Figure 1

We show two possible polytypes of TaSe${}_2$, the $2H$ and $1T$ phases, which consist of two TaSe${}_2$ hexagonal prisms rotated with respect to each other, and one trigonal prism. Se atoms are shown as gray spheres and Ta atoms as smaller red spheres. The coordination of Ta is trigonal prismatic in the $2H$ structure and octahedral in the $1T$ structure.Reuse & Permissions

Figure 2

We show a schematic representation of scanning tunneling microscopy (STM) images of the atomic arrangements discussed. We highlight the top sheet as $2H$. It shows a $3a_0\times 3a_0$ superlattice modulated charge-density wave (CDW). The layer immediately below, highlighted as $1T$, has a different Moiré pattern with a $\sqrt{13}{a}_0\times \sqrt{13}{a}_0$ CDW. In $2H$-TaSe${}_2$, top and bottom Se atoms are aligned [top figure in (c)]. In $1T$-TaSe${}_2$, the two Se triangles are rotated [bottom figure in (c)]. The middle panels (b) show in more detail the CDW patterns found in each area. There are three inequivalent atomic sites in the pattern, as highlighted by yellow, orange, and white points. The incommensurate CDW $\sqrt{13}{a}_0\times \sqrt{13}{a}_0$ pattern shown in the bottom panel of (b) consists of stars of David, with also three inequivalent sites. The arrangement shown in (a), with one $2H$-TaSe${}_2$ sheet on top of $1T$-TaSe${}_2$, presents the singular superconducting features discussed in the text.Reuse & Permissions

Figure 3

The resistance vs temperature of our samples normalized to its ambient temperature value is shown in the main panel down to 0.5 K. Residual resistivity ratio is of 26. Onset of charge-density-wave (CDW) order is shown by an arrow. The temperature-dependent susceptibility, which shows the superconducting transition, is shown in the inset.Reuse & Permissions

Figure 4

Tunneling conductance vs bias voltage in single-layer $2H$-TaSe${}_2$ on top of $1T$-TaSe${}_2$ (a), as in Fig. 2, in $1T$-TaSe${}_2$ (b) and in multilayer $2H$-TaSe${}_2$ (c) taken at 0.15 K. The black line on top of the yellow curve in $c$ is a fit to the superconducting gap as described in Sec. 4. Different tunneling conductance curves are taken when the tip moves from a Se atom (black) to an intersite (yellow). Insets show the path on atomic size topography images involving a hexagon of Se atoms. Following other paths of the sixfold symmetry leads to qualitatively the same features.Reuse & Permissions

Figure 5

Scanning tunneling microscopy (left panels) and zero-bias conductance map (right panels) images in single-layer $2H$-TaSe${}_2$ on top of $1T$-TaSe${}_2$ (a), as in Fig. 2, in $1T$-TaSe${}_2$ (b) and in multilayer $2H$-TaSe${}_2$ (c) taken at 0.15 K. Real-space (left) and Fourier transforms (right) are shown together in each panel. Green circles show the position of the Bragg peaks due to the atomic Se modulation and yellow circles show the peaks due to the CDW modulation. Lines are shown to highlight the angular difference between atomic and CDW modulations. The color scale of the zero-bias conductance maps is given in normalized conductance units (NCU), that is, the zero-bias conductance normalized to the conductance above 1 mV. The color scale of the upper panels corresponds to the colors used in the upper panel of Fig. 4. Black points correspond to curves similar to the black tunneling conductance curves shown in Fig. 4, and yellow points to yellow tunneling conductance curves. Images are unfiltered.Reuse & Permissions

Figure 6

Large topographic images in the top panels and zoom-ups of different areas in the middle panels. The bottom panels are conductance maps taken at zero bias in the same areas as the small size topographic images shown in the middle panels, showing similar color scales as in Fig. 5. We observe a $2H$-TaSe${}_2$ single layer on top of $1T$-TaSe${}_2$. The hexagonal layer shows the features in the conductance discussed in the top panels of Figs. 4 and 5, and the trigonal layer is featureless. Images here are unfiltered and have been taken at 0.15 K. The height profile marked by a blue line in the top right panel is shown in the top right inset.Reuse & Permissions

Figure 7

Topography (top panel) and tunneling conductance map at zero bias (bottom panel) of a hexagonal layer on top of a trigonal layer. Images, taken at 0.15 K, are filtered for clarity. The blue, dark, and light green curves of (b) are taken all three on top of Se atoms, corresponding to the color code shown in the bottom panel of (a). The yellow curve is taken in between Se atoms. The curves on top of the Se atoms all show a zero-bias conductance peak, whose height is modulated as a function of the position. Blue curves are located at the Se position, which also shows the highest contrast in the topography [white in top panel of (a)]. Dark green and light green curves are located at the other Se positions with different charge modulations. Yellow curve is independent of the position in the CDW modulation.Reuse & Permissions

Figure 8

The Fourier amplitude of the first three Bragg peaks in single layers of $2H$-TaSe${}_2$ on top of $1T$-TaSe${}_2$ along the direction of the sixfold modulation of highest contrast in the tunneling conductance maps. Note the use of log-scale to highlight the noise background. The central Bragg peak has been removed. The two peaks at the lower reciprocal lengths give the CDW pattern, and the third peak is due to the atomic Se lattice. When increasing the bias voltage, the sixfold modulation remains for the CDW peaks until it disappears above 300 $\mu$V. The largest part of this modulation comes from the local variations in the zero-bias peak amplitude. The modulation at distances of the atomic lattice (third Bragg peak) remains until 600 $\mu$V. This is due to the modulation of the V-shaped dip at intersites.Reuse & Permissions

Figure 9

The temperature dependence of the gap observed in multilayer $2H$-TaSe${}_2$ is shown as open black points at the left axis. The gap $\Delta \left(T\right)$ is normalized to its value at low temperatures. $\Delta \left(T\right)$ is obtained by fitting the curves shown in the lower left inset using a broadening parameter of 0.05 mV. The blue diamonds show the temperature dependence of the width of the Gaussian peak observed at Se sites, normalized to its value at low temperatures (0.1 mV) and inverted. Both quantities scale with each other, showing that the zero-bias anomaly in single layers is related to the superconducting gap observed in multilayers. In particular, the broadening of the zero-bias anomaly is not due to a temperature increase, but to a decreasing superconducting gap value.Reuse & Permissions

Figure 10

Sketch of the Fermi surface above and below the charge-density-wave transition temperature. The sketch has been obtained by adapting the figures of Ref. 16.Reuse & Permissions