Magnetic-field and spin-orbit interaction in restricted geometries: Solvable models

Spin and charge persistent currents in a Kane Meleα-T3quantum ring

We conduct a thorough study of different persistent currents in a spin-orbit coupledα-T3(pseudospin-1) fermionic quantum ring (QR) that smoothly interpolates between graphene (α = 0, pseudospin-1/2) and a dice lattice (α = 1, pseudospin-1) in presence of an external perpendicular magnetic field. In particular, we have considered effects of intrinsic (ISOC) and Rashba spin-orbit couplings (RSOC) that are both inherent to two dimensional quantum structures and yield interesting consequences. The energy levels of the system comprise of the conduction bands, valence bands, and flat bands which show non-monotonic dependencies on the radius,Rof the QR, in the sense that, for smallR, the energy levels vary as1/R, while the variation is linear for largeR. The dispersion spectra corresponding to zero magnetic field are benchmarked with those for finite fields to enumerate the role played by the spin-orbit coupling terms therein. Further, it is noted that the flat bands demonstrate dispersive behavior, and hence is able to contribute to the transport properties only for finite ISOC. Moreover, RSOC yields spin-split bands, thereby contributing to the spin-resolved currents. The charge and the spin-polarized persistent currents are hence computed in presence of these spin-orbit couplings. The persistent currents in both the charge and spin sectors oscillate as a function of the magnetic field with a period equal to the flux quantum, as they should be; although they now depend upon the spin-orbit coupling parameters. Interestingly, the ISOC distorts the current profiles, owing to the distribution of the flat band caused by it, whereas RSOC alone preserves the flat band and hence a perfect periodicity of the current characteristic is maintained. Further, we have explored the role played by the parameterαin our entire analysis to enable studies while interpolating from graphene to a dice lattice.

Confinement and inhomogeneous broadening effects in the quantum oscillatory magnetization of quantum dot ensembles

We report on the magnetization of ensembles of etched quantum dots with a lateral diameter of 460 nm, which we prepared from InGaAs/InP heterostructures. The quantum dots exhibit 1/B-periodic de-Haas-van-Alphen-type oscillations in the magnetization M(B) for external magnetic fields B  >  2 T, measured by torque magnetometry at 0.3 K. We compare the experimental data to model calculations assuming different confinement potentials and including ensemble broadening effects. The comparison shows that a hard wall potential with an edge depletion width of 100 nm explains the magnetic behavior. Beating patterns induced by Rashba spin-orbit interaction (SOI) as measured in unpatterned and nanopatterned InGaAs/InP heterostructures are not observed for the quantum dots. From our model we predict that signatures of SOI in the magnetization could be observed in larger dots in tilted magnetic fields.

Magnetometry of low-dimensional electron and hole systems

The high-magnetic-field, low-temperature magnetic properties of low-dimensional electron and hole systems reveal a wealth of fundamental information. Quantum oscillations of the thermodynamic equilibrium magnetization yield the total density of states, a central quantity in understanding the quantum Hall effect in 2D systems. The magnetization arising from non-equilibrium circulating currents reveals details, not accessible with traditional measurements, of the vanishingly small longitudinal resistance in the quantum Hall regime. We review how the technique of magnetometry has been applied to these systems, the most important discoveries that have been made, and their theoretical significance.

Pauli principle and chaos in a magnetized disk

We present results of a detailed quantum-mechanical study of a gas of N noninteracting electrons confined to a circular boundary and subject to homogeneous dc plus ac magnetic fields [B=B(dc)+B(ac)f(t), with f(t+2pi/omega(0))=f(t)]. We earlier found a one-particle classical phase diagram of the (scaled) Larmor frequency omega;(c)=omega(c)/omega(0) vs epsilon=B(ac)/B(dc) that separates regular from chaotic regimes. We also showed that the quantum spectrum statistics changed from Poisson to Gaussian orthogonal ensembles in the transition from classically integrable to chaotic dynamics. Here we find that, as a function of N and (epsilon,omega(c)), there are clear quantum signatures in the magnetic response, when going from the single-particle classically regular to chaotic regimes. In the quasi-integrable regime the magnetization nonmonotonically oscillates between diamagnetic and paramagnetic as a function of N. We quantitatively understand this behavior from a perturbation theory analysis. In the chaotic regime, however, we find that the magnetization oscillates as a function of N but it is always diamagnetic. Equivalent results are also presented for the orbital currents. We also find that the time-averaged energy grows as N2 in the quasi-integrable regime but changes to a linear N dependence in the chaotic regime. In contrast, the results with Bose statistics are akin to the single-particle case and thus different from the fermionic case. We also give an estimate of possible experimental parameters where our results may be seen in semiconductor quantum dot billiards.