Robust two-dimensional surface superconductivity and vortex lattice in the Weyl semimetal $γ$-PtBi$_2$

Abstract

The layered compound $γ$-PtBi$_2$ is a topological semimetal with Fermi arcs at the surface joining bulk Weyl points. Recent work has found signatures of surface superconductivity consisting of gap openings compatible with a critical temperature orders of magnitude larger than the bulk value. However, no superconducting vortices have been identified, raising questions about the robustness of the phase coherence. Here we use very low temperature Scanning Tunneling Microscopy (STM) and find robust superconductivity with T$_C=$2.9 K and H$_{C2}\approx$1.8 T linked to the Fermi arcs. We observe quantized superconducting vortices, demonstrating two-dimensional macroscopic quantum phase coherence.

Figures (17)

• Figure 1: (a) Unit cell of $\gamma$-PtBi$_2$ (space group No. 157), with Bi atoms in blue and green and Pt atoms in grey. The system is composed of layers where Pt is surrounded by Bi, so that the surface after cleaving is always composed of Bi. The Bi can however hold two different terminations, one where inequivalent Bi atoms form a buckled hexagonal surface (Bi$_1$ and Bi$_2$, termination A) and another one in which the Bi forms a single plane (Bi$_3$, termination B). (b,c) Atomically-resolved STM topography taken on the two possible terminations of $\gamma$-PtBi$_2$. White scale bar corresponds to $2$ nm. Colormap is shown to the right. Inset shows the FFT with the Bragg peaks marked with circles. The atomic arrangement of Bi atoms is schematically shown by colored circles in the main panels. The surface unit cell is shown as a black rhombus. Notice that the hexagonal pattern observed in the STM image for termination A (b) is formed by the Bi$_1$ atoms. The Bi$_2$ atoms are located farther below the surface, as schematically shown in (a). The hexagonal pattern observed in the STM image for termination B (c) is formed by groups of three Bi$_3$ atoms that lie at the surface plane. These two surfaces are similar to the ones found previously in Ref. Schimmel2024, although, as shown below, the tunneling conductance found here on these surfaces is very different. (d) Resistivity measurement as a function of temperature on $\gamma$-PtBi$_2$ showing no traces of superconductivity down to 1.8 K and a residual resistance ratio exceeding 200. Magnetization measurements are provided in the Supplemental Material SM_1. (e) Current vs voltage curve obtained with a normal tip. Inset shows conductance vs voltage curve in the same voltage range. We remark that the behavior is completely metallic. A superconducting gap opens below $\Delta_0/e=0.48$ mV. The temperature is of $T=0.1$ K, bias voltage $V=30$ mV, and setpoint current $I=1$ nA. (f) Tunneling conductance vs bias voltage obtained with the same parameters as in (e) and $V=1.2$ mV. Red line is a fit to a BCS density of states with a small distribution of gap values described in the text and in Fig. \ref{['fig:gapvst']}.
• Figure 2: (a) Atomically-resolved STM topography presenting a few defects on termination A. White scale bar corresponds to $10$ nm. Colormap is shown to the right. (b) Profile along the red arrow on the topography shown in (a). (c) Conductance as a function of bias voltage taken simultaneously as the topography, following the same profile as (b). Colormap is shown to the right. We see that the superconducting gap is homogeneous over the whole surface and over defects. (d) On left panel we show the tunneling conductance vs bias voltage as a function of temperature (dots) and calculated conductance curves obtained after convoluting the BCS DOS (shown on the right panel) with the derivative of the Fermi function at each temperature, as described in the text. Curves are shifted vertically for clarity. (e) Temperature dependence of the superconducting gap, obtained as described in the text. The solid line is the BCS temperature dependence of the superconducting gap. Inset shows the Gaussian distribution $\gamma_i(\Delta_i)$ centered around $\Delta_0=0.48$ meV with a width of 0.07 meV used for the T=100 mK fit.
• Figure 3: (a) Zero-bias tunneling conductance map of a single vortex at 0.1 T. White dashed line shows the boundary between an atomically flat surface on the left and a corrugated surface. Corresponding topography and more details are shown in Supplemental Material SM_1. (b,c,d) Tunneling conductance maps at zero bias showing the vortex lattice as a function of the magnetic field at 0.4 T (b), 0.8 T (c), and 1.3 T (d). The maps shown in (c,d) were taken on the same field of view. White scale bars correspond to $50$ nm in the main panels. Insets in (c,d) on the bottom right corner show the Fourier transform. (e) Intervortex distance as a function of the magnetic field is shown as red disks. The error bars are obtained by Delaunay triangulating vortex positions and measuring the width of the distance distribution. Solid line corresponds to the Abrikosov prediction for an hexagonal vortex lattice $d_{vortex}\sim1.075 \left(\frac{\Phi_0}{B}\right)^{1/2}$. (f) Topography taken simultaneously to the conductance map shown in (b). Notice that vortices are not observed on atomically flat surfaces. (g) Normalized tunneling conductance curves obtained at the core of the vortex (black dots, black cross in (a)) and away from the vortex (red and orange cross, taken far from the vortex core in an atomically flat region, orange and in a region with corrugation, red). (h) Top (bottom): Average of conductance curves over the regions marked with rectangles in (c,d) are shown by circles: in red the regions presenting a vortex lattice and in orange the regions presenting no apparent vortex lattice in STM measurements at 0.8 T (1.3 T).
• Figure 4: (a) Quasiparticle interference pattern in $\gamma-$PtBi$_2$ measured on the region shown in Fig. \ref{['fig:gapvst']} (a). The scattering intensity is shown on a color scale, following the bar on the left. The dashed contour is the first Brillouin zone and K and M denote high symmetry points. We mark the position of Bragg peaks with blue circles. We mark relevant scattering wavevectors $q_1$, $q_{2}$, $q_{2'}$, $q_{3}$ and $q_{4}$ by colored arrows. The pattern is obtained from a tunneling conductance map at the bias voltage of the BCS quasiparticle peak, V=-$\Delta_0/e=-0.48$ mV. (b) Joint density of states obtained from density functional theory (DFT) calculations of the band structure at the Fermi surface (shown in (c)). The colored arrows are the scattering wave vectors found in (a). (c) Fermi surface of $\gamma-$PtBi$_2$. Arrows show the scattering wave vectors found in (a). The Brillouin zone is shown by a dashed black line in (b,c).
• Figure S1: (a) Scanning Electron Microscope (SEM) image of the surface of $\gamma$-PtBi$_2$ at an edge of the sample. White scale bar is 2 $\mu$m long. Notice the presence of small flakes which have been caused during cleavage. (b) SEM image at the interior of the sample. We can see a large flat surface and several flakes lying on the flat. We have performed a compositional analysis using Energy Dispersive electron Spectroscopy (EDS). We find a homogeneous composition at sites marked as 1-4 in (b) which coincides with the stoichiometry of $\gamma-$PtBi$_2$ within 0.05 uncertainty in the Pt-Bi ratio. Sites 1-3 are on different flakes, and 4 is on a flat terrace. Results in other parts of the sample are similar. In (c) we show a zoom on the ocre rectangle shown in (b). Dashed purple lines are drawn with 120$^{\circ}$ vertices to highlight the hexagonal shape of flakes. Notice that, whereas the terrace is fully flat, the flakes has a strong corrugation, suggesting that there are often compositions of several flakes. White scale bar is 300 nm long in (b,c). (d) EDS spectra measured at the points marked in (b). Inset shows a zoom around the M lines of Pt and Bi. We mark the position of M and L lines of Pt and Bi with arrows.