Nonequilibrium spin density around surfaces of current-carrying topological insulator thin film: A first-principles quantum transport study
We study microscopic details, over $\lesssim 1$ \AA{} length scale, of the nonequilibrium spin density $\mathbf{S}(\mathbf{r})$ driven by unpolarized charge current injection into a ballistic thin film of Bi$_2$Se$_3$ as a prototypical topological insulator (TI) material. We find a complex nonequilibrium spin texture on the surfaces of TI, as well as within $\simeq 2$ nm thick layer near the surfaces driven by penetration of evanescent wavefunctions from the metallic surfaces into the bulk. Averaging the spin texture over few \AA{} yields large nonzero component of $\mathbf{S}(\mathbf{r})$ in the direction transverse to the current flow. 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 its surface. Our analysis is based on an extension of the nonequilibrium Green functions combined with density functional theory 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 Bi$_2$Se$_3$.