Strongly anisotropic spin-orbit splitting in a two-dimensional electron gas

Abstract

Near-surface two-dimensional electron gases on the topological insulator Bi2Te2Se are induced by electron doping and studied by angle-resolved photoemission spectroscopy. A pronounced spin-orbit splitting is observed for these states. The k-dependent splitting is strongly anisotropic to a degree where a large splitting (≈ 0.06Å −1 ) can be found in theΓM direction while the states are hardly split alongΓK. The direction of the anisotropy is found to be qualitatively inconsistent with results expected for a third-order anisotropic Rashba Hamiltonian. However, a k·p model that includes the possibility of band structure anisotropy as well as both isotropic and anisotropic third order Rashba splitting can explain the results. The isotropic third order contribution to the Rashba Hamiltonian is found to be negative, reducing the energy splitting at high k. The interplay of band structure, higher order Rashba effect and tuneable doping offers the opportunity to engineer not only the size of the spin-orbit splitting but also its direction.PACS numbers: 73.21.Fg, The spin-orbit interaction in solids is the basis for many fascinating phenomena, such as the spin Hall effect [1], quantum spin Hall effect [2-4] and the quantum anomalous Hall effect [5]. It is also of considerable importance in conceptual spintronics devices, for instance in the Datta Das spin field effect transistor [6,7]. An important starting point for the description of spin-orbit effects and the lifting of degeneracies in a (two-dimensional) free electron gas has been presented by Rashba and Bychkov [8] and this has been used to describe strong spinorbit splittings in a variety of surface electronic states such as Au (111) (111) [12] and others. More recently, it has been found that the bulk-derived two-dimensional electron gases (2DEGs) near the surfaces of the topological insulator Bi 2 Se 3 can also show a strong Rashba-type splitting and that the strength of the splitting can even be tuned by the filling of the state [13][14][15][16]. Indeed, even the dispersion of the topologically protected surface states on these materials can be viewed in the context of anisotropic Rashba-type splitting [17,18]. For several systems, it has been found that the simple Rashba effect which is linear in k is insufficient to describe the spin-orbit splitting and further correction terms such as a cubic anisotropy [17,18] and a cubic isotropic correction were introduced [19].Here we show that strongly Rashba-split 2DEGs with intriguing new properties can be created by surfacedoping of the topological insulator Bi 2 Te 2 Se. The band splitting in these 2DEGs is anisotropic to a degree that the bands are strongly spin-split in one direction and almost degenerate in another, possibly paving the way towards new anisotropic transport phenomena. At first glance, the observed anisotropy appears to be at odds with the spin-orbit splitting predicted for the C 3v symmetry of the material's (111) surface and the findings can only be reconciled with the results of a model Hamilton...

Fermiology and Superconductivity of Topological Surface States in PdTe2

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Tunable two-dimensional electron gas at the surface of thermoelectric materialIn4Se3

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Orbital angular momentum analysis for giant spin splitting in solids and nanostructures

“…Here α is a constant, σ x and σ y are Pauli matrices, and , − e , m , , and are the electron wavevector, charge, mass, spin, and momentum, respectively. This model has been used to describe spin-orbit-induced splitting in many materials 6 , 9 , 16 , 20 , 22 , 25 – 27 . However, the splitting size from H SO is too small to explain GSS if E ext in H SO is replaced with the symmetry-breaking part of internal and external electric fields.…”

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