Scanning tunneling spectroscopy of a dilute two-dimensional electron system exhibiting Rashba spin splitting

Abstract

Using scanning tunneling spectroscopy (STS) at 5 K in B-fields up to 7 T, we investigate the local density of states of a two-dimensional electron system (2DES) created by Cs adsorption on p-type InSb(110). The 2DES, which in contrast to previous STS studies exhibits a 2D Fermi level, shows standing waves at B = 0 T with corrugations decreasing with energy and with wave numbers in accordance with theory. In magnetic field percolating drift states are observed within the disorder broadened Landau levels. Due to the large electric field perpendicular to the surface, a beating pattern of the Landau levels is found and explained quantitatively by Rashba spin splitting within the lowest 2DES subband. The Rashba splitting does not contribute significantly to the standing wave patterns in accordance with theory.

Spectral properties and local density of states of disordered quantum Hall systems with Rashba spin-orbit coupling

“…In the light of previous formulas, we are now in a position to interpret the recent LDoS measurements 15,16 performed at high magnetic fields in InSb surface gases. We show in Fig.…”

“…The limit |S| → 0, for which the SO and the spin quantum numbers become equivalent λ ≡ σ, requires a relabeling of the energy level index according to the mapping n −σ + 1 → n, in order to reintroduce the picture of (Color online) Energy spectrum (in units of the cyclotron energy ωc) resulting from Eq. (19) in the absence of potential energy, as a function of the dimensionless SO parameter S. Values are taken from STS measurements 15,16 in InSb semiconductor: m * = 0.035m0, g = −21, α = 7 · 10 −11 eVm. The dashed line shows the particular value Sexp ≃ 0.88 (reached for B = 7 T) at which a pronounced spatial dispersion of the energy spin splitting has been noticed experimentally 16 .…”

“…Of course, we have chosen here the same material parameters as in Figs. 2 to 4, which are relevant for the experiments 15,16 . We have also considered a uniform Rashba coupling, so that the spatial dispersion of the energies is only induced by the scalar electrostatic disorder.…”

“…Recent STS measurements by Morgenstern et al 15,16 in InSb surface gases at high magnetic fields (within the quantum Hall regime) have shown that the energy spin splitting indeed varies spatially, what one could naively directly attribute to spatial fluctuations of the Rashba coupling. More precisely, a spin-split LDoS has been clearly observed only when the tip position is located close to the local extrema of the disorder potential, the energy spin splitting being typically 16 larger at hills of the potential landscape (close to local maxima), and smaller at valleys (near minima).…”

“…10) and HgTe 14 . Quite recently, it has also been determined by scanning tunneling spectroscopy (STS) in InSb surface gases 15,16 at high magnetic fields, with an extraction of the coupling constant α from the positions of the nodes of the density of states (DoS).…”