Purely linear response of the quantum Hall current to space-adiabatic perturbations
arXiv:2112.03071 · doi:10.1007/s11005-022-01574-7
Abstract
Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond the linear response regime. In particular, we prove that, in quantum Hall systems and Chern insulators, the transverse response current is quantized up to any order in the strength of the inducing electric field. The latter is introduced as a perturbation to a periodic, spectrally gapped equilibrium Hamiltonian by means of a linear potential; existing proofs of the exactness of Kubo formula rely instead on a time-dependent magnetic potential. The result applies to both continuum and discrete crystalline systems modelling the quantum (anomalous) Hall effect.
18 pages
References in corpus (5)
- High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
- On A Proper Definition of Spin Current
- Precise quantization of anomalous Hall effect near zero magnetic field
- Linear response theory for magnetic Schroedinger operators in disordered media
- From charge to spin: analogies and differences in quantum transport coefficients