Coherent and Incoherent Tunneling into Yu-Shiba-Rusinov States Revealed by Atomic Scale Shot-Noise Spectroscopy

The pair breaking potential of individual magnetic impurities in $s$-wave superconductors generates localized states inside the superconducting gap commonly referred to as Yu-Shiba-Rusinov (YSR) states whose isolated nature makes them promising building blocks for artificial structures that may host Majorana fermions. One of the challenges in this endeavor is to understand their intrinsic lifetime, $\hslash /\mathrm{\Lambda }$, which is expected to be limited by the inelastic coupling with the continuum thus leading to decoherence. Here we use shot-noise scanning tunneling microscopy to reveal that electron tunneling into superconducting $2\mathrm{H}\text{−}{\text{NbSe}}_2$ mediated by YSR states is not Poissonian, but ordered as a function of time, as evidenced by a reduction of the noise. Moreover, our data show the concomitant transfer of charges $e$ and $2e$, indicating that incoherent single particle and coherent Andreev processes operate simultaneously. From the quantitative agreement between experiment and theory we obtain $\mathrm{\Lambda }=1\mu \mathrm{eV}\ll k_{B}T$ demonstrating that shot noise can probe energy scales and timescales inaccessible by conventional spectroscopy whose resolution is thermally limited.

Figure 1

(a) Schematic depiction of the various tunneling processes into $2\mathrm{H}\text{−}{\text{NbSe}}_2$: direct elastic quasiparticle tunneling into the bulk (EQP, red) inelastic quasiparticle tunneling through the YSR state (IQP, purple) and Andreev reflection assisted by the YSR (AR, green). The right panels illustrate the passage of electrons as a function of time: random, ordered, or in pairs, respectively. (b) Differential conductance of fully gapped $2\mathrm{H}\text{−}{\text{NbSe}}_2$, setup conditions: $V=3\mathrm{mV}$, $I=3\mathrm{nA}$. The sample is cleaved in situ at $\sim 20\mathrm{K}$ and directly inserted in the STM head held at 4.2 K. All data throughout this Letter are recorded at $T=0.3\mathrm{K}$ (effective electron temperature $\sim 0.7$ K, see [30]) with an etched W tip. (c) Current noise power recorded simultaneously with (b), the black line is a fit for $F^{*}=1$. The inset highlights the effect of the strongly varying dynamical resistance on the measured voltage noise that is accurately captured by the fit. (d) Effective Fano factor for the data in (c) giving $F^{*}=1$ within error bars for all voltages. Data for currents $<10\mathrm{pA}$ are omitted for clarity.

Figure 2

(a) Atomically resolved constant current image of the Se surface of $2\mathrm{H}\text{−}{\text{NbSe}}_2$, $V=4.2\mathrm{mV}$, $I=100\mathrm{pA}$. (b) In-gap current recorded simultaneously with (a) showing a spatially extended YSR state generated by a subsurface impurity. (c) Tunneling spectrum taken at the core of the YSR and (d) simultaneously recorded current noise, $V=3\mathrm{mV}$, $I=3\mathrm{nA}$. The black line in (d) indicates $F^{*}=1$: the noise from the YSR deviates at both positive and negative sample bias (arrows), as can be clearly seen in the effective Fano factor, $F^{*}$, in (e). Outside the gap, $F^{*}$ converges to 1. (f)–(j) The same as (a)–(e) for a more compact, but relatively strong, YSR located elsewhere on the same sample [16]. $V=4\mathrm{mV}$, $I=100\mathrm{pA}$ for (f),(g); $V=6\mathrm{mV}$, $I=400\mathrm{pA}$ for (h)–(j).

Figure 3

(a) Constant current image of the same YSR state as Figs. 2 ($V=4\mathrm{mV}$, $I=100\mathrm{pA}$). The black cross marks the location of the core. (b) Differential conductance $G=dI/dV$ on two tail locations [blue and red crosses in (a)] with opposite particle-hole asymmetry, $V=4.2\mathrm{mV}$, $I=1.5\mathrm{nA}$, $G^{\pm }=G(\pm E_0)$ with $E_0$ the YSR resonance energy. The inset shows the corresponding currents on the same energy scale, dashed lines indicate where the current is dominated by the YSR and is sufficiently large for noise measurements. (c) Current noise recorded simultaneously with (a), the black lines indicate $F^{*}=1$. (d) Effective Fano factor, $F^{*}$, extracted from (c) showing clearly that the noise deviates from $F^{*}=1$ where the current is dominated by the YSR.

Figure 4

YSR peak conductance ($G_{\mathrm{YSR}}$) as function of normal state conductance ($G_N$) for the location of the blue (a) and red (b) spectrum of Fig. 3, reproduced here in the inset. A linear fit of the data taken at small conductance is used to extract $u$ and $v$. Subgap $F^{*}$ (symbols) for the blue (c) and red (d) spectrum of Fig. 3 and theoretical curves for three different values of $\mathrm{\Lambda }$. Pure Andreev reflection (AR, $\mathrm{\Lambda }=0\mu \mathrm{eV}$) and pure inelastic quasiparticle tunneling (IQP, $\mathrm{\Lambda }=1\mu \mathrm{eV}$) are shown for comparison.