arXiv subjects

B. L. Altshuler

Publications and source records attributed to B. L. Altshuler.

At least 109 records · Page 6Linked to original sources

arXiv2000

Mesoscopic Stoner Instability

The paper is devoted to the magnetic properties of isolated mesoscopic grains. We demonstrate that under very general conditions the electron - electron interactions in such grains can be taken into account by a simple interaction Hamiltonian. This Hamiltonian involves only three coupling constants which correspond to charging, exchange interaction, and superconducting correlations. The most important condition for such a description is that Thouless conductance of each grain is large. Under this condition sample-to-sample fluctuations of the coupling constants can be neglected. However, the thermodynamic properties can still remain sample-specific due to the one-electron part of the Hamiltonian. If the grain is made from a material which is close to the threshold of ferromagnetic instability the mesoscopic fluctuations of the magnetization are especially strong. Moreover, the situation becomes multi-stable: free energy of each grain as a function of the magnetization is characterized by a large number of local minima. We analyze the statistics of these minima and show that it possesses simple scaling properties. Numerical simulations confirm this scaling.

cond-mat.mes-hall↗

arXiv2000

Single parameter scaling in one-dimensional localization revisited

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained are applied to the Kronig-Penney model with the potential in the form of periodically positioned $δ$-functions with random strength.

cond-mat.dis-nn↗

arXiv1999

Mesoscopic Fluctuations of Adiabatic Charge Pumping in Quantum Dots

We consider the adiabatic charge transport through zero-dimensional mesoscopic sample (quantum dot) caused by two periodically changing external perturbations. Both the magnitude and the sign of the transmitted charge are extremely sensitive to the configuration of the dot and to the magnetic field. We find the correlation function characterizing the random value of this pumped charge for arbitrary strength of the perturbation. In contrast to previous theoretical and experimental claims, the charge is found not to have any symmetry with respect to the inversion of magnetic field. At strong pumping perturbation, the variance of the charge $ $ is found to be proportional to the length of the contour in parametric space.

cond-mat.mes-hall↗

arXiv1999

On the relationship between the noise-induced persistent current and dephasing rate

AC noise in disordered conductors causes both dephasing of the electron wave functions and a DC current around a mesoscopic ring. We demonstrate that the dephasing rate tau_ϕ^{-1} in long wires and the DC current, induced by the same noise and averaged over an ensemble of small rings are connected. The ensemble-averaged h/2e flux harmonic of the current and the dephasing rate caused by the same uniform in space high frequency AC field are related in a remarkably simple way: tau_ϕ=C e. Here e is an electron charge, and the constant C depends on the Dyson symmetry class. For a pure potential disorder the current is diamagnetic C = -(4/π) and in the presence of strong spin-orbit scattering it is paramagnetic C =(2/π). The relationship seems to agree reasonably with experiments. This suggests that the two puzzles: anomalously large persistent current [L.P.Levy et al., Phys.Rev.Lett., v.64, 2074 (1990)] and the low-temperature saturation of the dephasing [P.Mohanty et al., Phys.Rev.Lett., v.78, 3366 (1997)] may have a common solution.

cond-mat.mes-hall↗

arXiv1999

Metal-insulator transition in 2D: Anderson localization by temperature-dependent disorder?

A generalization of the single-parameter scaling theory of localization is proposed for the case when the random potential depends on temperature. The scaling equation describing the behavior of the resistance is derived. It is shown that the competition between the metallic-like temperature dependence of the Drude resistivity and localization leads to a maximum (minimum) at higher (lower) temperatures. An illustration of a metal-insulator transition in the model of charged traps, whose concentration depends on temperature, is presented.

cond-mat.mes-hall↗

arXiv1999

Theory of Interaction Effects in N-S Junctions out of Equilibrium

We consider a normal metal - superconductor (N-S) junction in the regime, when electrons in the normal metal are driven out of equilibrium. We show that the non-equilibrium fluctuations of the electron density in the N-layer cause the fluctuations of the phase of the order parameter in the S-layer. As a result, the density of states in the superconductor deviates from the BCS form, most notably the density of states in the gap becomes finite. This effect can be viewed as a result of the time reversal symmetry breaking due to the non-equilibrium, and can be described in terms of a low energy collective mode of the junction, which couples normal currents in N-layer and supercurrents. This mode is analogous to the Schmid-Schön mode. To interpret their measurements of the tunneling current, Pothier {\em et. al} [Phys. Rev. Lett. {\bf 79}, 3490 (1997)] had to assume that the energy relaxation rate in the normal metal is surprisingly high. The broadening of the BCS singularity of the density of states in the S-layer manifest itself similarly to the broadening of the distribution function. Mechanism suggested here can be a possible explanation of this experimental puzzle. We also propose an independent experiment to test our explanation.

cond-mat.mes-hall↗

arXiv1998

Comment on "Quantum Decoherence in Disordered Mesoscopic Systems"

In a recent paper, Phys. Rev. Lett. 81, 1074 (1998), Golubev and Zaikin (GZ) found that ``zero-point fluctuations of electrons'' contribute to the dephasing rate extracted from the magnetoresistance. As a result, the dephasing rate remains finite at zero temperature. GZ claimed that their results ``agree well with the experimental data''. We point out that the GZ results are incompatible with (i) conventional perturbation theory of the effects of interaction on weak localization (WL), and (ii) with the available experimental data. More detailed criticism of GZ findings can be found in cond-mat/9808053.

cond-mat.dis-nn↗

arXiv1998

Interaction effects and phase relaxation in disordered systems

This paper is intended to demonstrate that there is no need to revise the existing theory of the transport properties of disordered conductors in the so-called weak localization regime. In particular, we demonstrate explicitly that recent attempts to justify theoretically that the dephasing rate (extracted from the magnetoresistance) remains finite at zero temperature are based on the profoundly incorrect calculation. This demonstration is based on a straightforward evaluation of the effect of the electron-electron interaction on the weak localization correction to the conductivity of disordered metals. Using well-controlled perturbation theory with the inverse conductance $g$ as the small parameter, we show that this effect consists of two contributions. First contribution comes from the processes with energy transfer smaller than the temperature. This contribution is responsible for setting the energy scale for the magnetoresistance. The second contribution originates from the virtual processes with energy transfer larger than the temperature. It is shown that the latter processes have nothing to do with the dephasing, but rather manifest the second order (in $1/g$) correction to the conductance. This correction is calculated for the first time. The paper also contains a brief review of the existing experiments on the dephasing of electrons in disordered conductors and an extended qualitative discussion of the quantum corrections to the conductivity and to the density of electronic states in the weak localization regime.

cond-mat.dis-nn↗

arXiv1998

Phase Relaxation of Electrons in Disordered Conductors

Conduction electrons in disordered metals and heavily doped semiconductors at low temperatures preserve their phase coherence for a long time: phase relaxation time $τ_ϕ$ can be orders of magnitude longer than the momentum relaxation time. The large difference in these time scales gives rise to well known effects of weak localization, such as anomalous magnetoresistance. Among other interesting characteristics, study of these effects provide quantitative information on the dephasing rate $1/τ_ϕ$. This parameter is of fundamental interest: the relation between $\hbar/τ_ϕ$ and the temperature $T$ (a typical energy scale of an electron) determines how well a single electron state is defined. We will discuss the basic physical meaning of $1/τ_ϕ$ in different situations and its difference from the energy relaxation rate. At low temperatures, the phase relaxation rate is governed by collisions between electrons. We will review existing theories of dephasing by these collisions or (which is the same) by electric noise inside the sample. We also discuss recent experiments on the magnetoresistance of 1D systems: some of them show saturation of $1/τ_ϕ$ at low temperatures, the other do not. To resolve this contradiction we discuss dephasing by an external microwave field and by nonequilibrium electric noise.

cond-mat.dis-nn↗

arXiv1998

Theory of Tunneling Anomaly in Superconductor above Paramagnetic Limit

We study the tunneling density of states (DoS) in the superconducting systems driven by Zeeman splitting $E_Z$ into the paramagnetic phase. We show that, even though the BCS gap disappears, superconducting fluctuations cause a strong DoS singularity in the vicinity of energies $-E^*$ for electrons polarized along the magnetic field and $E^*$ for the opposite polarization. The position of this singularity $E^*=\case{1}{2}(E_Z + \sqrt{E_Z^2- Δ^2})$ (where $Δ$ is BCS gap at $E_Z=0$) is universal. We found analytically the shape of the DoS for different dimensionality of the system. For ultra-small grains the singularity has the shape of the hard gap, while in higher dimensions it appears as a significant though finite dip. The spin-orbit scattering, and the orbital magnetic field suppress the singularity. Our results are qualitatively consistent with recent experiments in superconducting films.

cond-mat.supr-con↗

arXiv1997

Tunneling Anomaly in Superconductor above Paramagnetic Limit

We study the tunneling density of states (DoS) in the superconducting systems driven by Zeeman splitting E_Z into the paramagnetic phase. We show that, even though the BCS gap disappears, superconducting fluctuations cause a strong DoS singularity in the vicinity of energies -E^* for electrons polarized along the magnetic field and E^* for the opposite polarization. The position of the singularity E^*=(1/2) (E_Z + \sqrt{E_Z^2- Δ^2}) (where Δis BCS gap at E_Z=0) is universal. We found analytically the shape of the DoS for different dimensionality of the system. For ultrasmall grains the singularity has the form of the hard gap, while in higher dimensions it appears as a significant though finite dip. Our results are consistent with recent experiments in superconducting films.

cond-mat.supr-con↗

arXiv1997

Weak Chaos in a Quantum Kepler Problem

Transition from regular to chaotic dynamics in a crystal made of singular scatterers $U(r)=λ|r|^{-σ}$ can be reached by varying either sigma or lambda. We map the problem to a localization problem, and find that in all space dimensions the transition occurs at sigma=1, i.e., Coulomb potential has marginal singularity. We study the critical line sigma=1 by means of a renormalization group technique, and describe universality classes of this new transition. An RG equation is written in the basis of states localized in momentum space. The RG flow evolves the distribution of coupling parameters to a universal stationary distribution. Analytic properties of the RG equation are similar to that of Boltzmann kinetic equation: the RG dynamics has integrals of motion and obeys an H-theorem. The RG results for sigma=1 are used to derive scaling laws for transport and to calculate critical exponents.

cond-mat↗

arXiv1997

Luttinger theorem for a spin-density-wave state

We obtained the analog of the Luttinger relation for a commensurate spin-density-wave state. We show that while the relation between the area of the occupied states and the density of particles gets modified in a simple and predictable way when the system becomes ordered, a perturbative consideration of the Luttinger theorem does not work due to the presence of an anomaly similar to the chiral anomaly in quantum electrodynamics.

cond-mat.str-el↗

arXiv1997

Long-Range Spatial Correlations of Eigenfunctions in Quantum Disordered Systems

This paper is devoted to the statistics of the quantum eigenfunctions in an ensemble of finite disordered systems (metallic grains). We focus on moments of inverse participation ratio. In the universal random matrix limit that corresponds to the infinite conductance of the grains, these moments are self-averaging quantities. At large but finite conductance the moments do fluctuate due to the long range correlations in the eigenfunctions. We evaluate the distributions of fluctuations at given conductance and geometry of the grains and express them through the spectrum of the diffusion operator in the grain.

cond-mat.mes-hall↗

arXiv1996

Compressibility, capacitance and ground state energy fluctuations in a weakly interacting quantum dot

We study the effect of electron-electron (e-e) interactions on compressibility, capacitance and inverse compressibility of electrons in a quantum dot or a small metallic grain. The calculation is performed in the random-phase approximation. As expected, the ensemble-averaged compressibility and capacitance decreases as a function of the interaction strength, while the mean inverse compressibility increases. Fluctuations of the compressibility are found to be strongly suppressed by the e-e interactions. Fluctuations of the capacitance and inverse compressibility also turn out to be much smaller than their averages. The analytical calculations are compared with the results of a numerical calculation for the inverse compressibility of a disordered tight-binding model. Excellent agreement for weak interaction values is found. Implications for the interpretation of current experimental data are discussed.

cond-mat.mes-hall↗

arXiv1996

Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach

The problem of electron--electron lifetime in a quantum dot is studied beyond perturbation theory by mapping it onto the problem of localization in the Fock space. We identify two regimes, localized and delocalized, corresponding to quasiparticle spectral peaks of zero and finite width, respectively. In the localized regime, quasiparticle states are very close to single particle excitations. In the delocalized state, each eigenstate is a superposition of states with very different quasiparticle content. A transition between the two regimes occurs at the energy $\simeqΔ(g/\ln g)^{1/2}$, where $Δ$ is the one particle level spacing, and $g$ is the dimensionless conductance. Near this energy there is a broad critical region in which the states are multifractal, and are not described by the Golden Rule.

cond-mat↗

arXiv1996

Semiclassical Field Theory Approach to Quantum Chaos

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix nonlinear $σ$-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.

cond-mat↗

arXiv1996

Relations Between Quantum and Classical Spectral Determinants (Zeta-Functions)

We demonstrate that beyond the universal regime correlators of quantum spectral determinants $Δ(ε)=\det (ε-\hat{H})$ of chaotic systems, defined through an averaging over a wide energy interval, are determined by the underlying classical dynamics through the spectral determinant $1/Z(z)=\det (z- {\cal L})$, where $e^{-{\cal L}t}$ is the Perron-Frobenius operator. Application of these results to the Riemann zeta function, allows us to conjecture new relations satisfied by this function.

cond-mat↗