{'fraction_non_alphanumeric': 0.02046783625730994, 'fraction_numerical': 0.005116959064327485, 'mean_word_length': 5.222727272727273, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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

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 an similar or equal to 2-nm-thick layer below the TI surfaces due to penetration of evanescent wave functions from the metallic surfaces into the bulk of TI. Averaging S(r) over a fewangstroms along the longitudinal direction defined by the current flow reveals a 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 the TI surface. Our analysis is based on an extension of the nonequilibrium Green's functions combined with density functional theory (NEGF+DFT) to situations involving noncollinear spins and spin-orbit coupling. We also demonstrate how DFT calculations with a properly optimized local orbital basis set can precisely match putatively more accurate calculations with a plane-wave basis set for the supercell of Bi2Se3.