We investigate spin transport in $2$-dimensional insulators, with the long-term goal of establishing whether any of the transport coefficients corresponds to the Fu-Kane-Mele index which characterizes $2d$ time-reversal-symmetric topological insulators. Inspired by the Kubo theory of charge transport, and by using a proper definition of the spin current operator cite{ShiZhangXiaoNiu}, we define the Kubo-like spin conductance $G_K^{s_z}$ and spin conductivity $sigma_K^{s_z}$. We prove that for any gapped, periodic, near-sighted discrete Hamiltonian, the above quantities are mathematically well-defined and the equality $G_K^{s_z} = sigma_K^{s_z}$ holds true. Moreover, we argue that the physically relevant condition to obtain the equality above is the vanishing of the mesoscopic average of the spin-torque response, which holds true under our hypotheses on the Hamiltonian operator. A central role in the proof is played by the trace per unit volume and by two generalizations of the trace, the emph{principal value trace} and its directional version.

Spin conductance and spin conductivity in topological insulators: analysis of Kubo-like terms / Marcelli, Giovanna; Panati, Gianluca; Tauber, Clément Adrien. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - (2019).

Spin conductance and spin conductivity in topological insulators: analysis of Kubo-like terms

Giovanna Marcelli;Gianluca Panati
;
Tauber, Clément Adrien
2019

Abstract

We investigate spin transport in $2$-dimensional insulators, with the long-term goal of establishing whether any of the transport coefficients corresponds to the Fu-Kane-Mele index which characterizes $2d$ time-reversal-symmetric topological insulators. Inspired by the Kubo theory of charge transport, and by using a proper definition of the spin current operator cite{ShiZhangXiaoNiu}, we define the Kubo-like spin conductance $G_K^{s_z}$ and spin conductivity $sigma_K^{s_z}$. We prove that for any gapped, periodic, near-sighted discrete Hamiltonian, the above quantities are mathematically well-defined and the equality $G_K^{s_z} = sigma_K^{s_z}$ holds true. Moreover, we argue that the physically relevant condition to obtain the equality above is the vanishing of the mesoscopic average of the spin-torque response, which holds true under our hypotheses on the Hamiltonian operator. A central role in the proof is played by the trace per unit volume and by two generalizations of the trace, the emph{principal value trace} and its directional version.
2019
Bloch frames Wannier functions; Chern insulators; Haldane model; periodic Schrödinger operators; quantum anomalous Hall effect; analysis
01 Pubblicazione su rivista::01a Articolo in rivista
Spin conductance and spin conductivity in topological insulators: analysis of Kubo-like terms / Marcelli, Giovanna; Panati, Gianluca; Tauber, Clément Adrien. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - (2019).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1248036
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