Voltage-tuned anomalous-metal to metal transition in hybrid Josephson junction arrays

Abstract

We report voltage-tuned phase transitions in arrays of hybrid semiconductor-superconductor islands arranged in a square lattice. A double-layer electrostatic gate geometry enables independent tuning of inter-island coupling and proximity-induced superconductivity. This design enables access to the superconductor-insulator, superconductor-metal, and metal-insulator transitions in a single device, revealing critical points and emergent intermediate phases. We find that the superconductor-insulator transition is interrupted by an anomalous metallic phase with saturating low-temperature resistivity. Across gate voltages, this regime extends over three orders of magnitude in resistivity and can be continuously tuned into the conventional metallic phase. The signature of the anomalous metallic phase is suppressed by magnetic frustration.

Figures (5)

• Figure 1: (a) Colorized scanning electron micrograph of a reference device, taken before depositing the global top gate. The square Al islands (gray) are patterned on top of the semiconducting heterostructure (green-gray) and are separated by a frame gate (yellow). (b) Schematic cross-section of the device illustrating dual gate geometry. The lower frame gate tunes the central part of the junctions, while the global top gate tunes the 2DEG surrounding the islands. (c) Optical micrograph of the measured Hall bar device showing measurement setup.
• Figure 2: (a) Map of resistivity, $\rho$, measured for the main hybrid array as a function of top-gate, $V_{\mathrm{TG}}$, and frame-gate, $V_{\mathrm{FG}}$, voltages, showing the superconducting, insulating, and metallic states. (b) Traces of $\rho$ as a function of $V_{\mathrm{FG}}$ for different temperatures, $T$, and fixed $V_{\mathrm{TG}}=-0.5$ V showing a crossing point around $h/4e^2$ indicating superconductor-insulator transition. (c) Similar to (b) but as a function of $V_{\mathrm{TG}}$ at fixed $V_{\mathrm{FG}}=-0.3$ V with a crossing point suggesting superconductor-metal transition.
• Figure 3: (a) Resistivity, $\rho$, as a function of temperature, $T$, measured for different frame-gate voltage, $V_{\mathrm{FG}}$, values ranging from $-1.060$ to $-1.225$ V, at fixed $V_{\mathrm{TG}}=0$. The dashed black lines are linear fits of $\ln(\rho)$ versus $\ln(T)$ up to $70$ mK. (b) Low-$T$ resistivity slope, $d \ln(\rho) / d \ln(T)$, taken from the fits in (a), plotted against the average resistivity, $\bar{\rho}$, in the same $T$ range. Error bars are the standard uncertainties of the fitting.
• Figure 4: (a) Average resistivity, $\bar{\rho}$, measured as a function of top-gate, $V_{\mathrm{TG}}$, and frame-gate, $V_{\mathrm{FG}}$, voltages, showing an enlargement of the region where the superconducting, insulating, and metallic states meet. The plot was constructed by averaging a set of $\rho$ maps over the temperature range from $T = 15$ to 55 mK, taken every $2.5$ mK. (b) Low-$T$$\rho$ slope, $d \ln(\rho)/d \ln(T)$, obtained by linear fitting of $\ln(\rho)$ versus $\ln(T)$ for the same data as in (a)
• Figure 5: (a) Resistivity, $\rho$, measured as a function of temperature, $T$ and magnetic frustration, $f$, shows peaks of the superconducting transition temperature around commensurate frustration values, mostly pronounced around $f=0$ and $1/2$. (b) Traces of $\rho$ as a function $T$, taken for three representative frustration values, $f=0$, irrational ($\approx 0.16$), and $f=1/2$, at fixed $V_{\mathrm{FG}} = -1.13$ V. The normal-state resistivity matches for all the traces, but nonzero $f$ show higher $\rho$ at low $T$ with finite slope. (c) Similar to (b) but at $V_{\mathrm{FG}}$ chosen such that $\rho$ at the base-$T$ match for all frustrations.