Nonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi$_2$Se$_3$: A first-principles quantum transport study

摘要

We predict that unpolarized charge current injected into a ballistic thinfilm of prototypical topological insulator (TI) Bi$_2$Se$_3$ will generate a{\it noncollinear spin texture} $\mathbf{S}(\mathbf{r})$ on its surface.Furthermore, the nonequilibrium spin texture will extend into $\simeq 2$ nmthick layer below the TI surfaces due to penetration of evanescentwavefunctions from the metallic surfaces into the bulk of TI. Averaging$\mathbf{S}(\mathbf{r})$ over few \AA{} along the longitudinal directiondefined by the current flow reveals large component pointing in the transversedirection. In addition, we find an order of magnitude smaller out-of-planecomponent when the direction of injected current with respect to Bi and Seatoms probes the largest hexagonal warping of the Dirac-cone dispersion on TIsurface. Our analysis is based on an extension of the nonequilibrium Greenfunctions combined with density functional theory (NEGF+DFT) to situationsinvolving noncollinear spins and spin-orbit coupling. We also demonstrate howDFT calculations with properly optimized local orbital basis set can preciselymatch putatively more accurate calculations with plane-wave basis set for thesupercell of Bi$_2$Se$_3$.