Scanning Tunneling Spectroscopy in the Superconducting State and Vortex Cores of the $\beta$-Pyrochlore $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$

We performed the first scanning tunneling spectroscopy measurements on the pyrochlore superconductor ${\mathrm{KOs}}_2{\mathrm{O}}_6$ ($T_c=9.6\mathrm{K}$) in both zero magnetic field and the vortex state at several temperatures above 1.95 K. This material presents atomically flat surfaces, yielding spatially homogeneous spectra which reveal fully gapped superconductivity with a gap anisotropy of 30%. Measurements performed at fields of 2 and 6 T display a hexagonal Abrikosov flux line lattice. From the shape of the vortex cores, we extract a coherence length of 31–40 Å, in agreement with the value derived from the upper critical field $H_{\mathrm{c}2}$. We observe a reduction in size of the vortex cores (and hence the coherence length) with increasing field which is consistent with the unexpectedly high and unsaturated upper critical field reported.

Figure 1

(a) Topography of ${\mathrm{KOs}}_2{\mathrm{O}}_6$ ($T=2\mathrm{K}$, $R_t=60\mathrm{M}\Omega$); the box shows the measurement area for the vortex maps. (b) Spectroscopic trace along a 100 Å path taken on an atomically flat region with one spectrum every 1 Å. The spectra show raw data offset vertically for clarity ($T=2\mathrm{K}$, $R_t=20\mathrm{M}\Omega$).

Figure 2

Experimental and theoretical tunneling spectra. (a) $dI/dV$ spectra normalized at $+6\mathrm{mV}$ for different temperatures from 1.95 to 10 K (spectra are offset vertically for clarity). (b) Optimal parameters and reduced ${\chi }^2$ (${\chi }_{\nu }^2$) for our fits performed in a $-2$ to $+2\mathrm{mV}$ energy window with different theoretical models. (c),(d) Comparison of the experimental spectrum (c) and its derivative $d^{2}I/d{V}^2$ (d) at low temperature and low energy with the different theoretical models; the thickness of the experimental curves corresponds to the variance of 0.05 for both $dI/dV$ and $d^{2}I/d{V}^2$.

Figure 3

Spectroscopic traces at $T=2\mathrm{K}$ across vortices for a field of 2 T (a) and 6 T (b). The spectra at the vortex centers are highlighted in red. The zero-bias conductance and the locations of the traces are shown in the corresponding insets.

Figure 4

(a),(b) Experimental ZBC maps ($T=2\mathrm{K}$, $I=0.5\mathrm{nA}$, $V=15\mathrm{mV}$) normalized to the background conductance (at $+6\mathrm{mV}$) for 2 and 6 T, respectively, with corresponding fits (c),(d); large values (red) correspond to normal regions (i.e., vortex cores) and low values (blue) to superconducting (gapped) regions. (e),(f) Experimental ZBC profiles across vortex centers (along the paths shown on the maps) together with the corresponding profiles from the 2D fits.