Unconventional superconductivity in the single-atom-layer alloy $\mathrm{Si}\left(111\right)\text{−}\surd 3\times \surd 3\text{−}\left(\mathrm{Tl},\mathrm{Pb}\right)$

We present results of low-temperature scanning tunneling microscopy/spectroscopy measurements on the one-atom-layer superconductor, $\mathrm{Si}\left(111\right)\text{−}\surd 3\times \surd 3\text{−}\left(\mathrm{Tl},\mathrm{Pb}\right)$ which has a spin-split band structure due to the Rashba-Bychkov effect. It was revealed that it has a multiple superconducting gap Δ with significant anisotropy and sizable magnitude of $2\mathrm{\Delta }/k_B{T}_C\sim 8.6(k_B$ is the Boltzmann constant and $T_C$ is the critical superconducting temperature). Under the magnetic field, a dip structure was observed even at the core of the vortex. The dip structure was like a “pseudogap” because it remained up to 2 T, well above the upper critical magnetic field determined in the transport measurements (∼0.7 T). This unconventional behavior suggests the possibility of spin-triplet Cooper pairs related to parity-broken superconductors.

Figure 1

(a) STM image of $\mathrm{Si}\left(111\right)\text{−}\surd 3\times \surd 3\text{−}\left(\mathrm{Tl},\mathrm{Pb}\right)$ at $T<0.5$ K, with the bias voltage $V_{\mathrm{set}}=80\mathrm{mV}$ and the tunneling current $I_{\mathrm{set}}=0.015\mathrm{nA}$. (b) Its high-resolution STM image at $T<0.5$ K, $V_{\mathrm{set}}=80\mathrm{mV}$, and $I_{\mathrm{set}}=0.3\mathrm{nA}$. (c) Schematics (upper: plane view; lower: sectional view) of the atomic arrangement. (d) The tunneling spectrum measured at $T<0.5$ K. The tunneling current was set $I_{\mathrm{set}}=1\mathrm{nA}$ with the tunneling bias voltage $V_{\mathrm{set}}=1.5\mathrm{V}$, superimposed with the modulation amplitude $V_{\mathrm{ac}}=0.07\mathrm{mV}$ at frequency $f=971\mathrm{Hz}$ for lock-in detection. (e) A series of spectra as a function of temperature. The measurement condition is the same as (d).

Figure 2

Tunneling spectrum calculated with the isotropic gap function (green: ${\mathrm{\Delta }}_0=0.88\mathrm{meV},\mathrm{\Gamma }=63\mu \mathrm{eV})$, the nodal gap function (blue: ${\mathrm{\Delta }}_1=1.05\mathrm{meV},\mathrm{\Gamma }=1.0\mu \mathrm{eV})$, and the nodeless gap function (red: ${\mathrm{\Delta }}_0=0.48\mathrm{meV},{\mathrm{\Delta }}_1=0.92\mathrm{meV},\mathrm{\Gamma }=1.0\mu \mathrm{eV})$. The extrinsic broadening effect including rf noise and lock-in bias modulation $(0.25\mathrm{meV}$ in total) is considered in these calculations.

Figure 3

(a) A series of STS spectra as a function of temperature (open circles) and fitting curves (red curves). Eq. (1) is used for fitting other than the curve of 0.5 K. (b) Temperature dependence of ${\mathrm{\Delta }}_0,{\mathrm{\Delta }}_1$, and Γ without magnetic field.

Figure 4

(a–d) The ZBC mappings (color code), superimposed on the topographic images (height) under surface-normal magnetic field $B$, measured at $T<0.5$ K. The scan area is $1\mu \mathrm{m}\times 1\mu \mathrm{m}$. The tunneling current was set $I_{\mathrm{set}}=1\mathrm{nA}$ with the tunneling bias voltage $V_{\mathrm{set}}=1.5\mathrm{V}$, superimposed with the modulation amplitude $V_{\mathrm{ac}}=0.07\mathrm{mV}$ at frequency $f=971\mathrm{Hz}$ for lock-in detection. The applied magnetic field in (a–(d) is $B=0$, 0.1, 0.2, and 1.2 T, respectively.

Figure 5

(a) ZBC mapping around a vortex at $B=0.2\mathrm{T}$. (b) A series of tunneling spectra measured across the vortex at positions indicated in (a). The color of the spectra indicates the point for measurement in (a). The spectra are offset vertically. (c) ZBC measured across a vortex (blue points) and theoretical fitting using Eq. (3) (red curve). Experimental points are normalized with respect to the value at the vortex center. Zero point on the $x$ axis corresponds to the center of the vortex.

Figure 6

(a,b) The tunneling spectra measured (a) outside vortices and (b) at the vortex center under different magnetic fields. (c) Magnetic field dependence of ${\mathrm{\Delta }}_0,{\mathrm{\Delta }}_1$, and Γ outside the vortex. (d) The magnetic field dependences of ZBC, measured outside vortices (blue), at the vortex center (red), and above 0.8 T (green) where vortices cover the whole surface. The dashed line is a guide to the eye.