Superconducting gap and vortex lattice of the heavy-fermion compound ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$

The order parameter and pairing mechanism for superconductivity in heavy-fermion compounds are still poorly understood. Scanning tunneling microscopy and spectroscopy at ultralow temperatures can yield important information about the superconducting order parameter and the gap structure. Here, we study the first heavy-fermion superconductor, ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$. Our data show the superconducting gap which is not fully formed and exhibits features that point to a multigap order parameter. Spatial mapping of the zero-bias conductance in magnetic field reveals the vortex lattice, which allows us to unequivocally link the observed conductance gap to superconductivity in ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$. The vortex lattice is found to be predominantly triangular with distortions at fields close to $\sim 0.7H_{c2}$.

Figure 1

(a) Body centered tetragonal crystal structure of ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$. (b) Topographic image of the surface after cleavage showing terraces which exhibit atomic periodicities and step heights of $\sim 2\AA (30\times 30{\mathrm{nm}}^2,T=4.5\mathrm{K}$). (c) High energy normalized tunneling spectrum taken at $T=200\mathrm{mK}$ showing a W-shaped feature close to the Fermi energy ($V_{\mathrm{rms}}=3\mathrm{mV}$). (d) Normalized tunneling spectrum recorded at $20\mathrm{mK} \left(V_{\mathrm{rms}}=40\mu \mathrm{V}\right)$, exhibiting a gaplike feature with two shoulders symmetric with respect to zero bias. Blue arrows indicate the main gap, and red arrows the low energy shoulder. The red line shows the best fit obtained for two gaps, one of $d$-wave symmetry at low energies and one of $s$-wave symmetry at high energies (for details see text and Ref. [28]).

Figure 2

(a) Differential conductance spectra (normalized at $-0.4\mathrm{mV}$ recorded at $200\mathrm{mK}$ in zero field (open black symbols) and in a field of $2\mathrm{T}$ (solid red symbols). (b) Scanning tunneling spectroscopy as a function of temperature ($V_{\mathrm{rms}}=24\mu \mathrm{V}$, except at 20 mK $V_{\mathrm{rms}}=40\mu \mathrm{V}$). Red lines represent fits with the Dynes equation for a single $s$-wave gap [29]; spectra have been shifted vertically for clarity. (c) Gap size as a function of temperature extracted from fits in (b); the red line represents the mean-field behavior expected for an $s$-wave order parameter, $\mathrm{\Delta }\left(T\right)={\mathrm{\Delta }}_{0}tanh\left(\frac{\pi }{2}\sqrt{\frac{T_{\mathrm{c}}}{T}-1}\right)$. The fit yields ${\mathrm{\Delta }}_0=67\pm 3\mu \mathrm{eV}$ and $T_{\mathrm{c}}=670\pm 30\mathrm{mK}$.

Figure 3

(a)–(e) Maps of the zero-bias tunneling conductance at 0.2 K ($150\times 150{\mathrm{nm}}^2,V_{\mathrm{rms}}=40\mu \mathrm{V}$) taken after cooling the sample in zero field as a function of magnetic field (0.5, 1, 1.5, 1.6, and 1.7 T), together with the autocorrelation. The data have been filtered for better contrast. The triangular vortex lattice is clearly seen. (f) Distance between the vortex cores as a function of magnetic field. The points are obtained from averaging the distances in the three high symmetry directions from the autocorrelation. Solid lines show the expected dependencies for a triangular (red line) and square lattice (blue line). (g) Anisotropy of the vortex lattice extracted from the autocorrelation of differential conductance maps as a function of magnetic field. As a measure for the anisotropy, we use $\chi$ [see Eq. (1); inset shows the anisotropy exemplarily for the autocorrelation of the map taken at $1.6\mathrm{T}]$. Maps taken with a tunneling set point of $U=5\mathrm{mV}$ [except (d) with $U=3\mathrm{mV}],I=0.6\mathrm{nA}$.

Figure 4

(a) Evolution of the azimuthal average of the normalized ZBTC $\sigma (r,0)$ at 0.2 K and 1, 1.5, and 1.6 T as a function of the radial distance $r$ from the vortex center (error bars represent the standard deviation of the data, average over multiple vortex cores). From fits of Eq. (2) to the individual curves we obtain $\xi =7.1\pm 0.3\mathrm{nm}$ on average (solid line). (b) Azimuthally averaged tunneling spectra as a function of distance from a vortex core measured at $1\mathrm{T}$. The zero-bias tunneling conductance is substantially larger inside the vortex core than away from the vortex core (data has been median filtered for clarity, spectra normalized at a bias voltage of $350\mu \mathrm{V}$). (c) Tunneling spectra from (b) in the vortex core (red triangles) and away from a vortex core (black squares). Even in the vortex core, the zero-bias tunneling conductance stays below the normal state value (i.e., at larger bias voltages).