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Alexander D. Mirlin

Publications and source records attributed to Alexander D. Mirlin.

At least 73 records · Page 4Linked to original sources
arXiv2013

Analytically solvable model of an electronic Mach-Zehnder interferometer

We consider a class of models of non-equilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the interferometer and transmission coefficients of the quantum quantum point contacts, defining the interferometer, which may take arbitrary values from zero to one. We establish an exact solution of these models in terms of single-particle quantities --- determinants and resolvents of Fredholm integral operators. In the general situation, the results can be obtained numerically. In the case of strong charging interaction, the operators acquire the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem, we reduce the result to certain singular single-channel determinants (which are a generalization of Toeplitz determinants with Fisher-Hartwig singularities), and obtain an analytic result for the interference current (and, in particular, for the visibility of Aharonov-Bohm oscillations). Our results, which are in good agreement with experimental observations, show an intimate connection between the observed "lobe" structure in the visibility of Aharonov-Bohm oscillations and multiple branches in the asymptotics of singular integral determinants.

cond-mat.mes-hall↗
arXiv2012

Weak localization and magnetoresistance in a two-leg ladder model

We analyze the weak localization correction to the conductivity of a spinless two-leg ladder model in the limit of strong dephasing τ_ϕ<< τ_tr, paying particular attention to the presence of a magnetic field, which leads to an unconventional magnetoresistance behavior. We find that the magnetic field leads to three different effects: (i) negative magnetoresistance due to the regular weak localization correction (ii) effective decoupling of the two chains, leading to positive magnetoresistance and (iii) oscillations in the magnetoresistance originating from the nature of the low-energy collective excitations. All three effects can be observed depending on the parameter range, but it turns out that large magnetic fields always decouple the chains and thus lead to the curious effect of magnetic field enhanced localization.

cond-mat.str-el↗
arXiv2012

Nonequilibrium functional bosonization of quantum wire networks

We develop a general approach to nonequilibrium nanostructures formed by one-dimensional channels coupled by tunnel junctions and/or by impurity scattering. The formalism is based on nonequilibrium version of functional bosonization. A central role in this approach is played by the Keldysh action that has a form reminiscent of the theory of full counting statistics. To proceed with evaluation of physical observables, we assume the weak-tunneling regime and develop a real-time instanton method. A detailed exposition of the formalism is supplemented by two important applications: (i) tunneling into a biased Luttinger liquid with an impurity, and (ii) quantum-Hall Fabry-Perot interferometry.

cond-mat.mes-hall↗
arXiv2012

Manifestation of electron-electron interaction in the magnetoresistance of graphene

We investigate the magnetotransport in large area graphene Hall bars epitaxially grown on silicon carbide. In the intermediate field regime between weak localization and Landau quantization the observed temperature-dependent parabolic magnetoresistivity (MR) is a manifestation of the electron-electron interaction (EEI). We can consistently describe the data with a model for diffusive (magneto)transport that also includes magnetic-field dependent effects originating from ballistic time scales. We find an excellent agreement between the experimentally observed temperature dependence of MR and the theory of EEI in the diffusive regime. We can further assign a temperature-driven crossover to the reduction of the multiplet modes contributing to EEI from 7 to 3 due to intervalley scattering. In addition, we find a temperature independent ballistic contribution to the MR in classically strong magnetic fields.

cond-mat.mes-hall↗
arXiv2011

Theory of non-equilibrium electronic Mach-Zehnder interferometer

We develop a theoretical description of interaction-induced phenomena in an electronic Mach-Zehnder interferometer formed by integer quantum Hall edge states (with ν=1 and 2 channels) out of equilibrium. Using the non-equilibrium functional bosonization framework, we derive an effective action which contains all the physics of the problem. We apply the theory to the model of a short-range interaction and to a more realistic case of long-range Coulomb interaction. The theory takes into account interaction-induced effects of dispersion of plasmons, charging, and decoherence. In the case of long-range interaction we find a good agreement between our theoretical results for the visibility of Aharonov-Bohm oscillations and experimental data.

cond-mat.mes-hall↗
arXiv2009

Tunneling into Nonequilibrium Luttinger Liquid with Impurity

We evaluate tunneling rates into/from a voltage biased quantum wire containing weak backscattering defect. Interacting electrons in such a wire form a true nonequilibrium state of the Luttinger liquid (LL). This state is created due to inelastic electron backscattering leading to the emission of nonequilibrium plasmons with typical frequency $\hbar ω\leq U$. The tunneling rates are split into two edges. The tunneling exponent at the Fermi edge is positive and equals that of the equilibrium LL, while the exponent at the side edge $E_F-U$ is negative if Coulomb interaction is not too strong.

cond-mat.mes-hall↗
arXiv2000

Statistics of energy levels and eigenfunctions in disordered systems

The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on low-dimensional (quasi-1D and 2D) systems. Calculations are based on the supermatrix sigma-model approach. The method reproduces, in so-called zero-mode approximation, the universal random matrix theory (RMT) results for the energy-level and eigenfunction fluctuations. Going beyond this approximation allows us to study system-specific deviations from universality, which are determined by the diffusive classical dynamics in the system. These deviations are especially strong in the far ``tails'' of the distribution function of the eigenfunction amplitudes (as well as of some related quantities, such as local density of states, relaxation time, etc.). These asymptotic ``tails'' are governed by anomalously localized states which are formed in rare realizations of the random potential. The deviations of the level and eigenfunction statistics from their RMT form strengthen with increasing disorder and become especially pronounced at the Anderson metal-insulator transition. In this regime, the wave functions are multifractal, while the level statistics acquires a scale-independent form with distinct critical features. Fluctuations of the conductance and of the local intensity of a classical wave radiated by a point-like source in the quasi-1D geometry are also studied within the sigma-model approach. For a ballistic system with rough surface an appropriately modified (``ballistic'') sigma-model is used. Finally, the interplay of the fluctuations and the electron-electron interaction in small samples is discussed, with application to the Coulomb blockade spectra.

cond-mat.dis-nn↗
arXiv1997

Correlations of Wave Functions in Disordered Systems

This is an extended version of the talk given by the author at the NATO Advanced Study Institute "Supersymmetry and Trace Formulae" (Isaac Newton Institute, Cambridge, UK, 8-19 Septemebr 1997). Contains the following sections: 1. Eigenfunction correlations in the weak localization regime. 2. Strong correlations of eigenfunctions and level repulsion at the Anderson localization transition. 3. Fluctuations in the addition spectra of quantum dots.

cond-mat.dis-nn↗
arXiv1997

Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots

We study fluctuations of the local density of states (LDOS) on a tree-like lattice with large branching number $m$. The average form of the local spectral function (at given value of the random potential in the observation point) shows a crossover from the Lorentzian to semicircular form at $α\sim 1/m$, where $α= (V/W)^2$, $V$ is the typical value of the hopping matrix element, and $W$ is the width of the distribution of random site energies. For $α>1/m^2$ the LDOS fluctuations (with respect to this average form) are weak. In the opposite case, $α<1/m^2$, the fluctuations get strong and the average LDOS ceases to be representative, which is related to the existence of the Anderson transition at $α_c\sim 1/(m^2\log^2m)$. On the localized side of the transition the spectrum is discrete, and LDOS is given by a set of $δ$-like peaks. The effective number of components in this regime is given by $1/P$, with $P$ being the inverse participation ratio. It is shown that $P$ has in the transition point a limiting value $P_c$ close to unity, $1-P_c\sim 1/\log m$, so that the system undergoes a transition directly from the deeply localized to extended phase. On the side of delocalized states, the peaks in LDOS get broadened, with a width $\sim\exp\{-{const}\log m[(α-α_c)/α_c]^{-1/2}\}$ being exponentially small near the transition point. We discuss application of our results to the problem of the quasiparticle line shape in a finite Fermi system, as suggested recently by Altshuler, Gefen, Kamenev, and Levitov.

cond-mat.dis-nn↗
arXiv1996

Strong eigenfunction correlations near the Anderson localization transition

We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of Anderson transition their mutual overlap is still found to be of the same order as self-overlap as long as energy separation is smaller than a critical value. The latter fact explains robustness of the Wigner-Dyson level statistics everywhere in the phase of extended states. The same picture is expected to hold for usual d-dimensional conductors, ensuring the $s^β$ form of the level repulsion at critical point.

cond-mat.mes-hall↗
arXiv1996

Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices

We study statistical properties of the ensemble of large $N\times N$ random matrices whose entries $ H_{ij}$ decrease in a power-law fashion $H_{ij}\sim|i-j|^{-α}$. Mapping the problem onto a nonlinear $σ-$model with non-local interaction, we find a transition from localized to extended states at $α=1$. At this critical value of $α$ the system exhibits multifractality and spectral statistics intermediate between the Wigner-Dyson and Poisson one. These features are reminiscent of those typical for the mobility edge of disordered conductors. We find a continuous set of critical theories at $α=1$, parametrized by the value of the coupling constant of the $σ-$model. At $α>1$ all states are expected to be localized with integrable power-law tails. At the same time, for $1<α<3/2$ the wave packet spreading at short time scale is superdiffusive: $\langle |r|\rangle\sim t^{\frac{1}{2α-1}}$, which leads to a modification of the Altshuler-Shklovskii behavior of the spectral correlation function. At $1/2<α<1$ the statistical properties of eigenstates are similar to those in a metallic sample in $d=(α-1/2)^{-1}$ dimensions. Finally, the region $α<1/2$ is equivalent to the corresponding Gaussian ensemble of random matrices $(α=0)$. The theoretical predictions are compared with results of numerical simulations.

cond-mat↗
arXiv1996

Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice and the Replica Limit

We solve $O(n,1)$ nonlinear vector model on Bethe lattice and show that it exhibits a transition from ordered to disordered state for $0 \leq n < 1$. If the replica limit $n\to 0$ is taken carefully, the model is shown to reduce to the corresponding supersymmetric model. The latter was introduced by Zirnbauer as a toy model for the Anderson localization transition. We argue thus that the non-compact replica models describe correctly the Anderson transition features. This should be contrasted to their failure in the case of the level correlation problem.

cond-mat↗
arXiv1995

Spatial structure of anomalously localized states in disordered conductors

The spatial structure of wave functions of anomalously localized states (ALS) in disordered conductors is studied in the framework of the $σ$--model approach. These states are responsible for slowly decaying tails of various distribution functions. In the quasi-one-dimensional case, properties of ALS governing the asymptotic form of the distribution of eigenfunction amplitudes are investigated with the use of the transfer matrix method, which yields an exact solution to the problem. Comparison of the results with those obtained in the saddle-point approximation to the problem shows that the saddle-point configuration correctly describes the smoothed intensity of an ALS. On this basis, the properties of ALS in higher spatial dimensions are considered. We study also the ALS responsible for the asymptotic behavior of distribution functions of other quantities, such as relaxation time, local and global density of state. It is found that the structure of an ALS may be different, depending on the specific quantity, for which it constitutes an optimal fluctuation. Relations between various procedures of selection of ALS, and between asymptotics of corresponding distribution functions, are discussed.

cond-mat↗
arXiv1995

Long--time relaxation of current in a 2D weakly disordered conductor

The long-time relaxation of the average conductance in a 2D mesoscopic sample is studied within the method recently suggested by Muzykantskii and Khmelnitskii and based on a saddle-point approximation to the supermatrix $σ$--model. The obtained far asymptotics is in perfect agreement with the result of renormalization group treatment by Altshuler, Kravtsov and Lerner.

cond-mat↗
arXiv1995

Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $σ-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.

cond-mat↗
arXiv1994

Fluctuations of the Energy Levels Number at the Mobility Edge

We present a detailed analysis of the behavior of two--level correlation function $R(s)$ in the disordered sample. We show that in the vicinity of the Anderson transition as well as in $2d$, the variance of the number of levels in an energy band of a width $E$ has a linear behavior as a function of $E$. This is related with an ``anomalous'' contribution to the sum rule for $R(s)$, which comes from the ``ballistic'' region of $s$.

cond-mat↗