We consider a 2-dimensional Bloch-Landau-Pauli Hamiltonian for a spinful electron in a constant magnetic field subject to a periodic background potential. Assuming that the z-component of the spin operator is conserved, we compute the linear response of the associated spin density of states to a small change in the magnetic field, and identify it with the spin Hall conductivity. This response is in the form of a spin Chern marker, which is in general quantized to a half-integer, and to an integer under the further assumption of time-reversal symmetry. Our result is thus a generalization to the context of the quantum spin Hall effect of the well-known formula by Středa, which is formulated instead for charge transport.
Středa formula for charge and spin currents / Monaco, D.; Moscolari, M.. - In: REVIEWS IN MATHEMATICAL PHYSICS. - ISSN 0129-055X. - 32:4(2020), p. 2060003. [10.1142/S0129055X2060003X]
Středa formula for charge and spin currents
Monaco D.
;Moscolari M.
2020
Abstract
We consider a 2-dimensional Bloch-Landau-Pauli Hamiltonian for a spinful electron in a constant magnetic field subject to a periodic background potential. Assuming that the z-component of the spin operator is conserved, we compute the linear response of the associated spin density of states to a small change in the magnetic field, and identify it with the spin Hall conductivity. This response is in the form of a spin Chern marker, which is in general quantized to a half-integer, and to an integer under the further assumption of time-reversal symmetry. Our result is thus a generalization to the context of the quantum spin Hall effect of the well-known formula by Středa, which is formulated instead for charge transport.File | Dimensione | Formato | |
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