ac Josephson effect in a gate-tunable ${\mathrm{Cd}}_3{\mathrm{As}}_2$ nanowire superconducting weak link

Three-dimensional topological Dirac semimetals have recently attracted significant attention since they possess exotic quantum states. When Josephson junctions are constructed utilizing these materials as the weak link, the fractional ac Josephson effect emerges in the presence of a topological supercurrent contribution. We investigate the ac Josephson effect in a Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ nanowire using two complementary methods: by probing the radiation spectrum and by measuring Shapiro patterns. With both techniques, we find that the conventional supercurrent dominates at all investigated doping levels and that any potentially present topological contribution falls below our detection threshold. The inclusion of thermal noise in a resistively and capacitively shunted junction (RCSJ) model allows us to reproduce the microwave characteristics of the junction. With this refinement, we explain how weak superconducting features can be masked and provide a framework to account for elevated electronic temperatures present in realistic experimental scenarios.

Figure 1

Device and measurement setup. (a) ${\mathrm{Cd}}_3{\mathrm{As}}_2$ nanowire Josephson junction embedded in a radiation (irradiation) setup using a spectrum analyzer (microwave source). Inset: False-colored SEM image of the junction defined by superconducting Al leads (blue) in the ${\mathrm{Cd}}_3{\mathrm{As}}_2$ nanowire (center axis along the black arrow). The top gate electrode (yellow) is isolated from the junction by a 20 nm thick ${\mathrm{HfO}}_2$ layer. The voltage $V_{\mathrm{tg}}$ applied on the Au gate allows tuning the charge carrier density. The junction is shunted by a resistor $R_s=10\mathrm{\Omega }$ that connects the rf line to the fridge ground on the PCB. (b) Cross-sectional illustration of the junction along the black arrow in (a). (c) Optical image showing the electrodes extending from the junction (top) towards the Au bonding pads shown on the overview of the chip (bottom).

Figure 2

Gate-dependent supercurrent. (a) Differential resistance $dV/dI$ as a function of current bias $I$ and top gate voltage $V_{\mathrm{tg}}$. (b) $dV/dI$ as a function of $I$ at different gate voltages taken from the line cut in (a) at the positions indicated by the arrows. The $dV/dI$-peak position is identified as the critical current $I_{\mathrm{c}}$. (c) $IV$ characteristic at $V_{\mathrm{tg}}=0$ V obtained by integrating the measured $dV/dI$ shown in logarithmic scale in (d). The violet shaded area indicates the current and voltage range that produces conventional Josephson radiation in a 2.5–3.8 GHz bandwidth.

Figure 3

Emission spectrum. (a) Normalized power spectral density (n. ${\mathrm{PSD}}_{\det }$) as a function of the voltage drop $V$ across the junction and detection frequencies $f_{\det }$ at $V_{\mathrm{tg}}=0$ V. The radiation spectrum is overlaid with the expected peak position of conventional Josephson emission. (b) Power spectral density (${\mathrm{PSD}}_{\det }$) as a function of $V$ and $V_{\mathrm{tg}}$, measured at a fixed detection frequency $f_{\det }=3$ GHz indicated by the blue arrow in (a). The gray mark on the voltage axis indicates the expected conventional emission peak position, whereas the pink mark is placed at the position of a potential topologically nontrivial emission peak. (c) ${\mathrm{PSD}}_{\det }$ in linear scale with a subtracted background ($\mathrm{\Delta }{\mathrm{PSD}}_{\det }$) as a function of $V$ at three gate voltages obtained from line cuts in (b) at the positions indicated by the arrows. (d) Emission strength $P_{\det }$ (W) plotted against the corresponding critical current squared $I_{\mathrm{c}}^2$.

Figure 4

Shapiro step measurement with drive frequency $f_{\mathrm{d}}=2$ GHz. (a) Differential resistance $dV/dI$ as a function of drive power $P_{\mathrm{s}}$ at the microwave source and current bias $I$. (b) $IV$ curves obtained by integrating $dV/dI$ for irradiation powers indicated by the arrows in (a), with the voltage axis normalized to the Shapiro step voltage $h{f}_{\mathrm{d}}/2e$. (c) Differential conductance $dI/dV$ as a function of $P_{\mathrm{s}}$ and $V$ in units of the Shapiro step voltage $h{f}_{\mathrm{d}}/2e$, measured on the hole side ($V_{\mathrm{tg}}=-5$ V), the electron side ($V_{\mathrm{tg}}=7$ V), and close to the Dirac point ($V_{\mathrm{tg}}=0$ V). Data are numerically converted from current-biased data; the center map constitutes the same measurement as in (a).

Figure 5

Results of RCSJ modeling with thermal fluctuations. (a) Simulated $IV$ characteristics (dark blue) fitted to the experimental curve at $V_{\mathrm{tg}}=0$ V (light blue). The fit parameters critical current $I_{\mathrm{c}}$, effective temperature $T$, shunt capacitance $C$, and shunt resistance $R$ are listed. $T$, $C$, and $R$ are kept constant for the subsequent plots. (b) Simulated power spectral density (PSD) as a function of mean voltage $V$ and frequency $f$ deduced from the voltage evolution in time for $I_{\mathrm{c}}=570$ nA. The map is overlaid with the fundamental (blue) voltage-to-frequency conversion and the first higher harmonic (gray). The orange vertical lines indicate the frequency range (2.5–3.8 GHz) of interest for the comparison with the experiment. (c) Simulated emission spectrum for different $I_{\mathrm{c}}$. (d) and (e) PSD in linear scale with a subtracted background ($\mathrm{\Delta }\mathrm{PSD}$) for different $I_{\mathrm{c}}$ deduced from the maps presented in (c) for a given frequency and voltage, respectively. In (d) $f=3$ GHz, and in (e) its voltage equivalent $V=6.2\mu \mathrm{V}$, which is related to vertical and horizontal cuts presented in (c). (f) Emission strength $P$ plotted against the corresponding critical current squared $I_{\mathrm{c}}^2$ by integrating over the voltage ($P_V$; purple) and by integrating over the frequency ($P_f$; blue).

Figure 6

Simulated Shapiro pattern reproducing the experimentally obtained features at $V_{\mathrm{tg}}=0$ V presented in Fig. 4. The parameters used in the RCSJ model with thermal fluctuations are listed. (a) Differential resistance $dV/dI$ as a function of drive power $P_{\mathrm{d}}$ at the device and current bias $I$. (b) Differential conductance $dI/dV$ as a function of $P_{\mathrm{d}}$ and $V$ in units of the Shapiro step voltage $h{f}_{\mathrm{d}}/2e$.