Ubiquitous missing first Shapiro step in Al-InSb nanosheet Josephson junctions

TL;DR

This work shows that the ubiquitous missing first Shapiro step in topologically trivial Al-InSb nanosheet Josephson junctions stems from sharp voltage switching that creates a measurement blind region, rather than from topological physics. The missing step reappears when the switching jump is softened by higher microwave power, temperature, magnetic field, or higher microwave frequency, and it can be qualitatively captured by an RSJ model incorporating a sharp jump. The findings urge caution in interpreting missing Shapiro steps as smoking-gun evidence for topology, highlighting non-topological mechanisms that can produce similar signatures in conventional devices. Overall, the study provides a framework for disentangling topological signatures from realistic device phenomena by analyzing frequency, power, and field dependence in a broader set of trivial regimes.

Abstract

The absence of odd-order Shapiro steps is a predicted signature of topological superconductors. Experimentally, the missing first-order Shapiro step has been reported in both putative topological superconducting systems and topologically trivial superconductor-semiconductor Josephson junctions. Here, we revisit this phenomenon in topologically trivial Al-InSb nanosheet Josephson junctions under microwave irradiation. The missing first Shapiro step coincides with a sharp voltage jump during superconducting switching, yet reappears when the jump is lowered and softened by increasing microwave power, temperature, or magnetic field. It also reappears at higher microwave frequencies, consistent with qualitative results from an RSJ model incorporating the sharp jump. These observations indicate that the absence of the first Shapiro step, associated with the sharp switching jump, simply results from their location within the measurement blind region. This work identifies a common but overlooked mechanism underlying the missing first Shapiro step, offering new insights into fractional Josephson effect experiments.

Figures (4)

• Figure 1: Device A characterization. (a) Scanning electron microscopy image of device A. The InSb nanosheet (bright gray) is in a hexagonal shape. Two T-shaped superconducting leads (Ti/Al, dark gray) are above the nanosheet. The metallic backgate (Ti/Au) is underneath the nanosheet and extends beyond the displayed range. (b) Differential resistance d$V$/d$I$ as a function of bias current $I$ and backgate voltage $V_{bg}$. (c) Hysteresis in $V-I$ curves scanned in the downward (blue) and upward (orange) directions. Retrapping ($I_{rt}$) and switching ($I_{sw}$) currents are indicated for the upward scanned curve. $V_{bg} = 2$ V. (d) Voltage-current characteristic at $V_{bg} = 0.5$ V. The dashed fitting line extrapolates to a finite excess current $I_{ex}$ at $V = 0$ (red arrow). (e) Differential conductance d$I$/d$V$ as a function of voltage bias $V$. The vertical dashed lines indicate peak positions due to multiple Andreev reflections, which are used for the fitting (red line) in the inset. An induced gap of 119.5 $\mu$eV is extracted. $V_{bg}$ = 0.5 V. (f) Differential resistance d$V$/d$I$ as a function of $I$ and the magnetic field $B$. The yellow line is the switching current fitted with the theoretical Fraunhofer curve. $V_{bg} = 0.5$ V.
• Figure 2: Temperature dependence of the missing first Shapiro step and the sharp switching jump. (a)-(d) are from device A. (e)-(g) are from device B. (a) The switching current (blue) and retrapping current (orange) as a function of the temperature $T$. (b) Voltage-current characteristics at $0.05$, $0.35$, and $0.5$ K without microwave irradiation. The blue (orange) curve is scanned in the positive (negative) direction. The sharp superconducting switching jump softens as the temperature increases. (c) Differential resistance $dV/dI$ as a function of microwave power $P$ and DC bias current $I$ at $0.02$, $0.35$, and $0.5$ K. (d) Corresponding voltage histograms of (c). (e) Switching current (blue) and retrapping current (orange) from device B. (f) and (g) Histogram maps of device B at 0.02 and 0.3 K, respectively. White arrows in (c), (d), and (g) indicate reappearance of the missing first Shapiro step at higher temperatures. The microwave frequency is 2.5 GHz for both devices. The bin size for all histogram maps is 0.14.
• Figure 3: Magnetic field dependence of the missing first Shapiro step in device A. (a) Differential resistance d$V$/d$I$ as a function of current $I$ and magnetic field $B$, without microwave irradiation. Three short vertical lines near the bottom axis indicate magnetic fields where curves in (b) are extracted. (b) Linecuts from (a) taken at fixed magnetic fields. The magnetic fields are indicated in each subpanel. The d$V$/d$I$ peaks near superconducting switchings are broadened by the magnetic field. (c) Voltage histograms taken at a microwave frequency of 2.5 GHz. The magnetic field is indicated in white text. The bin size is 0.17. The zero field histogram can be found in Fig. \ref{['fig_temperature']}d.
• Figure 4: Frequency dependence of the missing first Shapiro step in device A. (a) Voltage-current characteristics at a variety of microwave powers at 4 GHz. The voltage is normalized by $hf/2e$, thus the value corresponds to the Shapiro index. (b) Differential resistance dV/dI as a function of microwave power $P$ and current $I$ at a microwave frequency of 4 GHz. Shapiro step indexes are indicated in white text. (c) Voltage histograms that correspond to (b). The bin size is 0.14. (d)-(f) Similar to (a)-(c) but measured at a frequency of 6 GHz. The 2.5 GHz response can be found in Fig. \ref{['fig_temperature']}.