Edge states in mesoscopic Bi islands on superconducting Nb(110)

Islands of Bi showing (110)- and (111)-orientated facets were grown on a Nb(110) single crystal and were studied with a scanning tunneling microscope at low temperatures. On the (111) facets, several states localized at step edges are identified from maps of the local differential conductance. We find edge states on both types of zig-zag step edges that decay exponentially over a length scale of several nanometers into the terrace. These states agree with the necessary condition for topologically nontrivial edge states. Further, we find states localized at the atomic scale at the step edge, which we interpret as dangling bond states. To investigate the nature of these states, we studied the Bi(110) surface, where the sharply localized states form stripe patterns, while the more extended edge state does not show a strong lattice-periodic pattern. Thus, our findings indicate a causal link between the strongly localized edge states on Bi(111) and the stripe pattern on Bi(110) as they are both related to the zig-zag termination of the honeycomb structure of Bi. Finally, we observed a decay of the superconducting proximity gap of the Bi islands with island thickness.

Figure 1

Panels (a)–(c) are topographic STM images of Bi thin films of 1-, 7-, and 15-nm coverage grown at $60{}^{\circ }\mathrm{C}$. The height profiles along the dashed lines are shown below the respective images. Panels (d) and (e) are atomically resolved images of the (110) and (111) surfaces in the 7-nm sample. (f) Topographic image of a 50-nm sample annealed at $500{}^{\circ }\mathrm{C}$. (g) Sketch of the Bi(110) and Bi(111) islands, which are marked by dashed circles in panel (b).

Figure 2

(a) Topographic STM image of Bi(111) surface with ${120}^{\circ }$ zig-zag edges in the 7-nm sample (8.2 nm $\times$ 8.2 nm). (b) Maps of the differential conductance $dI/dV$ at different energies in the area marked by dashed lines in panel (a). (c) $dI/dV$ spectra taken on Edge 1, Edge 2, and the interior part of the terrace in panel (a).

Figure 3

(a) The $dI/dV$ evolution from the zig-zag edge to the interior terrace on the Bi(111) surface of the 15-nm sample ($V=350$ mV, $I=1.07$ nA, modulation is $U_{rms}=3$ mV, 3.07 kHz). The height profile of the step edge in constant current mode is shown in orange. The position of the step edge is marked by the solid line, and the edge states area and bulk states area are divided by the dashed line. We indicate the edge (E), near-edge (NE), and terrace regions. (b) Averaged spectra of the three areas shown in panel (a). (c) Topographic image and $dI/dV$ maps near the same step edge as in panel (a) (14.4 nm $\times$ 3.1 nm). (d) $dI/dV$ line profiles at the different energies shown in panel (a).

Figure 4

DOS near the edge of Bi(111) facet of islands of local thickness of (a) 35 nm [same data as in Fig. 3] and (b) 25 nm. Positions of step edges are marked by dashed lines. Their energies shift from $\approx 155$ to $\approx 180$ meV going to higher local thickness.

Figure 5

(a) Topographic image of the Bi(110) surface in the 15-nm sample, where the spectrum is measured for every pixel (25 nm $\times$ 25 nm, $V=0.3$ V, $I=950$ pA, modulation is $U_{rms}=7$ mV, 3.07 kHz). (b) The spectral weight of lattice spots and the averaged spectrum of the area in panel (a), and the data extracted from Ref. [28] are plotted together. (c) The DOS measured in the marked area of panel (a) at the energy marked by black arrows in panel (b) (8.7 nm $\times$ 8.7 nm) and the corresponding FFT results of panel (a). The yellow dashed lines are at the same position in different maps. The momentum of “lattice 1” is parallel to the island direction and that of “lattice 2” is perpendicular to the island direction. (d) The DOS distribution of the zig-zag edge of Bi(111) in Fig. 2 is compared to (e) the energy dependence of the intensity ratio of different lattice spots and (f) the phase of different lattice spots. (g) The sketch of the structure of the Bi(110) and Bi(111) surfaces, where the pink circles and ellipses indicate the dangling bond states. The dashed line indicates the mirror plane of the Bi(110) surface.

Figure 6

The typical tunneling spectra for samples with different thicknesses showing superconducting proximity gaps. The spectra of a 35-nm island were taken at $V=5$ mV and $I=155$ pA, and those for a 25-nm island were taken at $V=7$ mV and $I=660$ pA. Bias modulation of lock-in detection $U_{rms}=0.3$ mV, 3.07 kHz for all spectra.