Superconducting Density of States and Vortex Cores of 2H-${\mathrm{NbS}}_2$

Scanning tunneling microscopy and spectroscopy measurements in the superconducting dichalcogenide 2H-${\mathrm{NbS}}_2$ show a peculiar superconducting density of states with two well-defined features at 0.97 and 0.53 meV, located, respectively, above and below the value for the superconducting gap expected from the single band $s$-wave BCS model ($\Delta =1.76k_B{T}_c=0.9\mathrm{meV}$). Both features have a continuous temperature evolution and disappear at $T_c=5.7\mathrm{K}$. Moreover, we observe the hexagonal vortex lattice with radially symmetric vortices and a well-developed localized state at the vortex cores. The sixfold star shape characteristic of the vortex lattice of the compound 2H-${\mathrm{NbSe}}_2$ is, together with the charge density wave order, absent in 2H-${\mathrm{NbS}}_2$.

Figure 1

Atomic scale topographic images (left panels), taken with STM in 2H-${\mathrm{NbSe}}_2$ [(a) $V_{\mathrm{Bias}}=4\mathrm{mV}$, $I_{\mathrm{Tunnel}}=13\mathrm{nA}$] and in 2H-${\mathrm{NbS}}_2$ [(b) $V_{\mathrm{Bias}}=4\mathrm{mV}$, $I_{\mathrm{Tunnel}}=20\mathrm{nA}$] at 0.1 K, as well as their Fourier transforms (right panels). In (a) 2H-${\mathrm{NbSe}}_2$, a superimposed modulation due to the presence of the CDW is observed. The corresponding Fourier transform image (right panel) shows the wave vectors of the atomic and CDW modulations in the reciprocal space (marked by arrows in the inset). In (b) 2H-${\mathrm{NbS}}_2$, no CDW order is observed either in the topography (left) or in its Fourier transform (right).

Figure 2

Characteristic tunneling conductance curve obtained in 2H-${\mathrm{NbS}}_2$ and measured at 0.1 K (conductance $\sigma =1.6\mu \mathrm{S}$ at 4 mV). The derivative of the associated LDOS (shown in the inset) presents two peaks, at 0.97 and 0.53 meV (marked by black and gray arrows, respectively), which correspond to two peaks in a gap distribution.

Figure 3

(a) Temperature scan of tunneling conductance spectra (left, $\sigma =0.65\mu \mathrm{S}$ at 4 mV) and superconducting LDOS (right). The LDOS is obtained by deconvolution from tunneling conductance curves. The data are, from bottom to top, taken at 0.1, 0.9, 1.5, 2, 2.5, 3, 3.5, 4, 4.25, 4.5, 4.75, 5, 5.2, 5.4, and 5.6 K. Red lines in the left panel are the fits obtained from convoluting the LDOS shown in the right panel with temperature. (b) Temperature dependence of the two peaks in $d(\mathrm{LDOS})/dE$ (gray and black points, corresponding to the features marked by gray and black arrows in Fig. 2; dashed lines are guides to the eye). The solid line is the BCS expression taking $\Delta =1.76k_B{T}_c=0.87\mathrm{meV}$, with $T_c=5.7\mathrm{K}$.

Figure 4

(a) STS image of the vortex lattice in 2H-${\mathrm{NbS}}_2$ taken at 0.1 K and 0.15 T ($360\mathrm{nm}\times 360\mathrm{nm}$). In (b), we show, for comparison, a STS image of the same size area obtained in 2H-${\mathrm{NbSe}}_2$ under similar conditions (in both cases, $\sigma =4.2\mu \mathrm{S}$ at 5 mV). In (c), we present tunneling conductance curves in 2H-${\mathrm{NbS}}_2$ along a line of about 65 nm that goes from the middle point between vortices into the vortex core [using a similar color scheme as in (a) and (b)], following the line shown in (a).