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.

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

Magnetization in short-period mesoscopic electron systems

We calculate the magnetization of the two-dimensional electron gas in a short-period lateral superlattice, with the Coulomb interaction included in Hartree and Hartree-Fock approximations. We compare the results for a finite, mesoscopic system modulated by a periodic potential, with the results for the infinite periodic system. In addition to the expected strong exchange effects, the size of the system, the type and the strength of the lateral modulation leave their fingerprints on the magnetization.Comment: RevTeX4, 10 pages with 14 included postscript figures To be published in PRB. Replaced to repair figure

Planar cyclotron motion in unidirectional superlattices defined by strong magnetic and electric fields: Traces of classical orbits in the energy spectrum

We compare the quantum and the classical description of the two-dimensional motion of electrons subjected to a perpendicular magnetic field and a one-dimensional lateral superlattice defined by spatially periodic magnetic and electric fields of large amplitudes. We explain in detail the complicated energy spectra, consisting of superimposed branches of strong and of weak dispersion, by the correspondence between the respective eigenstates and the ``channeled'' and ``drifting'' orbits of the classical description.Comment: 11 pages, 11 figures, to appear in Physical Review

Transport through a quantum ring, a dot and a barrier embedded in a nanowire in magnetic field

We investigate the transport through a quantum ring, a dot and a barrier embedded in a nanowire in a homogeneous perpendicular magnetic field. To be able to treat scattering potentials of finite extent in magnetic field we use a mixed momentum-coordinate representation to obtain an integral equation for the multiband scattering matrix. For a large embedded quantum ring we are able to obtain Aharanov-Bohm type of oscillations with superimposed narrow resonances caused by interaction with quasi-bound states in the ring. We also employ scattering matrix approach to calculate the conductance through a semi-extended barrier or well in the wire. The numerical implementations we resort to in order to describe the cases of weak and intermediate magnetic field allow us to produce high resolution maps of the ``near field'' scattering wave functions, which are used to shed light on the underlying scattering processes.Comment: RevTeX, 13 pages with included postscript figures, high resolution version available at http://hartree.raunvis.hi.is/~vidar/Rann/VG_04.pd

Coulomb effects on the quantum transport of a two-dimensional electron system in periodic electric and magnetic fields

The magnetoresistivity tensor of an interacting two-dimensional electron system with a lateral and unidirectional electric or magnetic modulation, in a perpendicular quantizing magnetic field, is calculated within the Kubo formalism. The influence of the spin splitting of the Landau bands and of the density of states (DOS) on the internal structure of the Shubnikov-de Haas oscillations is analyzed. The Coulomb electron - electron interaction is responsible for strong screening and exchange effects and is taken into account in a screened Hartree-Fock approximation, in which the exchange contribution is calculated self-consistently with the DOS at the Fermi level. This approximation describes both the exchange enhancement of the spin splitting and the formation of compressible edge strips, unlike the simpler Hartree and Hartree-Fock approximations, which yield either the one or the other.Comment: 20 pages, revtex, 7 ps figures, to appear in Phys. Rev.

Geometrical effects and signal delay in time-dependent transport at the nanoscale

The nonstationary and steady-state transport through a mesoscopic sample connected to particle reservoirs via time-dependent barriers is investigated within the reduced density operator method. The generalized Master equation is solved via the Crank-Nicolson algorithm by taking into account the memory kernel which embodies the non-Markovian effects that are commonly disregarded. We propose a physically reasonable model for the lead-sample coupling which takes into account the match between the energy of the incident electrons and the levels of the isolated sample, as well as their overlap at the contacts. Using a tight-binding description of the system we investigate the effects induced in the transient current by the spectral structure of the sample and by the localization properties of its eigenfunctions. In strong magnetic fields the transient currents propagate along edge states. The behavior of populations and coherences is discussed, as well as their connection to the tunneling processes that are relevant for transport.Comment: 26 pages, 13 figures. To appear in New Journal of Physic

Anisotropic scattering and quantum magnetoresistivities of a periodically modulated 2D electron gas

We calculate the longitudinal conductivities of a two-dimensional noninteracting electron gas in a uniform magnetic field and a lateral electric or magnetic periodic modulation in one spatial direction, in the quantum regime. We consider the effects of the electron-impurity scattering anisotropy through the vertex corrections on the Kubo formula, which are calculated with the Bethe-Salpeter equation, in the self-consistent Born approximation. We find that due to the scattering anisotropy the band conductivity increases, and the scattering conductivities decrease and become anisotropic. Our results are in qualitative agreement with recent experiments.Comment: 19 pages, 8 figures, Revtex, to appear in Phys. Rev.

Coherent electronic transport in a multimode quantum channel with Gaussian-type scatterers

Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type scattering potentials, which can be used to model a single impurity, a quantum dot or more complicated structures in the wire. The well known dips in the conductance in the presence of attractive impurities is reproduced. A resonant transmission peak in the conductance is seen as the energy of the incident electron coincides with an energy level in the quantum dot. The conductance through a quantum wire in the presence of an asymmetric potential are also shown. In the case of a narrow potential parallel to the wire we find that two dips appear in the same subband which we ascribe to two quasi bound states originating from the next evanescent mode.Comment: RevTeX with 14 postscript figures include

Notes on bordered Floer homology

This is a survey of bordered Heegaard Floer homology, an extension of the Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is placed on how bordered Heegaard Floer homology can be used for computations.Comment: 73 pages, 29 figures. Based on lectures at the Contact and Symplectic Topology Summer School in Budapest, July 2012. v2: Fixed many small typo