Spin Current Density Functional Theory of the Quantum Spin-Hall Phase

Abstract

The spin current density functional theory (SCDFT) is the generalization of the standard DFT to treat a fermionic system embedded in the effective external field produced by the spin-orbit coupling interaction. Even in the absence of a spin polarization, the SCDFT requires the electron-electron potential to depend on the spin currents ${\mathbf{J}}^x$, ${\mathbf{J}}^y$ and ${\mathbf{J}}^z$, which only recently was made possible for practical relativistic quantum-mechanical simulations [Phys. Rev. B {\bf 102}, 235118 (2020)]. Here, we apply the SCDFT to the quantum spin-Hall phase and show how it improves (even qualitatively) the description of its electronic structure relative to the DFT. We study the Bi (001) 2D bilayer and its band insulator to topological insulator phase transition (via $s+p_z\leftrightarrow p_x+i{p}_y$ band inversion) as a function of mechanical strain. We show that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone at the $\Gamma$ point in the valence band structure at the onset of the topological phase transition. Finally, the valence band structure of this system is rationalized using a simple first-order $\mathbf{k}\cdot \mathbf{p}$ quasi-degenerate perturbation theory model.

5 pages, 2 figures

References in corpus (6)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
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Cited by in corpus (2)

• First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Modern Theory with Modern Functionals
• Inducing Quantum Phase Transitions in Non-Topological Insulators Via Atomic Control of Sub-Structural Elements