期刊
PHYSICAL REVIEW B
卷 69, 期 23, 页码 -出版社
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevB.69.235206
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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 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.
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