Vortex Tunneling and Critical State in an Oxide Heterostructure

Abstract

Two-dimensional superconductors offer an excellent platform for the study of vortex matter due to their low superfluid stiffness and inability to effectively screen applied magnetic fields. Here we explore vortices in a two-dimensional superconductor formed at the surface of the complex oxide KTaO$_3$. Multiple regimes of vortex-mediated transport are identified and studied, revealing switching behaviour attributed to nucleation of individual vortices. Analysis of this regime allows us to identify the quantum tunneling of vortices, which transitions to thermally activated behaviour at elevated temperatures. Magnetic field dependence reveals rich histograms of the switching currents which we attribute to different configurations of pinned vortices.

Figures (14)

• Figure 1: (a) An AFM image of constriction A studied here and in Figure \ref{['IVs']}. The light grey region denotes the conductive channel, whilst the darker regions denote the area etched and left insulating. The conductive regions around the constriction were intended to be used as gates in the style of our previous work mccourt_electrostatic_2025, but were left unused here. (b) Map of voltage across the constriction as a function of bias current $I$ and perpendicular magnetic field $B$. Note the logarithmic colour scale. (c) Extracted $I_C$ (circles) overlayed with curves corresponding to expressions from gaggioli_superconductivity_2024. Due to the small asymmetry of the junction (Supplementary Figure \ref{['supp_QPC3UpAndDown']}) the max $I_C$ is shifted from zero field. (d) Relative superfluid density, $\rho$ (black circles) with fit (blue dotted line) and the resistance of the film, $R(T)$, normalized to the normal state resistance, $R_N$ (red circles). $\rho$ is obtained from the slope $dI_C/dB$ extracted in the Meissner regime at different temperatures (supplementary Figure \ref{['supp_IcIrVsT']}). These slopes are then normalized to $dI_C/dB$ measured at the base temperature in panels (b) and (c). (e) IV curves for a range of temperatures at zero field and 5 mT. Solid and dashed lines correspond to IV sweeps with increasing and decreasing bias, respectively. Note that the switching currents depend on $T$ and $B$, while the retrapping currents and the $I-V$ curves in the high voltage state do not. These observations indicate that on the high voltage branch some part of the sample enters a normal state, which is then sustained by the dissipated power. (f) Same curves as in panel (e) on a much smaller voltage scale. The curves measured at finite field display an initial $\mu$V-scale segment, which we associate with the vortex flow.
• Figure 2: (a) Histograms of switching currents at zero field and several temperatures for device B. (b) Escape rate extracted from the histograms in panel (a). (c) Standard deviation of the switching current distributions and critical current over a range of temperatures. (d) Scaling of the escape rate divided by the current-dependent prefactor (see text), demonstrating the exponential dependence on the applied current.
• Figure 3: (a) Heat map of multiple switching histograms like in Figure \ref{['rate_T']}a, plotted as a function of $B$ at 0.09 K. (b) Histograms at various fields corresponding to the vertical cuts of panel (a). At $B \approx 1$ mT the histograms lose their asymmetric shape before transitioning to distributions with multiple peaks. (c) Escape rates calculated from histograms in panel (b) under the assumption of a single population of the initial states. (d,e) Histograms of switching currents at 3.0 mT (top) and 6.3 mT (bottom) for 0.09 K (blue), 0.24 K, 0.29 K and 0.33 K (red).
• Figure 4: (a)$I-V$ curves in the $\mu$V regime measured in device A for a range of temperatures $T \gtrsim 0.24$K at $B=5.6$ mT. Note that the curves are temperature-independent for $I \gtrsim 1.82 \mu$A. (b) The same data from (a) plotted on a logarithmic voltage scale, demonstrating the exponential temperature-dependent tail. (c)$I-V$ curves at several values of $B$ showing the vortex flow regime and the jump to the normal state. The voltage at the end point of the vortex flow regime is extracted for the next panel. (d) Voltage measured immediately prior to switching from the vortex flow ($\mu$V) regime to the normal (mV) regime, plotted as a function of magnetic field.
• Figure 5: Measured voltages in the device presented in Figures \ref{['Lambda']} and \ref{['IVs']} at 0.08 K. The left (right) plot displays the voltage as the current is swept from negative (positive) to positive (negative). On the right plot, the x and y axis have both been flipped.