arXiv subjects

B. I. Shklovskii

Publications and source records attributed to B. I. Shklovskii.

121 records · Page 7Linked to original sources

arXiv1998

Cyclotron resonance in a two-dimensional electron gas with long-range randomness

We show that the the cyclotron resonance in a two-dimensional electron gas has non-trivial properties if the correlation length of the disorder is larger than the de Broglie wavelength: (a) the lineshape assumes three different forms in strong, intermediate, and weak magnetic fields (b) at the transition from the intermediate to the weak fields the linewidth suddenly collapses due to an explosive growth in the fraction of electrons with a diffusive-type dynamics.

cond-mat.mes-hall↗

arXiv1997

Localization length at the resistivity minima of the quantum Hall effect

The resistivity minima of the quantum Hall effect arise due to the localization of the electron states at the Fermi energy, when it is positioned between adjacent Landau levels. In this paper we calculate the localization length $ξ$ of such states at even filling factors $ν= 2 N$. The calculation is done for several models of disorder (``white-noise,'' short-range, and long-range random potentials). We find that the localization length has a power-law dependence on the Landau level index, $ξ\propto N^α$ with the exponent $α$ between one and ${10/3}$, depending on the model. In particular, for a ``white-noise'' random potential $ξ$ roughly coincides with the classical cyclotron radius. Our results are in reasonable agreement with experimental data on low and moderate mobility samples.

cond-mat.mes-hall↗

arXiv1997

Charging Spectrum and Configurations of a Wigner Crystal Island

Charging of a clean two-dimensional island is studied in the regime of small concentration of electrons when they form the Wigner crystal. Two forms of electron-electron interaction potential are studied: the pure Coulomb interaction and the exponential interaction corresponding to the screening by a pair of close metallic gates. The electrons are assumed to reside in a parabolic external confining potential. Due to the crystalline symmetry the center of the confinement can be situated at distinct positions with respect to the crystal. With the increasing number of electrons $N$ the center periodically hops from one such a location to another providing the lowest total energy. These events occur with the period $\sim N^{1/2}$. At these moments in the case of the pure Coulomb interaction the charging energy of the island has a negative correction $\approx 15%$. For the case of the exponential interaction at the moments of switching the capacitance becomes negative and $\sim N^{1/4}$ new electrons enter the island simultaneously. The configurations of disclinations and dislocations in the island are also studied.

cond-mat↗

arXiv1997

Charging Spectrum of a Small Wigner Crystal Island

Charging of a clean two-dimensional island is studied in the regime of small concentration of electrons when they form the Wigner crystal. The number of electrons in the island is assumed to be not too big (N < 100). It is shown that the total energy of the island as a function of N has a quasi-periodic component of a universal shape, that is independent of the form of electron-electron interactions. These oscillations are caused by the combination of the geometric effects associated with packing of the triangular lattice into the circular island. These effects are: the shell effect, associated with starting a new crystalline row, and the so-called confinement polaronic effect. In the presence of close metallic gates, which eliminate the long-range part of the electron-electron interactions, the oscillations of the energy bring about simultaneous entering of the dot by a few electrons.

cond-mat↗

arXiv1997

Suppression of chaotic dynamics and localization of two-dimensional electrons by a weak magnetic field

We study a two-dimensional motion of a charged particle in a weak random potential and a perpendicular magnetic field. The correlation length of the potential is assumed to be much larger than the de Broglie wavelength. Under such conditions, the motion on not too large length scales is described by classical equations of motion. We show that the phase-space averaged diffusion coefficient is given by Drude-Lorentz formula only at magnetic fields $B$ smaller than certain value $B_c$. At larger fields, the chaotic motion is suppressed and the diffusion coefficient becomes exponentially small. In addition, we calculate the quantum-mechanical localization length as a function of $B$ in the minima of $σ_{xx}$. At $B < B_c$ it is exponentially large but decreases with increasing $B$. At $B > B_c$, the localization length drops precipitously, and ceases to be exponentially large at a field $B_\ast$, which is only slightly above $B_c$. Implications for the crossover from the Shubnikov-de Haas oscillations to the quantum Hall effect are discussed.

cond-mat.mes-hall↗

arXiv1997

Statistics of the Charging Spectrum of a Two-Dimensional Coulomb Glass Island

The fluctuations of capacitance of a two-dimensional island are studied in the regime of low electron concentration and strong disorder, when electrons can be considered classical particles. The universal capacitance distribution is found, with the dispersion being of the order of the average. This distribution is shown to be closely related to the shape of the Coulomb gap in the one-electron density of states of the island. Behavior of the the capacitance fluctuations near the metal - insulator transition is discussed.

cond-mat↗

arXiv1996

The Ground State of a Two-Dimensional Electron Liquid in a Weak Magnetic Field

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of the order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$.

cond-mat↗

arXiv1995

Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factor equal to one and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large $N$.

cond-mat↗

arXiv1995

Collapse of Spin-Splitting in the Quantum Hall Effect

It is known experimentally that at not very large filling factors $ν$ the quantum Hall conductivity peaks corresponding to the same Landau level number $N$ and two different spin orientations are well separated. These peaks occur at half-integer filling factors $ν= 2 N + 1/2$ and $ν= 2 N + 3/2$ so that the distance between them $δν$ is unity. As $ν$ increases $δν$ shrinks. Near certain $N = N_c$ two peaks abruptly merge into a single peak at $ν= 2N + 1$. We argue that this collapse of the spin-splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron $g$-factor. We use the mean-field approach to show that in the limit of zero Zeeman energy $δν$ experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for $N_c$ in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures $N_c = 0.9 d n^{5/6} n_i^{-1/3},$ where $d$ is the spacer width, $n$ is the density of the two-dimensional electron gas, and $n_i$ is the two-dimensional density of randomly situated remote donors.

cond-mat↗

arXiv1994

The Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum

We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of finding a two-dimensional charge distribution on the interface of a semiconductor heterostructure under the influence of a split gate.

cond-mat↗

arXiv1994

Universal Prefactor of Activated Conductivity in the Quantum Hall Effect

The prefactor of the activated dissipative conductivity in a plateau range of the quantum Hall effect is studied in the case of a long-range random potential. It is shown that due to long time it takes for an electron to drift along the perimeter of a large percolation cluster, phonons are able to maintain quasi-equilibrium inside the cluster. The saddle points separating such clusters may then be viewed as ballistic point contacts between electron reservoirs with different electrochemical potentials. The prefactor is universal and equal to 2$e^2/h$ at an integer filling factor $ν$ and to 2$e^2/q^{2}h$ at $ν=p/q$.

cond-mat↗

arXiv1994

Thermally Activated Deviations from Quantum Hall Plateaus

The Hall conductivity $σ_{\rm xy}$ of a two-dimensional electron system is quantized in units of $e^2/h$ when the Fermi level is located in the mobility gap between two Landau levels. We consider the deviation of $σ_{\rm xy}$ from a quantized value caused by the thermal activation of electrons to the extended states for the case of a long range random potential. This deviation is of the form $σ_{\rm xy}^*\exp(-Δ/T)$. The prefactor $σ_{\rm xy}^*$ is equal to $e^2/h$ at temperatures above a characteristic temperature $T_2$. With the temperature decreasing below $T_2$, $σ_{\rm xy}^*$ decays according to a power law: $σ_{\rm xy}^* = \frac{e^2}{h}(T/T_2)^γ$. Similar results are valid for a fractional Hall plateau near filling factor $p/q$ if $e$ is replaced by the fractional charge $e/q$.

cond-mat↗

arXiv1993

Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime

We study variable range hopping in the quantum Hall effect regime in the presence of a metallic gate parallel to the plane of a two-dimensional electron gas. Screening of the Coulomb interaction by the gate causes the partial ``filling'' of the Coulomb gap in the density of localized states. At low enough temperatures this leads to a substantial enhancement and a new temperature behavior of the hopping conductivity. As a result, the diagonal conductivity peaks become much wider. The power law dependence of the width of the peaks on the temperature changes: the corresponding exponent turns out to be twice as small as that for gateless structures. The width dependences on the current in non-ohmic regime and on the frequency for the absorption of the electromagnetic waves experience a similar modification. The experimental observation of the crossovers predicted may demonstrate the important role of the Coulomb interaction in the integer quantum Hall regime.

cond-mat↗