We consider electrostatically coupled quantum dots in topological insulators, otherwise confined and gapped by a magnetic texture. By numerically solving the (2+1) Dirac equation for the wave packet dynamics, we extract the energy spectrum of the cou
pled dots as a function of bias-controlled coupling and an external perpendicular magnetic field. We show that the tunneling energy can be controlled to a large extent by the electrostatic barrier potential. Particularly interesting is the coupling via Klein tunneling through a resonant valence state of the barrier. The effective three-level system nicely maps to a model Hamiltonian, from which we extract the Klein coupling between the confined conduction and valence dots levels. For large enough magnetic fields Klein tunneling can be completely blocked due to the enhanced localization of the degenerate Landau levels formed in the quantum dots.
Recent experiments on resonant tunneling structures comprising (Ga,Mn)As quantum wells [Ohya et al., Nature Physics 7, 342 (2011)] have evoked a strong debate regarding their interpretation as resonant tunneling features and the near absences of ferr
omagnetic order observed in these structures. Here, we present a related theoretical study of a GaAs/(Ga,Mn)As double barrier structure based on a Greens function approach, studying the self-consistent interplay between ferromagnetic order, structural defects (disorder), and the hole tunnel current under conditions similar to those in experiment. We show that disorder has a strong influence on the current-voltage characteristics in efficiently reducing or even washing out negative differential conductance, offering an explanation for the experimental results. We find that for the Be lead doping levels used in experiment the resulting spin density polarization in the quantum well is too small to produce a sizable exchange splitting.
Theory of the electron spin relaxation in graphene on the SiO$_2$ substrate is developed. Charged impurities and polar optical surface phonons in the substrate induce an effective random Bychkov-Rashba-like spin-orbit coupling field which leads to sp
in relaxation by the Dyakonov-Perel mechanism. Analytical estimates and Monte Carlo simulations show that the corresponding spin relaxation times are between micro- to milliseconds, being only weakly temperature dependent. It is also argued that the presence of adatoms on graphene can lead to spin lifetimes shorter than nanoseconds.
