Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulatorBi2Se3: A first-principles quantum transport study

Abstract

We predict that unpolarized charge current injected into a ballistic thin film of prototypical topological insulator (TI) Bi2Se3 will generate a noncollinear spin texture S(r) on its surface. Furthermore, the nonequilibrium spin texture will extend into 2 nm thick layer below the TI surfaces due to penetration of evanescent wavefunctions from the metallic surfaces into the bulk of TI. Averaging S(r) over few Å along the longitudinal direction defined by the current flow reveals large component pointing in the transverse direction. In addition, we find an order of magnitude smaller out-of-plane component when the direction of injected current with respect to Bi and Se atoms probes the largest hexagonal warping of the Dirac-cone dispersion on TI surface. Our analysis is based on an extension of the nonequilibrium Green functions combined with density functional theory (NEGF+DFT) to situations involving noncollinear spins and spin-orbit coupling. We also demonstrate how DFT calculations with properly optimized local orbital basis set can precisely match putatively more accurate calculations with plane-wave basis set for the supercell of Bi2Se3.

Giant Spin Pumping and Inverse Spin Hall Effect in the Presence of Surface and Bulk Spin−Orbit Coupling of Topological Insulator Bi2Se3

“…17−22 Recent experiments studying spin torque ferromagnetic resonance (ST-FMR), spin-dependent tunneling and dc current-driven switching have indeed demonstrated that TIs are characterized by charge-to-spin conversion efficiency which is an order of magnitude larger than that generated by heavy-metals at room temperature (in Bi 2 Se 3 ) 23, 24 and up to 2 orders of magnitude larger at liquid helium temperature (in (Bi,Sb) 2 Te 3 ). 25 In the absence of bulk charge carriers, one of the key mechanisms 22 behind spin torque is current-driven nonequilibrium spin density due to spin-momentum locking on the surface of TI, which is a substantially enhanced 26,27 variant of the so-called Edelstein 28 effect originally predicted for two-dimensional electron gases with the Rashba SOC.…”

Antidamping spin-orbit torque driven by spin-flip reflection mechanism on the surface of a topological insulator: A time-dependent nonequilibrium Green function approach

“…Here H 0 is the minimal tight-binding model for 3D TIs like Bi 2 Se 3 on a cubic lattice of spacing a with four orbitals per site [37]. The thickness, L TI z = 8a of the TI layer is sufficient to prevent hybridization between its top and bottom metallic surface states [18]. The time-dependent potential…”

“…1. In fact, electrons also flow within a thin layer (of thickness 2 nm in Bi 2 Se 3 as the prototypical TI material) underneath the top and bottom surfaces due to top and bottom metallic surfaces of the TI doping the bulk via evanescent wave functions [18]. Therefore, in this study we consider more realistic and experimentally relevant [28] F/TI bilayer geometries, illustrated in Fig.…”

“…For example, very recent experiments [14][15][16] have replaced HM with threedimensional topological insulators (3D TIs) [17]. The TIs enhance [18][19][20] (by a factor v F /α R , where v F is the Fermi velocity on the surface of TI and α R is the Rashba SOC strength [21,22] at the F/HM interface) the transverse nonequilibrium spin density driven by the longitudinal charge current, which is responsible for the large fieldlike SOT component [20,23] observed experimentally [14][15][16].…”

Dirac spin-orbit torques and charge pumping at the surface of topological insulators

“…Various phenomena such as the topological magnetoelectric effect [30,31], STT and current-driven magnetization dynamics [32][33][34][35][36][37], the interplay between spin and charge [38][39][40][41][42], and spin transport in magnetic TIs [43][44][45][46][47][48] have been studied theoretically. Despite these important theoretical efforts, major puzzles remain to be understood such as the emergence of gigantic dampinglike torque [19,20], the sizable angular dependence of the SOT [20], and the significant discrepancies between the spin-charge conversion rates reported in the SOT experiments [19,20,26,27] and the spin-pumping experiments [22][23][24][25].…”