Hysteresis effect due to the exchange Coulomb interaction in short-period superlattices in tilted magnetic fields

We calculate the ground-state of a two-dimensional electron gas in a short-period lateral potential in magnetic field, with the Coulomb electron-electron interaction included in the Hartree-Fock approximation. For a sufficiently short period the dominant Coulomb effects are determined by the exchange interaction. We find numerical solutions of the self-consistent equations that have hysteresis properties when the magnetic field is tilted and increased, such that the perpendicular component is always constant. This behavior is a result of the interplay of the exchange interaction with the energy dispersion and the spin splitting. We suggest that hysteresis effects of this type could be observable in magneto-transport and magnetization experiments on quantum-wire and quantum-dot superlattices.Comment: 3 pages, 3 figures, Revtex, to appear in Phys. Rev.

Specific Plateaus of the Quantum Hall Effect Induced by an Applied Bias

The spectrum and the eigenstates of a finite 2D tight-binding electronic system, with Dirichlet boundary conditions, in magnetic field and external linear potential are studied. The eigenstates show an equipotential character and may cross the plaquette in the direction perpendicular to the electric field. When leads are added to the plaquette, the channels carrying the current may be shortcut by equipotentials, resulting in additional plateaus situated inbetween the usual IQHE plateaus. This idea is confirmed by a numerical calculation within the four-terminal Landauer-B\"{u}ttiker approach.Comment: 9 pages, revtex, 2 gif figures and 5 postscript figure

Gap prediction in hybrid graphene - hexagonal boron nitride nanoflakes using artificial neural networks

The electronic properties graphene nanoflakes (GNFs) with embedded hexagonal boron nitride (hBN) domains are investigated by combined {\it ab initio} density functional theory calculations and machine learning techniques. The energy gaps of the quasi-0D graphene based systems, defined as the differences between LUMO and HOMO energies, depend on the sizes of the hBN domains relative to the size of the pristine graphene nanoflake, but also on the position of the hBN domain. The range of the energy gaps for different configurations is increasing as the hBN domains get larger. We develop two artificial neural network (ANN) models able to reproduce the gap energies with high accuracies and investigate the tunability of the energy gap, by considering a set of GNFs with embedded rectangular hBN domains. In one ANN model, the input is in one-to-one correspondence with the atoms in the GNF, while in the second model the inputs account for basic structures in the GNF, allowing potential use in up-scaled structures. We perform a statistical analysis over different configurations of ANNs to optimize the network structure. The trained ANNs provide a correlation between the atomic system configuration and the magnitude of the energy gaps, which may be regarded as an efficient tool for optimizing the design of nanostructured graphene based materials for specific electronic properties.Comment: 6 pages, 5 figure

The Fano regime of one-dot Aharonov-Bohm interferometers

We use the Landauer-B\"{u}ttiker formalism to study the mesoscopic Fano effect in Aharonov-Bohm rings with an embedded two-dimensional noninteracting dot. The magnetic field dependence of the dot levels leads to a global shift of the Fano lines which becomes important for small ring/dot area ratios. As the magnetic field is varied the Fano dips move periodically from one side of the peak to the other, as reported by Kobayashi {\it et al.} [Phys. Rev. Lett. {\bf 88}, 256806 (2002)]. We show that this effect appears due to a specific magnetic control of the difference between the phase of the single nonresonant path via the free arm of the ring and the global phase of all trajectories involving resonant tunnelings through the dot.Comment: To appear in Phys. Rev.

Memorization of short-range potential fluctuations in Landau levels

We calculate energy spectra of a two-dimensional electron system in a perpendicular magnetic field and periodic potentials of short periods. The Coulomb interaction is included within a screened Hartree-Fock approximation. The electrostatic screening is poor and the exchange interaction amplifies the energy dispersion. We obtain, by numerical iterations, self-consistent solutions that have a hysteresis-like property. With increasing amplitude of the external potential the energy dispersion and the electron density become periodic, and they remain stable when the external potential is reduced to zero. We explain this property in physical terms and speculate that a real system could memorize short-range potential fluctuations after the potential has been turned off.Comment: 11 pages with 4 included figures, Revte