Short Range Interaction Effects on the Density of States of Disordered Two Dimensional Crystals with a half--filled band

The Density of electronic States (DoS) of a two--dimensional square lattice with substitutional impurities is calculated in the presence of short--range electron--electron interactions. In the middle of the energy band, the Bragg reflections off the Brillouin zone boundary are shown to lead to additional quantum corrections to the DoS, the sign of which is opposite to the sign of the Altshuler--Aronov's logarithmic correction. The resulting quantum correction to the DoS at half--filling is positive, i.e. the DoS increases logarithmically as the Fermi energy is approached. However, far from the commensurate points where the Bragg reflections are suppressed, the negative logarithmic corrections to the DoS survive.Comment: 5 pages 2 figure

Formation of three-particle clusters in hetero-junctions and MOSFET structures

A novel interaction mechanism in MOSFET structures and $GaAs/AlGaAs$ hetero-junctions between the zone electrons of the two-dimensional (2D) gas and the charged traps on the insulator side is considered. By applying a canonical transformation, off-diagonal terms in the Hamiltonian due to the trapped level subsystem are excluded. This yields an effective three-particle attractive interaction as well as a pairing interaction inside the 2D electronic band. A type of Bethe- Goldstone equation for three particles is studied to clarify the character of the binding and the energy of the three-particle bound states. The results are used to offer a possible explanation of the Metal-Insulator transition recently observed in MOSFET and hetero-junctions.Comment: 4 page

Mesoscopic fluctuations of the Density of States and Conductivity in the middle of the band of Disordered Lattices

The mesoscopic fluctuations of the Density of electronic States (DoS) and of the conductivity of two- and three- dimensional lattices with randomly distributed substitutional impurities are studied. Correlations of the levels lying above (or below) the Fermi surface, in addition to the correlations of the levels lying on opposite sides of the Fermi surface, take place at half filling due to nesting. The Bragg reflections mediate to increase static fluctuations of the conductivity in the middle of the band which change the distribution function of the conductivity at half- filling.Comment: 5 pages, 3 figure

Comment on ``Density of States of Disordered Two-Dimensional Crystals with Half-Filled Band''

In a recent letter (PRL 84, 3930 (2000)) Nakhmedov et al. claimed that the Van Hove singularity at $\epsilon=0$ in the density of states (DoS) of the two-dimensional crystal with half-filled tight-binding band survives the addition of substitutional impurities. This derivation suffers from several inconsistencies. We resolve them and show that the DoS at the band center is finite, as one might naively expect

Exactly solvable model of three interacting particles in an external magnetic field

The quantum mechanical problem of three identical particles, moving in a plane and interacting pairwise via a spring potential, is solved exactly in the presence of a magnetic field. Calculations of the pair--correlation function, mean distance and the cluster area show a quantization of these parameters. Especially the pair-correlation function exhibits a certain number of maxima given by a quantum number. We obtain Jastrow pre-factors which lead to an exchange correlation hole of liquid type, even in the presence of the attractive interaction between the identical electrons.Comment: 8 pages 3 figure

Critical disorder effects in Josephson-coupled quasi-one-dimensional superconductors

Effects of non-magnetic randomness on the critical temperature T_c and diamagnetism are studied in a class of quasi-one dimensional superconductors. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between the wires and T_c vanishes discontinuously when the randomness reaches a critical value. The parallel and transverse components of the penetration depth are found to diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and phase-coherence breaking. The interplay between disorder and quantum phase fluctuations results in quantum critical behavior at T=0, manifesting itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.Comment: 4 pages, 2 figure

Weak Field Magnetoresistance in Quasi-One-Dimensional Systems

Theoretical studies are presented on weak localization effects and magnetoresistance in quasi-one-dimensional systems with open Fermi surfaces. Based on the Wigner representation, the magnetoresistance in the region of weak field has been studied for five possible configurations of current and field with respect to the one-dimensional axis. It has been indicated that the anisotropy and its temperature dependences of the magnetoresistance will give information on the degree of one-dimensionality and the phase relaxation time.Comment: pages 11, LaTeX, 5 figures, uses jpsj.sty. To be published in J. Phys. Soc. Jpn. (Vol.67(1998) No.4); Added some references and a Note at Feb. 13 199

Effect of Substitutional Impurities on the Electronic States and Conductivity of Crystals with Half-filled Band

Low temperature quantum corrections to the density of states (DOS) and the conductivity are examined for a two-dimensional(2D) square crystal with substitutional impurities. By summing the leading logarithmic corrections to the DOS its energy dependence near half-filling is obtained. It is shown that substitutional impurities do not suppress the van Hove singularity at the middle of the band, however they change its energy dependence strongly. Weak disorder due to substitutional impurities in the three-dimensional simple cubic lattice results in a shallow dip in the center of the band. The calculation of quantum corrections to the conductivity of a 2D lattice shows that the well-known logarithmic localization correction exists for all band fillings. Furthermore the magnitude of the correction increases as half-filling is approached. The evaluation of the obtained analytical results shows evidence for delocalized states in the center of the band of a 2D lattice with substitutional impurities

Dimensional Crossover of Weak Localization in a Magnetic Field

We study the dimensional crossover of weak localization in strongly anisotropic systems. This crossover from three-dimensional behavior to an effective lower dimensional system is triggered by increasing temperature if the phase coherence length gets shorter than the lattice spacing $a$. A similar effect occurs in a magnetic field if the magnetic length $L_m$ becomes shorter than $a(D_{||}/D_\perp)^\gamma$, where \D_{||}/D_\perp is the ratio of the diffusion coefficients parallel and perpendicular to the planes or chains. $\gamma$ depends on the direction of the magnetic field, e.g. $\gamma=1/4$ or 1/2 for a magnetic field parallel or perpendicular to the planes in a quasi two-dimensional system. We show that even in the limit of large magnetic field, weak localization is not fully suppressed in a lattice system. Experimental implications are discussed in detail.Comment: RevTeX, 11 pages, 4 figures; three references added and discusse