Observation of Caroli–de Gennes–Matricon Vortex States in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$

The copper oxides present the highest superconducting temperature and properties at odds with other compounds, suggestive of a fundamentally different superconductivity. In particular, the Abrikosov vortices fail to exhibit localized states expected and observed in all clean superconductors. We have explored the possibility that the elusive vortex-core signatures are actually present but weak. Combining local tunneling measurements with large-scale theoretical modeling, we positively identify the vortex states in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. We explain their spectrum and the observed variations thereof from one vortex to the next by considering the effects of nearby vortices and disorder in the vortex lattice. We argue that the superconductivity of copper oxides is conventional, but the spectroscopic signature does not look so because the superconducting carriers are a minority.

Figure 1

(a) The self-consistent LDOS calculated in the BCS theory for an isolated vortex in a $d$-wave superconductor with Y123 band structure is shown along two paths starting at the vortex core (blue) and ending at two points 20 nm away from the core (green) along the nodal (11) and antinodal (10) directions. (b) Same data with the zero-field DOS subtracted from all curves. The vertical scale is arbitrary and the curves are shifted vertically for clarity. The insets show the ${\mathrm{CuO}}_2$ unit cell with the two crystallographic directions, and representations of the vortex core (gray disks and arrows indicating the supercurrent direction) with the color-coded paths of the two spectral traces.

Figure 2

(a) and (b) A $90\times 90{\mathrm{nm}}^2$ area on the (001) surface of Y123 in a 6 T field, colored by (a) the ratio of the STS tunneling conductance at $+5$ and $+17\mathrm{mV}$, and (b) the conductance at zero bias. The inset in (b) shows the STS spectrum averaged over the small outlined region between vortices. Two series of difference spectra (raw STS data minus average spectrum shown in the inset) along the 20 nm paths indicated in (a) are displayed in (c) and (d). The color encodes distance from the core as in Fig. 1. Panels (e) and (f) show the raw $dI/dV$ data along the two paths.

Figure 3

Series of difference spectra [generated as in Figs. 2 and 2] along several paths connecting (a) nearest-neighbor and (b) next-nearest-neighbor vortices. The spectra are shifted vertically and colored from blue (vortex center) to green (in-between two vortices).

Figure 4

(a) Same data as in Fig. 3 for traces joining nearest-neighbor (No. 1 and No. 3) and next-nearest-neighbor vortices (No. 6 and No. 8). (b) Calculated ratio $[N(\mathit{r},5\mathrm{meV})+N_{\mathrm{NSC}}(5\mathrm{meV})]/[N(\mathit{r},17\mathrm{meV})+N_{\mathrm{NSC}}(17\mathrm{meV})]$, where $N(\mathit{r},E)$ is the theoretical LDOS and $N_{\mathrm{NSC}}(E)$ represents the nonsuperconducting background [45]. The simulated spectral traces are deduced from the theoretical LDOS by following the exact same procedure as applied to the experimental data. The white dots in (a) and (b) show the vortex positions, determined as the locations of maxima in (a) and corresponding to the phase singularity points of the order parameter in the simulation (b).