critical current, $I_{0}$ at $f=$ 0, 1/4, 1/3, 1/2, 2/3, and 1. d) Line cuts of c shows dips in $R_s$ at $f=$ 0, 1/2, and 1, going to $R_{s} \sim 0$ for low $I_{\rm dc}$. e-f) Evolution of dips in differential resistance, $dV/dI_{s} \equiv (W/L)\ dV_{ac}/dI_{\rm ac}$, as a function of $B_{\perp}$ into a split peak at $f=0$, a symmetric peak at $f=1/2$, and an asymmetric peak at $f=1$. Each case is discussed in the text.
• Figure 2: Zero-field dynamical transition from the anomalous metal phase. a) Sheet resistance, $R_{s}$, as a function of perpendicular magnetic field, $B_\perp$ over a range of dc currents, $I_{\rm dc}$. For all dc currents, zero field remains a resistance minimum, similar to the superconducting regime, Fig. \ref{['fig1']}(d) b) Dip-to-peak transition at $f=0$ over the same range of dc currents. This behavior contrasts the superconducting regime in Fig. \ref{['fig1']}(f), which shows a split peak at $B_\perp = 0$. The dip-to-peak transition suggests that vortices and antivortices are absent at $f=0$ in the superconducting phase but present in the anomalous metal phase.
• Figure 3: Dynamical transitions, scaling, and critical exponents. a-b) Differential sheet resistance, $dV/dI_s$, shows a dip-to-peak transition is a function of dc current, $I_{\rm dc}$, at commensurate frustration. ($f=1/2$) and full ($f=1$). Insets: the transitions on each side, denoted as the left and right branches of $f=1/2$ and $f=1$, are represented as superconductor-insulator transitions: down-bending curves are transitions to the pinned vortex state, while upward-bending curves are transitions to a state of vortex flow. The horizontal field-independent curves separating each state are marked as separatrices used in the scaling analysis (Left: black solid line. Right: black dotted line). Scaling plots of $f=1/2$ (c-d) and $f=1$ (e-f), showing that left and right branches yield different scaling exponents, i.e. there is an asymmetry around each critical frustration field. Exponents extracted for $f=1/2$ are $\epsilon =2.1$ (left) and 1.2 (right), while at $f=1$ we extract $\epsilon = 1.5$ (left) and 2.5 (right).
• Figure 4: Even, odd and zero flux states. a) Differential sheet resistance curves for different values of dc current as a function of perpendicular magnetic field, $B_\perp$, at gate voltage $V_g=-2.8$ V, showing the evolution of vortex states for half-integer frustration $f=1/2$ and integers $f=1,2,3$ and 4. Odd minima (black dots) move down in field with increasing dc current, while even minima (green dots) move up in field. Minima at $f=1/2$ is roughly insenstive to dc current, consistent with the overall symmetry in $f$ of the $f=1/2$ transition. b) Differential sheet resistance (color) as a function of $B_\perp$ and $I_{\rm dc}$ shows commensurate features at factional and integer frustration, $f$. Bright features at the tips of the zero-resistance spikes are the dip-to-peak signature of the dynamical transition. Note the alternating, even-odd asymmetric bright features at integer $f$ values, the symmetric bright feature at $f=\pm 1/2$, and the vanishing differential sheet resistance remaining at large $I_{\rm dc}$ at $f=0$.
• Figure S1: Extracting scaling exponents. a-d) Log-log plots of the slope of the differential resistance, with the separatrix subtracted, constructed to extract of scaling exponents, $\varepsilon$, separately for left and right branches around $f=1/2$ and $f=1$. Means of logs are calculated for each value of $b$ (solid black curve) then means fit to a linear function (dashed green line).