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A. D. Mirlin

Publications and source records attributed to A. D. Mirlin.

At least 145 records · Page 8Linked to original sources
arXiv2002

Multifractality at the spin quantum Hall transition

Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $η$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $Δ_q\simeq q(1-q)/8$ and $X_q\simeq q(3-q)/4$.

cond-mat.mes-hall↗
arXiv2001

Dimensionality dependence of the wave function statistics at the Anderson transition

The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.

cond-mat.dis-nn↗
arXiv2001

From quantum disorder to quantum chaos

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $σ$-model approach. We analyze conditions of applicability of the $σ$-model, emphasizing the role played by the single-particle mean free path and the Lyapunov exponent due to the random potential. In particular, we present a resolution of the puzzle of repetitions of periodic orbits counted differently by the $σ$-model and by the trace formula.

cond-mat.mes-hall↗
arXiv2001

Nonadiabatic scattering of a quantum particle in an inhomogenous magnetic field

We investigate the quantum effects, in particular the Landau-level quantization, in the scattering of a particle the nonadiabatic classical dynamics of which is governed by an adiabatic invariant. As a relevant example, we study the scattering of a drifting particle on a magnetic barrier in the quantum limit where the cyclotron energy is much larger than a broadening of the Landau levels induced by the nonadiabatic transitions. We find that, despite the level quantization, the exponential suppression $\exp(-2πd/δ)$ (barrier width $d$, orbital shift per cyclotron revolution $δ$) of the root-mean-square transverse displacement experienced by the particle after the scattering is the same in the quantum and the classical regime.

cond-mat.mes-hall↗
arXiv2001

Multifractality of wavefunctions at the quantum Hall transition revisited

We investigate numerically the statistics of wavefunction amplitudes $ψ({\bf r})$ at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of $|ψ|^2$ is log-normal, so that the multifractal spectrum $f(α)$ is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition.

cond-mat.mes-hall↗
arXiv2001

Wave function correlations on the ballistic scale: Exploring quantum chaos by quantum disorder

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by Hortikar and Srednicki is proven to hold on sufficiently short distances, while it is found to be strongly violated on larger scales. This also resolves the conflict between the above conjecture and the wave function normalization. The method is further used to study ballistic correlations of wave functions in a random magnetic field.

cond-mat.mes-hall↗
arXiv2001

Quasiclassical magnetotransport in a random array of antidots

We study theoretically the magnetoresistance $ρ_{xx}(B)$ of a two-dimensional electron gas scattered by a random ensemble of impenetrable discs in the presence of a long-range correlated random potential. We believe that this model describes a high-mobility semiconductor heterostructure with a random array of antidots. We show that the interplay of scattering by the two types of disorder generates new behavior of $ρ_{xx}(B)$ which is absent for only one kind of disorder. We demonstrate that even a weak long-range disorder becomes important with increasing $B$. In particular, although $ρ_{xx}(B)$ vanishes in the limit of large $B$ when only one type of disorder is present, we show that it keeps growing with increasing $B$ in the antidot array in the presence of smooth disorder. The reversal of the behavior of $ρ_{xx}(B)$ is due to a mutual destruction of the quasiclassical localization induced by a strong magnetic field: specifically, the adiabatic localization in the long-range Gaussian disorder is washed out by the scattering on hard discs, whereas the adiabatic drift and related percolation of cyclotron orbits destroys the localization in the dilute system of hard discs. For intermediate magnetic fields in a dilute antidot array, we show the existence of a strong negative magnetoresistance, which leads to a nonmonotonic dependence of $ρ_{xx}(B)$.

cond-mat.dis-nn↗
arXiv2001

Quasiclassical negative magnetoresistance of a 2D electron gas: interplay of strong scatterers and smooth disorder

We study the quasiclassical magnetotransport of non-interacting fermions in two dimensions moving in a random array of strong scatterers (antidots, impurities or defects) on the background of a smooth random potential. We demonstrate that the combination of the two types of disorder induces a novel mechanism leading to a strong negative magnetoresistance, followed by the saturation of the magnetoresistivity $ρ_{xx}(B)$ at a value determined solely by the smooth disorder. Experimental relevance to the transport in semiconductor heterostructures is discussed.

cond-mat.dis-nn↗
arXiv2001

Magnetotransport in 2D lateral superlattices with smooth disorder: Quasiclassical theory of commensurability oscillations

Commensurability oscillations in the magnetoresistivity of a two-dimensional electron gas in a two-dimensional lateral superlattice are studied in the framework of quasiclassical transport theory. It is assumed that the impurity scattering is of small-angle nature characteristic for currently fabricated high-mobility heterostructures. The shape of the modulation-induced magnetoresistivity $Δρ_{xx}$ depends on the value of the parameter $γ\equiv η^2 ql/4$, where $η$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport mean free path. For $γ\ll 1$, the oscillations are described, in the regime of not too strong magnetic fields $B$, by perturbation theory in $η$ as applied earlier to the case of one-dimensional modulation. At stronger fields, where $Δρ_{xx}$ becomes much larger than the Drude resistivity, the transport takes the advection-diffusion form (Rayleigh-Bénard convection cell) with a large Péclet number, implying a much slower ($\propto B^{3/4}$) increase of the oscillation amplitude with $B$. If $γ\gg 1$, the transport at low $B$ is dominated by the modulation-induced chaos (rather than by disorder). The magnetoresistivity drops exponentially and the commensurability oscillations start to develop at the magnetic fields where the motion takes the form of the adiabatic drift. Conditions of applicability, the role of the type of disorder, and the feasibility of experimental observation are discussed.

cond-mat.dis-nn↗
arXiv2000

Magnetotransport in lateral superlattices with small-angle impurity scattering: Low-field magnetoresistance

An analytical study of the low-field magnetoresistance of a two-dimensional electron gas subject to a weak periodic modulation is presented. We assume small-angle impurity scattering characteristic for high-mobility semiconductor heterostructures. It is shown that the condition for existence of the strong low-field magnetoresistance induced by so-called channeled orbits is $η^{3/2}ql\gg 1$, where $η$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport mean free path. Under this condition, the magnetoresistance scales as $η^{7/2}$.

cond-mat.dis-nn↗
arXiv2000

Level and Eigenfunction Statistics in Billiards with Surface Scattering

Statistical properties of billiards with diffusive boundary scattering are investigated by means of the supersymmetric sigma-model in a formulation appropriate for chaotic ballistic systems. We study level statistics, parametric level statistics, and properties of electron wavefunctions. In the universal regime, our results reproduce conclusions of the random matrix theory, while beyond this regime we obtain a variety of system-specific results determined by the classical dynamics in the billiard. Most notably, we find that level correlations do not vanish at arbitrary separation between energy levels, or if measured at arbitrarily large difference of magnetic fields. Saturation of the level number variance indicates strong rigidity of the spectrum. To study spatial correlations of wavefunction amplitudes, we reanalyze and refine derivation of the ballistic version of the sigma-model. This allows us to obtain a proper matching of universal short-scale correlations with system-specific ones.

cond-mat↗
arXiv2000

Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance

We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic field. Our result is universal, i.e. it does not depend on the type (random potential or random magnetic field) or correlation length of disorder. This contradicts recent sigma-model calculations of Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well as for the renormalization of the conductivity. We show explicitly that the new term in the sigma-model derived by TS&E and claimed to lead to delocalization does not exist. The error in the derivation of TS&E is traced to an incorrect ultraviolet regularization procedure violating current conservation and gauge invariance.

cond-mat.mes-hall↗
arXiv2000

Comment on "Antilocalization in a 2D Electron Gas in a Random Magnetic Field"

In a recent Letter, Taras-Semchuk and Efetov reconsider the problem of electron localization in a random magnetic field in two dimensions. They claim that due to the long-range nature of the vector potential correlations an additional term appears in the effective field theory ($σ$-model) of the problem, leading to delocalization at the one-loop level. This calls into question the results of earlier analytical studies, where the random magnetic field problem was mapped onto the conventional unitary-class $σ$-model, implying that the leading quantum correction is of two-loop order and of a localizing nature. We show in this Comment, however, that the new term in fact does not exist and was erroneously obtained by Taras-Semchuk and Efetov because of an inconsistent treatment violating gauge invariance.

cond-mat.dis-nn↗
arXiv2000

Multifractality and critical fluctuations at the Anderson transition

Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse participation ratios (IPR) $P_q$ are scale-invariant at the critical point, with a power-law asymptotic tail. The IPR distribution, the multifractal spectrum and the level statistics are calculated analytically in the limits of weak and strong couplings, as well as numerically in the full range of couplings.

cond-mat.mes-hall↗
arXiv2000

Fluctuations of the inverse participation ratio at the Anderson transition

Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale-invariant, with a power-law asymptotic ``tail''. This scale invariance implies that the fractal dimensions $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility $χ$ is violated in the regime of strong multifractality, with $χ\to 1$ in the limit $D_2\to 0$.

cond-mat.mes-hall↗
arXiv1999

Zero-frequency anomaly in quasiclassical ac transport: Memory effects in a two-dimensional metal with a long-range random potential or random magnetic field

We study the low-frequency behavior of the {\it ac} conductivity $σ(ω)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|ω|$ correction to ${\rm Re} σ$, which corresponds to a $1/t^2$ long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this $|ω|$-term is positive and proportional to $(d/l)^2$ for RP, while it is of opposite sign and proportional to $d/l$ in the weak RMF case, where $l$ is the mean free path and $d$ the disorder correlation length. This non-analytic correction also exists in the strong RMF regime, when the transport is of a percolating nature. The analytical results are supported and complemented by numerical simulations.

cond-mat.mes-hall↗
arXiv1999

Strong magnetoresistance induced by long-range disorder

We calculate the semiclassical magnetoresistivity $ρ_{xx}(B)$ of non-interacting fermions in two dimensions moving in a weak and smoothly varying random potential or random magnetic field. We demonstrate that in a broad range of magnetic fields the non-Markovian character of the transport leads to a strong positive magnetoresistance. The effect is especially pronounced in the case of a random magnetic field where $ρ_{xx}(B)$ becomes parametrically much larger than its B=0 value.

cond-mat.dis-nn↗