Electrically Tunable Macroscopic Quantum Tunneling in a Graphene-Based Josephson Junction

Stochastic switching-current distribution in a graphene-based Josephson junction exhibits a crossover from the classical to quantum regime, revealing the macroscopic quantum tunneling of a Josephson phase particle at low temperatures. Microwave spectroscopy measurements indicate a multiphoton absorption process occurring via discrete energy levels in washboard potential well. The crossover temperature for macroscopic quantum tunneling and the quantized level spacing are controlled with the gate voltage, implying its potential application to gate-tunable superconducting quantum bits.

Figure 1

(a) Optical image of the device. A graphene flake was placed in the region bound by the yellow dotted line, and the junction area is denoted in red. (b) Typical $I\mathrm{\text{−}}V$ curves for various $V_{\mathrm{bg}}$ at $T=50\mathrm{mK}$. Inset: $V_{\mathrm{bg}}$ dependence of $R_N$ (black), $I_c$ (red), and $I_r$ (blue). $R_N$ was measured in a perpendicular magnetic field of $H=50\mathrm{mT}$. (c) $I_c$ distribution obtained at $V_{\mathrm{bg}}=-60\mathrm{V}$. Solid lines are best fits to the thermal activation (TA, solid symbols) and phase diffusion (PD, void symbols) models. Inset: Schematic of washboard potential and dynamics of a phase particle escaping from the local minimum.

Figure 2

(a) $T$ dependence of the normalized SD of the $I_c$ distribution, $P(I_c)$, obtained for $V_{\mathrm{bg}}=-60\mathrm{V}$. Inset: $T_{\mathrm{esc}}$ versus $T$ plot obtained from a fit to the TA (black) and PD (red) models. The error bars are smaller than the symbol size. (b) Escape rate $\Gamma$ (symbols) as a function of bias current at $V_{\mathrm{bg}}=-60\mathrm{V}$. Solid lines represent fits to the TA (filled symbols) and PD (void symbols) models. Each data set corresponds to the one in Fig. 1c with the same color code. (c) $I_c$ distribution obtained for varying $T$ at $V_{\mathrm{bg}}=0\mathrm{V}$. The rightmost three curves are not distinguishable. Inset: $T$ dependence of the normalized standard deviation. (d) Escape rate (symbols) overlaid with best-fit curves to the TA (filled symbols) and PD (void symbols) models.

Figure 3

(a) Normalized SD versus $T$ plot with $V_{\mathrm{bg}}=-60$, $-40$, $-20$, $-10$, and 0 V from bottom to top. Arrows indicate $T_{\mathrm{MQT}}^{*}$ and $T_{\mathrm{TA}}^{*}$ for each value of $V_{\mathrm{bg}}$. (b) $V_{\mathrm{bg}}$ dependence of the crossover temperatures of $T_{\mathrm{MQT}}^{*}$ (blue circle) and $T_{\mathrm{TA}}^{*}$ (green square). $T_{\mathrm{MQT}}^{*}$ estimated from microwave spectroscopy measurements are also shown, multiplied by a factor of 2 (red triangle). (c) Proportionality relationship between $T_{\mathrm{MQT}}^{*}$ and $I_{c0}^{1/2}$. The dotted line is a guide for the eyes. (d) $T_{\mathrm{TA}}^{*}$ normalized by $E_{J0}$ as a function of $V_{\mathrm{bg}}$.

Figure 4

(a) $P(I_c)$ under microwave irradiation of varying power. The microwave frequency was $f_{\mathrm{mw}}=8.1\mathrm{GHz}$, and $T=50\mathrm{mK}$. (b) Color-coded density plot of $P(I_c)$ with varying microwave power. (c) $\Gamma (I)$ plot corresponding to the data in (a). (d) Applied microwave frequency $f_{\mathrm{mw}}$ versus normalized resonant bias current $I_{\mathrm{res}}/I_{c0}$ (symbols). Solid lines are best fits to the formula for the multiphoton absorption transition (see the text) with the corresponding number of photons ($n=4–10$) from top to bottom.