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 (Shi et al. in Phys Rev Lett 96:076604, 2006), we define the Kubo-like spin conductance GKsz and spin conductivity sigmaKsz . We prove that for any gapped, periodic, near-sighted discrete Hamiltonian, the above quantities are mathematically well defined and the equality GKsz =sigmaKsz 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 principal value trace and its directional version.
Marcelli, G., Panati, G., Tauber, C. (2019). Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-Like Terms. ANNALES HENRI POINCARE', 20(6), 2071-2099 [10.1007/s00023-019-00784-5].
Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-Like Terms
Marcelli, Giovanna;
2019-01-01
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 (Shi et al. in Phys Rev Lett 96:076604, 2006), we define the Kubo-like spin conductance GKsz and spin conductivity sigmaKsz . We prove that for any gapped, periodic, near-sighted discrete Hamiltonian, the above quantities are mathematically well defined and the equality GKsz =sigmaKsz 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 principal value trace and its directional version.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.