Abstract
The spin Hall effect is investigated in a two-orbital tight-binding model on a honeycomb lattice. We show that the model exhibits three topologically-different insulating phases at half filling, which are distinguished by different quantized values of the spin Hall conductivity. We analytically determine the phase boundaries, where the valence and conduction bands touch with each other with forming the Dirac nodes at the Fermi level. The results are discussed in terms of the effective antisymmetric spin-orbit coupling. The relation to the Kane- Mele model and implications for a magnetoelectric effect are also discussed.
Highlights
The spin-orbit coupling has drawn much interest in condensed matter physics since it leads to various fascinating phenomena in spin-charge-orbital coupled systems, such as the magetoelectric effect [1, 2, 3, 4, 5], the spin Hall effect [6, 7, 8], and the noncentrosymmetric superconductivity [9, 10]
When the mirror symmetry along the z direction is broken, the so-called Rashba-type antisymmetric spin-orbit coupling exists, whose g vector is given by g(k) = [17, 18]
Summary and Concluding Remarks We have investigated the topological aspect of a two-orbital model on a honeycomb lattice
Summary
The spin-orbit coupling has drawn much interest in condensed matter physics since it leads to various fascinating phenomena in spin-charge-orbital coupled systems, such as the magetoelectric effect [1, 2, 3, 4, 5], the spin Hall effect [6, 7, 8], and the noncentrosymmetric superconductivity [9, 10]. A key concept in understanding of such phenomena is the antisymmetric spin-orbit coupling. It is written in a general form in the momentum representation: HASOC = α g(k) · s(k), (1). In Eq (1), g(k) is antisymmetric with respect to k, and the direction of the g vector is determined by the symmetry of the crystal. When the mirror symmetry along the z direction is broken, the so-called Rashba-type antisymmetric spin-orbit coupling exists, whose g vector is given by g(k) = (ky, −kx, 0) [17, 18]
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