Transport in Luttinger Liquids

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz-Shastry exactly solvable Luttinger-like model.Comment: Latex file, 15 pages, four eps figure

Magnitude and crystalline anisotropy of hole magnetization in (Ga,Mn)As

Theory of hole magnetization Mc in zinc-blende diluted ferromagnetic semiconductors is developed relaxing the spherical approximation of earlier approaches. The theory is employed to determine Mc for (Ga,Mn)As over a wide range of hole concentrations and a number of crystallographic orientations of Mn magnetization. It is found that anisotropy of Mc is practically negligible but the obtained magnitude of Mc is significantly greater than that determined in the spherical approximation. Its sign and value compares favorably with the results of available magnetization measurements and ferromagnetic resonance studies.Comment: 5 pages, 3 figure

Bose-Fermi Mixtures in One Dimension

We analyze the phase stability and the response of a mixture of bosons and spin-polarized fermions in one dimension (1D). Unlike in 3D, phase separation happens for low fermion densities. The dynamics of the mixture at low energy is independent of the spin-statistics of the components, and zero-sound-like modes exist that are essentially undamped.Comment: 5 pages; 1 figur

A Non-equilibrium STM model for Kondo Resonance on surface

Based on a no-equilibrium STM model, we study Kondo resonance on a surface by self-consistent calculations. The shapes of tunneling spectra are dependent on the energy range of tunneling electrons. Our results show that both energy-cutoff and energy-window of tunneling electrons have significant influence on the shapes of tunneling spectra. If no energy-cutoff is used, the Kondo resonances in tunneling spectrum are peaks with the same shapes in the density of state of absorbed magnetic atoms. This is just the prediction of Tersoff theory. If we use an energy cutoff to remove high-energy lectrons, a dip structure will modulate the Kondo resonance peak in the tunneling spectrum. The real shape of Kondo peak is the mixing of the peak and dip, the so-called Fano line shape. The method of self-consistent non-equilibrium matrix Green function is discussed in details.Comment: 11 pages and 8 eps figur

Bosonization of Fermi liquids

We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.Comment: 42 pages, RevteX, preprint UIUC (1993

Evaluation of the optical conductivity tensor in terms of contour integrations

For the case of finite life-time broadening the standard Kubo-formula for the optical conductivity tensor is rederived in terms of Green's functions by using contour integrations, whereby finite temperatures are accounted for by using the Fermi-Dirac distribution function. For zero life-time broadening, the present formalism is related to expressions well-known in the literature. Numerical aspects of how to calculate the corresponding contour integrals are also outlined.Comment: 8 pages, Latex + 2 figure (Encapsulated Postscript

A Solvable Model of Interacting Fermions in Two Dimensions

We introduce and study an exactly solvable model of several species of fermions in which particles interact pairwise through a mutual magnetic field; the interaction operates only between particles belonging to different species. After an unitary transformation, the model reduces to one in which each particle sees a magnetic field which depends on the total numbers of particles of all the other species; this may be viewed as the mean-field model for a class of anyonic theories. Our model is invariant under charge conjugation C and the product PT (parity and time reversal). For the special case of two species, we examine various properties of this system, such as the Hall conductivity, the wave function overlap arising from the transfer of one particle from one species to another, and the one-particle off-diagonal density matrix. Our model is a generalization of a recently introduced solvable model in one dimension.Comment: Revtex, 7 page

Tunneling between two Luttinger liquids with long range interaction

The non linear charge transfer through a tunnel junction between two Luttinger systems is studied for repulsive, finite range interaction between electrons on the same, V_{11}, and on different,V_{12}, sides of the junction. Features of the Coulomb blockade effect are observed if V_{12}=0. We predict a novel interaction induced enhancement of the current if V_{12}>0. When V_{12}=V_{11}, the current is suppressed at small bias, but the ``charging energy'', obtained from the asymptotic behavior at high bias voltage, vanishes.Comment: 4 pages, RevTeX, to be published in Physical Review B (Brief Report

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

In this paper we present calculations on the electronic band structure of a two-dimensional lateral superlattice subject to a perpendicular magnetic field by employing a projection operator technique based on the ray-group of magnetotranslation operators. We construct a new basis of appropriately symmetrized Bloch-like wavefunctions as linear combination of well-localized magnetic-Wannier functions. The magnetic field was consistently included in the Wannier functions defined in terms of free-electron eigenfunctions in the presence of external magnetic field in the symmetric gauge. Using the above basis, we calculate the magnetic energy spectrum of electrons in a lateral superlattice with bi-directional weak electrostatic modulation. Both a square lattice and a triangular one are considered as special cases. Our approach based on group theory handles the cases of integer and rational magnetic fluxes in a uniform way and the provided basis could be convenient for further both analytic and numerical calculations.Comment: 19 pages, 5 figures. accepted to Int. J. Mod. Phys. B (April 2006

Experiments on the Fermi to Tomonaga-Luttinger liquid transition in quasi-1D systems

We present experimental results on the tunneling into the edge of a two dimensional electron gas (2DEG) obtained with GaAs/AlGaAs cleaved edge overgrown structures. The electronic properties of the edge of these systems can be described by a one-dimensional chiral Tomonaga-Luttinger liquid when the filling factor of the 2DEG is very small. Here we focus on the region where the Tomonaga-Luttinger liquid breaks down to form a standard Fermi liquid close to $\nu=1$ and show that we recover a universal curve, which describes all existing data.Comment: 5 pages, localisation 2002, conference proceeding