Anisotropic vortices on superconducting Nb(110)

We investigate the electronic properties of type-II superconducting Nb(110) in an external magnetic field. Scanning tunneling spectroscopy reveals a complex vortex shape which develops from circular via coffee bean shaped to elliptical when decreasing the energy from the edge of the superconducting gap to the Fermi level. This anisotropy is traced back to the local density of states of Caroli–de Gennes–Matricon states which exhibits a direction-dependent splitting. Oxidizing the Nb(110) surface triggers the transition from the clean to the dirty limit, attenuates the vortex bound states, and leads to an isotropic appearance of the vortices. Density functional theory shows that the Nb(110) Fermi surface is stadium shaped near the $\overline{\mathrm{\Gamma }}$ point. Calculations within the Bogoliubov–de Gennes theory using these Fermi contours consistently reproduce the experimental results.

Figure 1

(a) Topography of clean Nb(110). (b) Atomic resolution scan with the indicated unit cell. (c) Tunneling spectrum of the superconducting gap. (d)–(g) Constant-separation $dI/dU$ maps taken at the voltages marked by colored circles in (c) at ${\mu }_{0}H=100$ mT. Whereas the vortices appear round shaped at a bias voltage close to the edge of the gap, they deform into ellipses when approaching zero bias. (h) Stacked representation showing the bias-dependent LDOS inside the vortex in the energy window from 0 to 2 mV. (i) Fermi level $(U=0$ V) $dI/dU$ map revealing an elliptical shape elongated along the [001] direction with a compression $b/a=0.55\pm 0.1$. (j),(k) Waterfall plot of tunneling spectra taken along the lines labeled $b$ and $a$ in (i), respectively. With increasing distance from the vortex core along the [$1\overline{1}0$] direction the zero-bias peak splits into two ridges, resulting in the appearance of an $\mathsf{X}$-shaped feature as indicated by two arrows and dashed lines in (j). In contrast, along the [001] direction only a vanishing of the peak without any splitting is observed (k). Scan parameters: (a)–(k) $I_{\mathrm{set}}=200$ pA; $T=1.4$ K (a) $U_{\mathrm{set}}=-1$ V; (c) $U_{\mathrm{set}}=-10$ mV; (d)–(g) $U_{\mathrm{set}}=-100$ mV; (h)–(i) $U_{\mathrm{set}}=-10$ mV; (j)–(k) $U_{\mathrm{set}}=-7$ mV.

Figure 2

(a) Tunneling spectra measured on different Nb surfaces in an external magnetic field: (black) the fully gapped tunneling spectrum of clean Nb(110) far away from any vortex; (blue) intense zero-bias peak in the center of the vortex on clean Nb(110); (green) less intensive peak in a vortex core on ${\mathrm{NbO}}_x$ phase II; (red) Ohmic behavior in vortex core on ${\mathrm{NbO}}_x$ phase I. Stabilization parameters: $U_{\mathrm{set}}=-7$ mV, $I_{\mathrm{set}}=100$ pA. (b)–(d) show differential conductance $dI/dU$ maps of a single vortex on ${\mathrm{NbO}}_x$ phase I imaged at (b) $U=1$ mV, (c) $U=0.8$ mV, and (d) $U=0$ mV. (e) Tunneling spectra measured along the line in (d). No zero-bias feature is observed. Stabilization parameters: $U_{\mathrm{set}}=-5$ mV, $I_{\mathrm{set}}=100$ pA, ${\mu }_{0}H=100$ mT, $T=1.5$ K.

Figure 3

(a) Calculated Fermi surface of Nb(110). Red lines denote pockets around the $\overline{\mathrm{\Gamma }}$ point. (b) Hypothetical Fermi surface and (c) Fermi velocity of the dominant Fermi contour. (d) Calculated LDOS along the two principal directions crossing the vortex core. (e) Excitation energy-dependent LDOS profiles after thermal broadening with $k_{B}T\simeq 0.26{\mathrm{\Delta }}_0$.