Local detection of spin-orbit splitting by scanning tunneling spectroscopy

We demonstrate that the spin-orbit coupling of two-dimensional surface states can be detected locally by scanning-tunneling spectroscopy (STS). The spin splitting of the surface state induces a singularity in the local density of states which can be detected as a distinct peak in the differential conductance spectrum. From the STS spectrum we can determine the Rashba energy as a measure of the strength of the spin splitting. Its detection and imaging are demonstrated for the surface alloys Bi and Pb on Ag(111), which exhibit particularly large spin-split band structures. The influence of the spin splitting on the surface-state STS spectra of close-packed noble metal surfaces is also discussed.

Figure 1

(Color online) (a) Topography by STM of the long-range-ordered $\sqrt{3}\times \sqrt{3}R30°$ $\mathrm{Bi}∕\mathrm{Ag}\left(111\right)$ surface alloy (bias voltage, $-3\mathrm{mV}$; tunneling current, $1\mathrm{nA}$). (b) Local density of states measured by STS.

Figure 2

(Color online) Band structure measurements by ARPES in the vicinity of the $\overline{\Gamma }$ point. The dispersion is traced by two blue (dark gray) parabolas to guide the eye. (a) Spin-split bands of the $\mathrm{Bi}∕\mathrm{Ag}\left(111\right)$ surface alloy with band maximum in the occupied states. (b) Spin-split bands of the $\mathrm{Pb}∕\mathrm{Ag}\left(111\right)$ surface alloy with band maximum in the empty states. (c) Calculated energy dispersion in the nearly free electron model with (red solid lines) and without (blue dashed line) spin-orbit coupling. (d) The corresponding density of states.

Figure 3

(Color online) Differential conductance spectra near the surface-state onsets for different systems: (a) $\mathrm{Bi}∕\mathrm{Ag}\left(111\right)$ surface alloy and (b) $\mathrm{Pb}∕\mathrm{Ag}\left(111\right)$ surface alloy. The red dotted lines correspond to the measured $dI∕dV$ spectra, while the blue (dark gray) lines show a fit to the density of states within the Tersoff-Hamann model. The green (light gray) lines show the unconvoluted density of states.

Figure 4

(a) Topography of the $\mathrm{Bi}∕\mathrm{Ag}\left(111\right)$ surface alloy measured at a bias voltage of $-0.137\mathrm{V}$ in a region with smaller island sizes. The bright spots are associated with Bi atoms. (b) Simultaneously acquired $dI∕dV$ map. Bright areas indicate a strong spin-split peak. Toward the island boundaries the peak vanishes.

Figure 5

(Color online) $dI∕dV$ spectra along a line across an alloy patch. The corresponding topographic line section (solid line) is superimposed onto the image with the borders marked as vertical lines. The peak intensity rapidly decreases near the border of the alloy patch.