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SU ( 2 ) non-Abelian holonomy and dissipationless spin current in semiconductors

2004; American Physical Society; Volume: 69; Issue: 23 Linguagem: Inglês

10.1103/physrevb.69.235206

1550-235X

Shuichi Murakami, Naoto Nagosa, Shoucheng Zhang,

Physics of Superconductivity and Magnetism

Following our previous work [S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003)] on the dissipationless quantum spin current, we present an exact quantum-mechanical calculation of this novel effect based on the linear-response theory and the Kubo formula. We show that it is possible to define an exactly conserved spin current, even in the presence of the spin-orbit coupling in the Luttinger Hamiltonian of $p$-type semiconductors. The light- and the heavy-hole bands form two Kramers doublets, and an $\text{SU}(2)$ non-Abelian gauge field acts naturally on each of the doublets. This quantum holonomy gives rise to a monopole structure in momentum space, whose curvature tensor directly leads to the novel dissipationless spin Hall effect, i.e., a transverse spin current is generated by an electric field. The result obtained in the current work gives a quantum correction to the spin current obtained in the previous semiclassical approximation.