arXiv subjects

A. L. Efros

Publications and source records attributed to A. L. Efros.

35 records · Page 2Linked to original sources

arXiv2001

Variable-range-hopping in two-dimensional system

Computer modeling of the VRH conductivity in the two-dimensional system has been done by kinetic Monte Carlo method, which includes some new elements. Study of the temperature dependence of the conductivity, testing of the different scaling relations, and study of the size effect show that the Efros-Shklovskii mechanism of the VRH is valid in the slightest details. It has been also shown that simultaneous transitions of many electrons are not important. The reasons of disagreement with previous works are thoroughly analyzed.

cond-mat.str-el↗

arXiv2001

Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals

We calculate analytically the spectra of plasma waves and electromagnetic waves (EMW) in metallic photonic crystal consisting of the parallel thin infinite metallic cylinders embedded in the dielectric media. The axes of metallic cylinders form a regular square lattice in a plane perpendicular to them. The metal inside the cylinders is assumed to be in the high frequency regime $ωτ>> 1$, where $τ$ is the relaxation time. The proposed analytical theory is based upon small parameters $f << 1$, where $f$ is the volume fraction of the metal, and $kR << 1$, where $k$ is the wave vector and $R$ is the radius of the cylinder. It is shown that there are five different branches of the EMW that cover all frequency range under consideration except one very small omnidirectional gap in the vicinity of the frequency of the surface plasmon. However, at some directions of propagation and polarizations the gap may be much larger. The reflection and refraction of the EMW is also considered. The general theory of refraction is proposed which is complicated by the spatial dispersion of the dielectric constant, and one particular geometry of the incident EMW is considered.

cond-mat↗

arXiv2001

A New Class of Magnetoresistance Oscillations: Interaction of a Two-Dimensional Electron Gas with Leaky Interface Phonons

We report on a new class of magnetoresistance oscillations observed in a high-mobility two-dimensional electron gas (2DEG) in GaAs-Al$_x$Ga$_{1-x}$As heterostructures. Appearing in a weak magnetic field ($B<$ 0.3 T) and only in a narrow temperature range (2 K $<T<$ 9 K), these oscillations are periodic in 1/B with a frequency proportional to the electron Fermi wave vector, $k_F$. We interpret the effect as a magnetophonon resonance of the 2DEG with leaky interface-acoustic phonon modes carrying a wave vector $q=2k_F$. Calculations show a few branches of such modes on the GaAs-Al$_x$Ga$_{1-x}$As interface, and their velocities are in quantitative agreement with the data.

cond-mat.mes-hall↗

arXiv2000

Leaky interface phonons in AlGaAs/GaAs structures

A dispersion equation for the interface waves has been derived for the interface of two cubic crystals in the plane perpendicular to [001]. A reasonable hypothesis has been made about the total number of the acoustic modes. Due to this hypothesis the number is 64, but not all of the modes have physical meaning of the interface waves. The rules have been worked out to select physical branches among all 64 roots of dispersion equation. The physical meaning of leaky interface waves is discussed. The calculations have been made for the interface Al$_{0.3}$Ga$_{0.7}$As/GaAs. In this case all physical interface modes have been shown to be leaky. The velocities of the interface waves are calculated as a function of an angle in the plane of interface. The results support a recent interpretation of a new type oscillations of magnetoresistance as a resonant scattering of two-dimensional electron gas by the leaky interface phonons.

cond-mat.mes-hall↗

arXiv2000

Thermodynamics and transport properties of interacting systems with localized electrons

The review of the modern results in the theoretical and experimental study of the localized interacting electrons is given. After theoretical prediction of the Coulomb gap and the new temperature law in the variable range hopping conduction many efforts have been made to discover it experimentally. The most important of them are attempts to demonstrate experimentally that the long range Coulomb interaction is not screened in this system and that it is the origin of the gap. The next stage begins when the recent experiments have discovered glassy properties of the interacting system with localized electrons. This review is concentrated on the origin of the glassy properties of this system and it connects the glassy properties with another interesting phenomenon - insulator-metal transition.

cond-mat.str-el↗

arXiv2000

Crossover from percolation to diffusion

A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is completely new. It describes the increase of the diffusion below percolation threshold. As an example, an exact solution of one dimensional lattice problem is given. In this case the new exponent $q=2$.

cond-mat↗

arXiv2000

Glassy properties and localization of interacting electrons in two-dimensional systems

We present a computer simulation study of a disordered two-dimensional system of localized interacting electrons at thermal equilibrium. It is shown that the configuration of occupied sites within the Coulomb gap persistently changes at temperatures much less than the gap width. This is accompanied by large time dependent fluctuations of the site energies. The observed thermal equilibration at low temperatures suggests a possible glass transition only at T=0. We interpret the strong fluctuations in the occupation numbers and site energies in terms of the drift of the system between multiple energy minima. The results also imply that interacting electrons may be effectively delocalized within the Coulomb gap. Insulating properties, such as hopping conduction, appear as a result of long equilibration times associated with glassy dynamics. This may shine new light on the relation between the metal-insulator transition and glassy behavior.

cond-mat.dis-nn↗

arXiv1999

Calculations of exchange interaction in impurity band of two-dimensional semiconductors with out of plane impurities

We calculate the singlet-triplet splitting for a couple of two-dimensional electrons in the potential of two positively charged impurities which are located out of plane. We consider different relations between vertical distances of impurities $h_1$ and $h_2$ and their lateral distance $R$. Such a system has never been studied in atomic physics but the methods, worked out for regular two-atomic molecules and helium atom, have been found to be useful. Analytical expressions for several different limiting configurations of impurities are obtained an interpolated formula for intermediate range of parameters is proposed. The $R$-dependence of the splitting is shown to become weaker with increasing $h_1,h_2$.

cond-mat.str-el↗

arXiv1999

Electrostatics of Inhomogeneous Quantum Hall Liquid

The distribution of electron density in the quantum Hall liquid is considered in the presence of macroscopic density gradient caused by side electrodes or inhomogeneous doping. In this case different Landau levels are occupied in different regions of a sample. These regions are separated by incompressible liquid. It is shown that the applicability of the approach by Chklovskii et al. is substantially restricted if the density gradient is not very large and disorder is important. Due to the fluctuations of the remote donor's density the liquid in the transition region can not be considered as completely incompressible. In the typical situation, when the gap between Landau levels is not much larger than the energy of disorder, the transition region is a wide band where electron density, averaged over the fluctuations, is independent of magnetic field. The band is a random mixture of regions occupied by electrons of upper level, by holes of lower level and by incompressible liquid. The width of this band is calculated and an analytical expression for the fraction of incompressible liquid in different parts of this band is given.

cond-mat.mes-hall↗

arXiv1999

Spin structure of impurity band of semiconductors in two and three-dimensional cases

The exchange interaction between electrons located at different randomly distributed impurities is studied for small density of impurities. The singlet-triplet splitting 2J(R) is calculated for two Coulomb centers at a distance R. Interpolated formulas are found which work for all distances R from zero to infinity. The data from atomic physics are used for the interpolation in three-dimensional case. For two-dimensional case the original calculations are performed to find asymptotic behavior of the splitting at large R, the splitting for the ``two-dimensional helium atom'' (R=0) and the splitting at $R=a_B$, where $a_B$ is the effective Bohr radius. The spin structure of impurity band is described by the Heisenberg Hamiltonian. The ground state of a system consists of localized singlets. The new results are obtained for the distribution of the singlet pairs in the ground state. These results are exact at low density. The problem is reduced to a non-trivial geometric problem which is solved in the mean field approximation and by computer modeling. The density of free electrons is found as a function of temperature and the distribution function of the singlet-triplet transitions energies is calculated. Both functions are given in an analytical form.

cond-mat.str-el↗

arXiv1997

Unusual metallic phase in a chain of strongly interacting particles

We consider a one-dimensional lattice model with the nearest-neighbor interaction $V_1$ and the next-nearest neighbor interaction $V_2$ with filling factor 1/2 at zero temperature. The particles are assumed to be spinless fermions or hard-core bosons. Using very simple assumptions we are able to predict the basic structure of the insulator-metal phase diagram for this model. Computations of the flux sensitivity support the main features of the proposed diagram and show that the system maintains metallic properties at arbitrarily large values of $V_1$ and $V_2$ along the line $V_1-2V_2=γJ$, where $J$ is the hopping amplitude, and $γ\approx1.2$. We think that close to this line the system is a ``weak'' metal in a sense that the flux sensitivity decreases with the size of the system not exponentially but as $1/L^α$ with $α>1$.

cond-mat↗

arXiv1997

Structural and insulator-metal quantum phase transitions on a lattice

We consider 2D gas of spinless fermions with the Coulomb and the short range interactions on a square lattice at T=0. Using exact diagonalization technique we study finite clusters up to 16 particles at filling factors $ν=1/2$ and 1/6. By increasing the hopping amplitude we obtain the low-energy spectrum of the system in a wide range from the classical Wigner crystal to almost free gas of fermions. The most efforts are made to study the mechanism of the structural and insulator-metal transitions. We show that both transitions are determined by the energy band of the defect with the lowest energy in the Wigner crystal.

cond-mat↗

arXiv1997

Giant persistent current in free-electron model with flat Fermi surface

For the first time the persistent current in a 2D free-electron system has been calculated analytically. The tight binding model is considered on a square lattice with filling factor 1/2. The array has a shape of rectangle with boundary conditions in both directions twisted by $2πϕ_x$ and $2πϕ_y$. The components of the twist are associated with two components of the magnetic flux in torus geometry. An analytical expression is obtained for the energy and for the components of the persistent current (PC) at a given flux and temperature. It is shown that at zero temperature the PC density is proportional to the vector potential with the coefficient which does not depend on the size of the system. This happens because the Fermi surface for a square lattice at filling factor 1/2 is flat. Both the energy and the PC are periodic functions of the two flux components with the periods $ϕ_0/q$ and $ϕ_0/s$ where $ϕ_0=hc/e$, and $q$ and $s$ are integers which depend on the aspect ratio of the rectangle. The magnitude of PC is the same as in superconductors. Therefore, a 3D system constructed from a macroscopic number of isolated coaxial cylinders at zero temperature reminds the London's superconductor. It exhibits the quantization of trapped flux as well as the Meissner effect. However, all the phenomena are of a mesoscopic nature. The critical field $H_c$ decays with an effective size of the system, $H_c\sim 1/R_{ef}$. The magnitude of PC decays with $T$ as $\exp(-πTR_{ef}/2at)$, where $t$ is the hopping amplitude and $a$ is the lattice constant.

cond-mat↗

arXiv1997

Anomalous magnetophotoluminescence as a result of level repulsion in arrays of quantum dots

Selectively excited photoluminescence (SPL) of an array of self-organized In$_{0.5}$Ga$_{0.5}$As quantum dots has been measured in a magnetic field up to 11T. Anomalous magnetic field sensitivity of the SPL spectra has been observed under conditions for which the regular photoluminescence spectra is insensitive to the magnetic field due to large inhomogeneous broadening. The anomalous sensitivity is interpreted in terms of the repulsion of excited levels of the dots in a random potential. A theory presented to describe this phenomena is in excellent agreement with the experimental data. The data estimated the correlation in the positions of excited levels of the dots to be 94%. The magnetic field dependence allows the determination of the reduced cyclotron effective mass in a dot. For our sample we have obtained $m_em_h/(m_e+m_h)=0.034m_0$.

cond-mat↗

arXiv1996

Single-Electron Charging and Coulomb Interaction in InAs Self-Assembled Quantum Dot Arrays

Sequential single-electron charging is observed in InAs Self-Assembled Quantum Dots using capacitance spectroscopy. In this system, the Coulomb energy is smaller than the inter-level energy spacings due to the quantum confinement and both effects can be separately identified. A theoretical model is proposed for this system and the capacitance experiments were devised in order to experimentally observe the effects of Coulomb interaction between electrons on the dots. The effects of inter- and intra-dot Coulomb interaction have been observed in the capacitanc e spectra. A good agreement between the proposed model and experiment is achieved.

cond-mat↗

arXiv1996

Orthogonal localized wave functions of an electron in a magnetic field

We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.

cond-mat↗

arXiv1996

Quantum melting on a lattice and a delocalization transition

We consider 2d gas of spinless fermions with the Coulomb interaction on a lattice at T=0 and at different values of the hopping amplitude J. At small J electrons form a periodic structure. At filling factor ν=1/6 this structure melts at J as low as 0.02--0.03 in units of the nearest-neighbor Coulomb energy. We argue that this transition is connected to the dielectric-metal and dielectric-superconductor transitions. To demonstrate this point we perform computer modeling of the systems 6x6 with 6 and 7 electrons and 6x12 with 12 electrons. By sweeping J we compute simultaneously persistent current and structural characteristics of the electron distribution.

cond-mat↗