Revisiting dissipation-driven phase transition in a Josephson junction

Abstract

Despite extensive experimental and theoretical work over several decades, Schmid-Bulgadaev quantum phase transition remains a subject of debate. Here we revisit this problem by performing systematic experiments on low-frequency current-voltage characteristics of Josephson junctions over a wide range of parameters. The experiments are conducted in a true resistive environment formed by a metallic on-chip resistor located near the junction. Over the parameter range of the experiment, we find that the transition occurs when the resistance crosses the quantum value $h/(4e^2)\simeq 6.5$ k$Ω$ for Cooper pairs, as originally predicted. The temperature $T$ of the experiment is naturally non-zero, but our basic theoretical modeling corroborates that the observations under these conditions can serve as the basis for the conclusions made, in particular, the crossover resistance from superconducting to insulating regime is the same as that at $T=0$.

Figures (4)

• Figure 1: (a) Schematic illustration of the Schmid–Bulgadaev phase transition in a Josephson junction. False-colored SEM images (scale bar= 2 $\mu$m) of (b) a single Josephson junction (Al in blue) and (c) a SQUID connected in series to an ohmic environment of resistance $R_{\mathrm{e}}$ (Cr in orange).
• Figure 2: (a) $IV$-characteristic of a JJ connected to various normal resistors with varying $R_\mathrm{e}$ at the base temperature of the cryostat (8 mK). The solid black line represents the $IV$ of the bare Josephson junction for batch I. (b) Theoretical results using $P(E)$-theory in an $RC-$ environment. (c), (d), (e), (f), (g).- Differential conductance $G\equiv dI/dV$ near zero voltage bias. (h) Effect of the temperature on the conductance $G\equiv dI/dV$ calculated within the $P(E)$-theory for a Josephson junction coupled to an environment with resistance $R_{\mathrm{e}}= 8.8$ k$\Omega$. As expected, the conductance drops to zero at absolute zero temperature, but remains nonvanishing at finite temperatures. Thus the weak drop at $V= 0$ observed in panel (e) can be attributed to the influence of temperature.
• Figure 3: (a) SB phase transition of a Josephson junction. Triangles and circles correspond to data from this work for sample batches I and II, respectively, while stars indicate our prior results from Ref. subero2023bolometric. Open (solid) symbols denote superconducting (insulating) behavior, respectively. (b) Power-law scaling (exponent $\gamma$) extracted from the IV characteristic shown in Fig. \ref{['Fig2']}(a) in the very low bias voltage regime $eV<< R_\mathrm{Q}E_\mathrm{C}/R_\mathrm{e}$ as a function of $R_\mathrm{Q}/R_\mathrm{e}$. (c) Theoretical predictions for $\gamma$ based on the $P(E)-$theory at various temperatures.
• Figure 4: (a)-(c) Differential conductance of three SQUID devices connected to a Cr resistor with $R_\mathrm{e} \simeq 19~\mathrm{k}\Omega$ as a function of bias voltage at various normalized magnetic flux values $\Phi/\Phi_0$= 0, 0.1, 0.2, 0.3, 0.4, 0.5, from top to bottom. The inset shows the normal-state $IV$ characteristics at 8 mK, where the solid red line represents the $P(E)$ theory fit, allowing us to determine the junction capacitance within an $RC$ environment. (d)-(e) Differential conductance of another two SQUIDs coupled to Cr resistors with $R_\mathrm{e} \simeq 3.3~\mathrm{k}\Omega$ and $\simeq 4.5~\mathrm{k}\Omega$, respectively, as a function of bias voltage for different $\Phi/\Phi_0$. (f) Zero-bias conductance of all devices mapped onto the Schmid-Bulgadaev phase diagram where $E_\mathrm{J}/E_\mathrm{C}$ is controlled by varying magnetic flux.