Experimental Evidence for $s$-Wave Pairing Symmetry in Superconducting ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ Single Crystals Using a Scanning Tunneling Microscope

Topological superconductors represent a newly predicted phase of matter that is topologically distinct from conventional superconducting condensates of Cooper pairs. As a manifestation of their topological character, topological superconductors support solid-state realizations of Majorana fermions at their boundaries. The recently discovered superconductor ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ has been theoretically proposed as an odd-parity superconductor in the time-reversal-invariant topological superconductor class, and point-contact spectroscopy measurements have reported the observation of zero-bias conductance peaks corresponding to Majorana states in this material. Here we report scanning tunneling microscopy measurements of the superconducting energy gap in ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ as a function of spatial position and applied magnetic field. The tunneling spectrum shows that the density of states at the Fermi level is fully gapped without any in-gap states. The spectrum is well described by the Bardeen-Cooper-Schrieffer theory with a momentum independent order parameter, which suggests that ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ is a classical $s$-wave superconductor contrary to previous expectations and measurements.

Figure 1

Structural characterization of the cleaved (111) surface of ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$. (a) Structural model of ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ (side view). (b) Structural model of the top Se plane of ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ (top view, Se atoms large orange, Bi atoms purple, unit cell green). (c) Large scale STM topography measurements of the cleaved (111) ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface showing large scale atomically flat terraces separated by multilayer steps. Image size is $1\mu \mathrm{m}\times 1\mu \mathrm{m}$. Tunneling parameters: $I=10\mathrm{pA}$, $V_B=0.5V$. (d) Medium scale STM topography, $50\mathrm{nm}\times 50\mathrm{nm}$, showing cluster decoration and grain boundaries on the cleaved surface. Tunneling parameters: $I=50\mathrm{pA}$, $V_B=0.1\mathrm{V}$. (e) Atomic resolution STM image, $10\mathrm{nm}\times 10\mathrm{nm}$, of the grain boundary in the blue boxed area in (d).Tunneling parameters: $I=100\mathrm{pA}$, $V_B=0.05\mathrm{V}$. (f) Atomic resolution STM image of the top Se plane in the cleaved surface of ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ showing the atomic unit cell (white parallelogram). Image size is $4\mathrm{nm}\times 4\mathrm{nm}$. Tunneling parameters: $I=20\mathrm{pA}$, $V_B=-10\mathrm{mV}$.

Figure 2

Tunneling spectroscopy of ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$. (a) Tunnel spectrum covering $\pm 30\mathrm{mV}$ showing the background and superconducting gap near zero bias. Tunnel parameters: $I=70\mathrm{pA}$, $V_B=29\mathrm{mV}$, $V_{\mathrm{mod}}=100\mu \mathrm{V}$, $T_{\mathrm{eff}}=0.95\mathrm{K}$. (b) Low energy tunnel spectrum (red dots) showing a fully gapped ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ consistent with BCS $s$-wave pairing. A fit (blue line) to BCS Maki theory with $T_{\mathrm{eff}}=280\mathrm{mK}$ yields $\Delta =0.399\pm 0.001\mathrm{meV}$ and $\zeta =0.0092\pm 0.0002$ [18]. Tunnel parameters: $I=300\mathrm{pA}$, $V_B=2\mathrm{mV}$, $V_{\mathrm{mod}}=15\mu \mathrm{V}$. (c) Tunnel spectrum of ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ with a probe tip crashed into the sample as a function of junction impedance. At high impedance the spectrum is well fit (red dashed line) by a BCS SIS model with the sample ${\Delta }_{\mathrm{Sample}}=0.44\pm 0.01\mathrm{meV}$ and a probe tip gap ${\Delta }_{\mathrm{Tip}}=0.16\pm 0.01\mathrm{meV}$, and $T_{\mathrm{eff}}=390\pm 100\mathrm{mK}$ [18]. At lower junction impedance the spectrum develops a peak at zero bias owing to Josephson tunneling. Tunnel parameters: $V_B=2\mathrm{mV}$, $V_{\mathrm{mod}}=10\mu \mathrm{V}$, $I=2\mathrm{nA}$ to 900 nA. (d) Tunneling spectrum on a second cleavage of the sample in (a) with a new probe tip showing no evidence of zero bias states at low impedance with a normal probe tip. Tunnel parameters: $V_{\mathrm{mod}}=20\mu \mathrm{V}$, $V_B=1\mathrm{mV}$ to 4 mV, $I=18\mathrm{nA}$ to 300 nA, $T_{\mathrm{eff}}=280\mathrm{mK}$.

Figure 3

Superconducting energy gap inhomogeniety in ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$. (a) STM topographic image, $50\mathrm{nm}\times 50\mathrm{nm}$, of a superconducting terrace region. Tunneling parameters: $I=50\mathrm{pA}$, $V_B=0.1\mathrm{V}$. The white line indicates where the $dI/dV$ measurements were made in (b). (b) $dI/dV$ spectra from the region in (a) showing a relatively uniform energy gap across the terraces, grain boundaries, and Cu clusters in (a). The average gap from BSC fits is $0.41\pm 0.03\mathrm{meV}$. Tunnel parameters: $I=400\mathrm{pA}$, $V_B=5\mathrm{mV}$, $V_{\mathrm{mod}}=20\mu \mathrm{V}$, $T_{\mathrm{eff}}=280\mathrm{mK}$. (c) STM topographic image, $160\mathrm{nm}\times 160\mathrm{nm}$, of a superconducting-normal interface region. Tunneling parameters: $I=50\mathrm{pA}$, $V_B=0.1V$. The white line indicates where the $dI/dV$ measurements were made in (d). (d) $dI/dV$ spectral map along the line in (c) showing the gradual disappearance of the gap across the boundary. Each horizontal row is the $dI/dV$ vs $V_B$ spectra, where the $dI/dV$ magnitude is given by the color intensity scale and the vertical axis is the distance along the line in (c). Tunnel parameters: $I=200\mathrm{pA}$, $V_B=5\mathrm{mV}$, $V_{\mathrm{mod}}=20\mu \mathrm{V}$, $T_{\mathrm{eff}}=280\mathrm{mK}$.

Figure 4

Superconducting properties of ${\mathrm{Cu}}_{0.2}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ in an applied magnetic field. (a) Tunneling spectra as a function of an applied perpendicular magnetic field, $B$. The spectra show a transition to the normal state above $B=1.7\mathrm{T}$. The spectra are normalized to the spectra at high field ($B=1.75–2\mathrm{T}$). Tunnel parameters: $I=80\mathrm{pA}$, $V_B=10\mathrm{mV}$, $V_{\mathrm{mod}}=50\mu \mathrm{V}$, $T_{\mathrm{eff}}=0.95\mathrm{K}$. (b) The superconducting energy gap determined from fitting the spectra in (a) to the BCS density of states. The uncertainties given by 1 standard deviation in the gap energy determined from the fit to the BCS density of states are smaller than the symbol size [18]. (c) $dI/dV$ spectral map showing the disappearance of the superconducting gap in the center of the vortex core in the top of the image in (f). Each vertical line is a $dI/dV$ vs $V_B$ spectra, and the horizontal axis is the distance along the line in (f). The color scale is the $dI/dV$ intensity from 0 to 30 nS. $T_{\mathrm{eff}}=280\mathrm{mK}$. (d)–(f) Density of states maps at the Fermi level, $dI/dV(V_B=0\mathrm{mV})/dI/dV(V_B=-0.5\mathrm{mV})$, $110\mathrm{nm}\times 110\mathrm{nm}$, showing the evolution of vortices (orange circles) as a function of applied magnetic field, (d) 0.5 T, (e) 0.75 T, and (f) 1.0 T. White line in (f) indicates path for the spectral map in (c). Tunnel parameters: $I=200\mathrm{pA}$, $V_B=5\mathrm{mV}$, $V_{\mathrm{mod}}=50\mu \mathrm{V}$, $T_{\mathrm{eff}}=280\mathrm{mK}$.