Abstract
We consider a quantum Hall system with an antidot acting as a energy dependent scatterer. In the purely charge case, we find deviations from the Wiedemann-Franz law that take place in the nonlinear regime of transport. We also discuss Peltier effects beyond linear response and describe both effects using magnetic-field asymmetric transport coefficients. For the spin case such as that arising along the helical edge states of a two-dimensional topological insulator, we investigate the generation of spin currents as a result of applied voltage and temperature differences in samples attached to ferromagnetic leads. We find that in the parallel configuration the spin current can be tuned with the leads' polarization even in the linear regime of transport. In contrast, for antiparallel magnetizations the spin currents has a strict nonlinear dependence on the the applied fields.
Highlights
We have analysed the nonlinear transport of quantum Hall setups subjected to the voltage and temperature biases
The potential landscape of the nanostructure depends on the injected charges due to both, the voltage and temperature gradients
Using this theory we find the symmetry relations of the nonlinear transport coefficients for a quantum Hall bar with an inserted antidot
Summary
Under the application of strong fields, electron transport becomes nonlinear and new effects arise: rectification [1, 2, 3, 4, 5, 6, 7], magnetic-field asymmetries[8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], and the generation of higher harmonics [25, 26, 27]. The self-consistent procedure must include electron-electron interactions that restore current conservation and gauge invariance beyond linear response It is the nontrivial dependence of the screening potential on voltage and magnetic fields that explains both rectification effects and magnetic-asymmetries, respectively. The former leads to the creation of a voltage drop in response to a temperature difference θ in the open circuit case The latter is based on the fact that electrons carry energy in addition to charge, and a heat current flows in the presence of an electric current. We discuss thermoelectric effects beyond linear response for quantum Hall bars with an inserted antidot This system allows for an investigation of the underlying symmetries while providing, at the same time, a strong interaction and energy dependent scattering [49, 50]. Whereas the normal case already leads to the generation of pure spin currents [52], we here find a competition with the polarized currents injected from the magnetic contacts
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