Anisotropic Electron-Electron Interactions in Topological Insulators
HgTe forms a two-dimensional topological insulator when sandwiched between CdTe barriers for a HgTe layer wider than the critical thickness. In this study we derive single-particle interaction Hamiltonians describing the physics of these compounds by using k • p theory and extended Kane model. We include contributions from upper conduction bands with orbital states of p-symmetry that bring about the terms describing lack of inversion symmetry in host semiconductors. A crucial ingredient is hetero-interface contribution to intrinsic spin-orbit interactions that drives significant anticrossing gaps in spectra at zero wavevector, but results in a circle of spectral degeneracies at finite wavevectors. This term arises naturally from a correct treatment of probability current conservation through the heterostructure as a whole, and couples to the Dirac velocity and effective particle mass to yield a shift in the trivial to topological-insulator transition point. We further demonstrate a coupling to spin-orbit terms such as Dresselhaus and Rashba interactions and discuss a probable method of achieving control of the quantized spin Hall current via a gated potential. Additionally we study the effects of new interactions on Berry curvature and spin-Hall conductance. In the second part of this study we derive two-particle interaction Hamiltonians by treating k • p band mixing terms in the extended Kane model on the same footing as the Coulomb interaction. We obtain a third order contribution to the exchange interaction arising via two mechanisms, both Coulomb mediated: i) a coupling of the spin of one charge carrier to the relative orbital motion of the other and ii) valence-conduction band mixing of spin carriers. We construct an edge model description of the system and by projecting novel bulk terms onto the edge. Although the starting model incorporates terms which break bulk inversion asymmetry we will show the new spin coupling terms no not require either BIA or Rashba coupling, making it applicable to any zincblende lattice. We find that the spin-dependent contribution does not conserve total spin, leading, e.g., to Dzyaloshinskii-Moriya exchange term. Such potential in an electron-electron collision provides a new mechanism for relaxation of spin polarization and a non-vanishing contribution to the quantized spin Hall conductance.
Lyanda-Geller, Purdue University.
Quantum physics|Physics|Condensed matter physics
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