The anomalous spin texture as the probe for interactions in $Bi_{2-y} Sb_y Se_x Te_{3-x}$

Abstract

The surface state of a three dimensional strong topological insulator (TI) is well described in the independent particle picture (IPP) by an isotropic Dirac cone at the Γ-point and perpendicular spin-momentum locking. Away from this point, the crystal point group symmetry causes anisotropic effects on the surface spectrum where a number of unusual effects are experimentally observed. In particular, the perturbative violations of the perpendicular spin-momentum locking frequently observed in many experiments remains to be a poorly understood feature theoretically. In parallel, the existence of electron-phonon interaction has been unquestionably verified by a number of experimental groups. In this article, we device an interacting theory of the spin texture using the spin-dependent self-energy formalism. We observe that the interactions lead to the observable spintexture anomalies in the presence of a Fermi surface anisotropy while weakly affecting the energy bands. In particular, the experimental observation of the six-fold symmetric modulation of the in-plane spin in the Bi2−ySbySe3−xT ex family and the resulting violation of the spin-momentum locking is explained using the coupling of an optical surface phonon to the surface electrons reported in earlier experiments. We also discuss recent puzzling results of the out-of-plane spin polarization experiments in this context.Our results introduce an interacting approach to the spin-related anomalies where the anisotropy of the Dirac cone around the Fermi surface proves to have an unconventional role. New experiments reporting unusual spin orientations in other materials with different symmetries signify that the theory introduced here may be relevant to a larger set of Dirac materials.