From Shapiro steps to photon-assisted tunneling in microwave-driven atomic-scale Josephson junctions with a single (magnetic) adatom

TL;DR

Phase-coherent Cooper-pair tunneling in atomic-scale Josephson junctions is probed under microwave drive; Shapiro steps appear at $V_n= n\,rac{\hbar \omega}{2e}$, demonstrating coherence, but the coherence rapidly degrades with increasing AC amplitude, especially in Mn-doped junctions. The Mn adatoms reduce the Josephson energy and introduce Yu-Shiba-Rusinov (YSR) states, enabling photon-assisted quasi-particle tunneling that competes with supercurrent. Photon-assisted transport through YSR states is described within a Tien–Gordon framework, revealing asymmetric damping and nonreciprocal effects. The results underscore the importance of controlling dissipation and environment in nanoscale superconducting devices and offer a route to engineer coherence via YSR engineering.

Abstract

Ultra-small Josephson junctions are strongly influenced by noise and damping due to energy dissipation into the environment, which are expected to suppress phase coherence. Here, we investigate the coherence properties of atomic-scale Josephson junctions in a scanning tunneling microscope under microwave excitation. Plain Pb-Pb junctions exhibit hysteretic Shapiro steps as signature of a coherent resonant state. With increasing AC amplitude, phase coherence is reduced due to an increase of thermal fluctuations. In the presence of magnetic adatoms the Josephson coupling energy is reduced and quasi-particle tunneling is enhanced. With AC driving we observe a rapid suppression of coherence that we ascribe to photon-assisted quasi-particle tunneling through Yu-Shiba-Rusinov states. Our results highlight the presence of phase coherence and shed light on the origin of the transition to incoherent transport, thereby revealing the importance of controlling dissipation in nanoscale superconducting devices.

Figures (7)

• Figure 1: Experimental realization of an AC driven Josephson junction in STM: a) Josephson junctions are formed between a Pb STM tip and a Pb(111) surface with an additional atom for stabilizing the junction. An antenna close to the junction is used to irradiate the junction with frequencies between 30 GHz and 40 GHz. b) Representative $V(I)$ curve with $I_\mathrm{sw}$ and $I_\mathrm{re}$ currents marked in both biasing ($+/-$) direction. A finite slope around zero shows the presence of phase diffusion in the trapped state. This curve was recorded at 60 $\mu$S (feedback opened at 10mV and 600nA). To capture the statistics the presented data shows the average of 100 sweeps in each direction. c) Equivalent circuit of the Josephson junction with an additional $R_\mathrm{S}-C_\mathrm{b}$ component in parallel to the common RCSJ model to account for frequency-dependent damping.
• Figure 2: Response of Pb-Pb Josephson junction to AC driving at 40 GHz. a) Selected $V(I)$ curves subject to different amplitudes of AC driving. With increasing AC amplitude, $I_\mathrm{sw}$ is reduced and $I_\mathrm{re}$ increased. Hysteretic transitions between Shapiro steps can be observed at 0.25 mV with vanishing hysteresis at larger AC amplitude. Curves are offset by 0.5 mV for clarity, hysteretic Shapiro transitions are marked by a green circle. Upward sweeps are marked in blue while downward sweeps are shown in red. The bottom curve shows the same data as shown in Fig \ref{['fig:JJSetup']}b and all curves are recorded at a normal state conductance of 60 $\mu$S and averaged over 100 sweeps. b,c) 2D-colormaps of the numerical derivative $\mathrm{d}V/\mathrm{d}I$ of the recorded $V(I)$ curves with increasing AC amplitude of the two sweep directions indicated by colored arrows. The extracted curves in (a) are highlighted by orange lines. All spectra recorded at 60 $\mu$S normal state conductance (at $V_{\text{bias}}$= 10 mV).
• Figure 3: Response of Pb-Mn-Pb Josephson junction to AC driving at 40 GHz. a) Selected $I(V)$ curves for different AC amplitude. Hysteretic transitions between Shapiro steps can be observed. Curves are offset by 0.5 mV for clarity. All curves are recorded at a normal state conductance of 50 $\mu$S and averaged over 100 sweeps. Upward sweeps are marked by blue while downward sweeps are shown in red. b,c) 2D-color maps of $\mathrm{d}V/\mathrm{d}I$ curves with increasing AC amplitude at the two sweep directions indicated by colored arrows. The extracted curves in (a) are highlighted by orange lines in (b) and (c). All junctions are current-biased at 50 $\mu$S normal state conductance (at $V_{\text{bias}}$= 10 mV).
• Figure S1: a) $V(I)$ characteristics of single (not averaged) current-bias sweeps on the 60 $\mu$S Pb junction in the presence of finite HF irradiation ($V_\mathrm{HF}$ = 0.25 mV). The sweeps are offset by 0.5 mV for better visibility. b) Comparison of Josephson junctions formed on a Pb and Mn adatom for both sweep directions at 50 $\mu$S. The presence of the magnetic adatom reduces $I_\mathrm{sw}$ and increases the phase diffusion slope.
• Figure S2: Measured d$I$/d$V$ spectra in the presence of HF irradiation in comparison to the calculated spectra using the Tien-Gordon model. a) shows the measured data of a Pb-Pb junction at 60 $\mu$S under 40 GHz HF irradiation. In b) the Tien-Gordon model was used to calculate the photon-assisted tunneling processes for the same junction starting from the experimental d$I$/d$V$ spectrum at zero HF amplitude. For Andreev and Cooper-pair tunneling processes the transmission of two electrons was assumed in the calculation in b). In c) an exemplary data set at finite amplitude (red dashed line in a and b) comparing the measured data to the simulated data is shown. This comparison was used to determine the damping properties of the HF cabling in the cryostat.