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Sep 19, 2013
09/13

by
D. G. Polyakov

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We study the system-size dependence of the averaged critical conductance $g(L)$ at the Anderson transition. We have: (i) related the correction $\delta g(L)=g(\infty)-g(L)\propto L^{-y}$ to the spectral correlations; (ii) expressed $\delta g(L)$ in terms of the quantum return probability; (iii) argued that $y=\eta$ -- the critical exponent of eigenfunction correlations. Experimental implications are discussed.

Source: http://arxiv.org/abs/cond-mat/9804259v2

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30

Sep 23, 2013
09/13

by
D. G. Polyakov

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Recent work on the temperature-driven delocalization in the quantum Hall regime is reviewed, with emphasis on the role of electron-electron interactions and the correlation properties of disorder. We have stressed (i) the crucial role of the Coulomb interaction in the integer quantum Hall effect; (ii) the classical aspects of electron dynamics in samples with long-range disorder.

Source: http://arxiv.org/abs/cond-mat/9608013v1

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27

Sep 23, 2013
09/13

by
D. G. Polyakov

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We present a microscopic theory of spin-orbit coupling in the integer quantum Hall regime. The spin-orbit scattering length is evaluated in the limit of long-range random potential. The spin-flip rate is shown to be determined by rare fluctuations of anomalously high electric field. A mechanism of strong spin-orbit scattering associated with exchange-induced spontaneous spin-polarization is suggested. Scaling of the spin-splitting of the delocalization transition with the strength of spin-orbit...

Source: http://arxiv.org/abs/cond-mat/9511123v2

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35

Sep 22, 2013
09/13

by
D. G. Polyakov; B. I. Shklovskii

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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...

Source: http://arxiv.org/abs/cond-mat/9409104v1

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38

Sep 21, 2013
09/13

by
D. G. Polyakov; K. V. Samokhin

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We argue that the finite temperature dynamics of the integer quantum Hall system is governed by two independent length scales. The consistent scaling description of the transition makes crucial use of two temperature critical exponents, reflecting the interplay between charging effects and interaction-induced dephasing. Experimental implications of the two-scale picture are discussed.

Source: http://arxiv.org/abs/cond-mat/9705154v3

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Sep 22, 2013
09/13

by
D. G. Polyakov; M. E. Raikh

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The quantum Hall regime in a smooth random potential is considered when two disorder-broadened Zeeman levels overlap strongly. Spin-orbit coupling is found to cause a drastic change in the percolation network which leads to a strong enhancement of the dissipative conductivity at finite temperature, provided the Fermi level $E_F$ lies between the energies of two delocalized states $E=\pm\Delta$, $2\Delta$ being the Zeeman splitting. The conductivity is shown to exhibit a box-like behavior with...

Source: http://arxiv.org/abs/cond-mat/9503005v1

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36

Sep 18, 2013
09/13

by
D. G. Polyakov; I. V. Gornyi

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We generalize the fermionic renormalization group method to describe analytically transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent...

Source: http://arxiv.org/abs/cond-mat/0212355v2

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38

Sep 18, 2013
09/13

by
A. D. Mirlin; D. G. Polyakov; P. Woelfle

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We study transport in a smooth random magnetic field, with emphasis on composite fermions (CF) near half-filling of the Landau level. When either the amplitude of the magnetic field fluctuations or its mean value $\bar B$ is large enough, the transport is of percolating nature. While at $\bar{B}=0$ the percolation effects enhance the conductivity $\sigma_{xx}$, increasing $\bar B$ (which corresponds to moving away from half-filling for the CF problem) leads to a sharp falloff of $\sigma_{xx}$...

Source: http://arxiv.org/abs/cond-mat/9710135v1

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35

Sep 17, 2013
09/13

by
D. G. Polyakov; F. Evers; I. V. Gornyi

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We study the dynamical properties of an electron gas scattered by impenetrable antidots in the presence of a strong magnetic field. We find that the lineshape of the cyclotron resonance is very different from the Lorentzian and is not characterized by the Drude scattering rate. We show that the dissipative dynamical response of skipping orbits, $S_c(\omega)$, is broadened on a scale of the cyclotron frequency $\omega_c$ and has a sharp dip $\propto |\omega-\omega_c|$. For small antidots,...

Source: http://arxiv.org/abs/cond-mat/0108233v1

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3.0

Jun 28, 2018
06/18

by
A. P. Dmitriev; I. V. Gornyi; D. G. Polyakov

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We investigate the influence of the chemical potential mismatch $\Delta$ (different electron densities) on Coulomb drag between two parallel ballistic quantum wires. For pair collisions, the drag resistivity $\rho_{\rm D}(\Delta)$ shows a peculiar anomaly at $\Delta=0$ with $\rho_{\rm D}$ being finite at $\Delta=0$ and vanishing at any nonzero $\Delta$. The "bodyless" resonance in $\rho_{\rm D}(\Delta)$ at zero $\Delta$ is only broadened by processes of multi-particle scattering. We...

Topics: Strongly Correlated Electrons, Mesoscale and Nanoscale Physics, Condensed Matter

Source: http://arxiv.org/abs/1512.00373

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Sep 18, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov

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We develop a systematic theory of microwave-induced oscillations in magnetoresistivity of a 2D electron gas in the vicinity of fractional harmonics of the cyclotron resonance, observed in recent experiments. We show that in the limit of well-separated Landau levels the effect is dominated by a change of the distribution function induced by multiphoton processes. At moderate magnetic field, a single-photon mechanism originating from the microwave-induced sidebands in the density of states of...

Source: http://arxiv.org/abs/0707.0990v2

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38

Sep 19, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov

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The frequency-dependent conductivity $\sigma_{xx}(\omega)$ of 2D electrons subjected to a transverse magnetic field and smooth disorder is calculated. The interplay of Landau quantization and disorder scattering gives rise to an oscillatory structure that survives in the high-temperature limit. The relation to recent experiments on photoconductivity by Zudov {\it et al.} and Mani {\it et al.} is discussed.

Source: http://arxiv.org/abs/cond-mat/0304529v2

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2.0

Jun 28, 2018
06/18

by
I. V. Gornyi; A. D. Mirlin; D. G. Polyakov

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We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak...

Topics: Strongly Correlated Electrons, Mesoscale and Nanoscale Physics, Condensed Matter

Source: http://arxiv.org/abs/1512.01807

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57

Sep 20, 2013
09/13

by
A. P. Dmitriev; I. V. Gornyi; D. G. Polyakov

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We develop a kinetic equation description of Coulomb drag between ballistic one-dimensional electron systems, which enables us to demonstrate that equilibration processes between right- and left-moving electrons are crucially important for establishing dc drag. In one-dimensional geometry, this type of equilibration requires either backscattering near the Fermi level or scattering with small momentum transfer near the bottom of the electron spectrum. Importantly, pairwise forward scattering in...

Source: http://arxiv.org/abs/1207.1089v2

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38

Sep 20, 2013
09/13

by
I. V. Gornyi; A. D. Mirlin; D. G. Polyakov

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We study transport of interacting electrons in a low-dimensional disordered system at low temperature $T$. In view of localization by disorder, the conductivity $\sigma(T)$ may only be non-zero due to electron-electron scattering. For weak interactions, the weak-localization regime crosses over with lowering $T$ into a dephasing-induced "power-law hopping". As $T$ is further decreased, the Anderson localization in Fock space crucially affects $\sigma(T)$, inducing a transition at...

Source: http://arxiv.org/abs/cond-mat/0506411v1

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32

Sep 18, 2013
09/13

by
D. A. Bagrets; I. V. Gornyi; D. G. Polyakov

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We develop a kinetic theory for strongly correlated disordered one-dimensional electron systems out of equilibrium, within the Luttinger liquid model. In the absence of inhomogeneities, the model exhibits no relaxation to equilibrium. We derive kinetic equations for electron and plasmon distribution functions in the presence of impurities and calculate the equilibration rate $\gamma_E$. Remarkably, for not too low temperature and bias voltage, $\gamma_E$ is given by the elastic backscattering...

Source: http://arxiv.org/abs/0809.3166v2

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40

Sep 20, 2013
09/13

by
I. V. Gornyi; A. D. Mirlin; D. G. Polyakov

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We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of...

Source: http://arxiv.org/abs/cond-mat/0608590v2

40
40

Sep 20, 2013
09/13

by
A. D. Mirlin; D. G. Polyakov; V. M. Vinokur

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We consider the interplay of the elastic pinning and the Anderson localization in the transport properties of a charge-density wave in one dimension, within the framework of the Luttinger model in the limit of strong repulsion. We address a conceptually important issue of which of the two disorder-induced phenomena limits the mobility more effectively. We argue that the interplay of the classical and quantum effects in transport of a very rigid charge-density wave is quite nontrivial: the...

Source: http://arxiv.org/abs/cond-mat/0612663v2

57
57

Sep 22, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov

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We have analyzed the quasiclassical mechanism of magnetooscillations in the ac- and photoconductivity, related to non-Markovian dynamics of disorder-induced electron scattering. While the magnetooscillations in the photoconductivity are found to be weak, the effect manifests itself much more strongly in the ac conductivity, where it may easily dominate over the oscillations due to the Landau quantization. We argue that the damping of the oscillatory photoconductivity provides a reliable method...

Source: http://arxiv.org/abs/cond-mat/0403598v2

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36

Sep 19, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov

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We develop a systematic theory of microwave-induced oscillations in the magnetoresistivity of a two-dimensional electron gas, focusing on the regime of strongly overlapping Landau levels. At linear order in microwave power, two novel mechanisms of the oscillations (``quadrupole'' and ``photovoltaic'') are identified, in addition to those studied before (``displacement'' and ``inelastic''). The quadrupole and photovoltaic mechanisms are shown to be the only ones that give rise to oscillations in...

Source: http://arxiv.org/abs/cond-mat/0703080v2

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48

Sep 21, 2013
09/13

by
I. V. Gornyi; A. D. Mirlin; D. G. Polyakov

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We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron...

Source: http://arxiv.org/abs/cond-mat/0407305v4

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34

Sep 17, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov

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We develop a systematic theory of microwave-induced oscillations in magnetoresistivity of a 2D electron gas in the vicinity of fractional harmonics of the cyclotron resonance, observed in recent experiments. We show that in the limit of well-separated Landau levels the effect is dominated by the multiphoton inelastic mechanism. At moderate magnetic field, two single-photon mechanisms become important. One of them is due to resonant series of multiple single-photon transitions, while the other...

Source: http://arxiv.org/abs/0711.4249v1

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35

Sep 21, 2013
09/13

by
D. G. Polyakov; F. Evers; A. D. Mirlin; P. Woelfle

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We study theoretically the magnetoresistance $\rho_{xx}(B)$ 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 $\rho_{xx}(B)$ which is absent for only one kind of disorder. We demonstrate...

Source: http://arxiv.org/abs/cond-mat/0104417v1

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2.0

Jun 29, 2018
06/18

by
N. Kainaris; I. V. Gornyi; A. Levchenko; D. G. Polyakov

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We theoretically study Coulomb drag between two helical edges with broken spin-rotational symmetry, such as would occur in two capacitively coupled quantum spin Hall insulators. For the helical edges, Coulomb drag is particularly interesting because it specifically probes the inelastic interactions that break the conductance quantization for a single edge. Using the kinetic equation formalism, supplemented by bosonization, we find that the drag resistivity $\rho_D$ exhibits a nonmonotonic...

Topics: Mesoscale and Nanoscale Physics, Condensed Matter, Strongly Correlated Electrons

Source: http://arxiv.org/abs/1610.01100

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63

Sep 21, 2013
09/13

by
A. D. Mirlin; D. G. Polyakov; F. Evers; P. Woelfle

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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 $\rho_{xx}(B)$ at a value determined solely by the smooth disorder. Experimental...

Source: http://arxiv.org/abs/cond-mat/0104096v1

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55

Sep 18, 2013
09/13

by
F. Evers; A. D. Mirlin; D. G. Polyakov; P. Woelfle

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We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift...

Source: http://arxiv.org/abs/cond-mat/9901070v1

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30

Sep 22, 2013
09/13

by
F. Evers; A. D. Mirlin; D. G. Polyakov; P. Woelfle

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We study the violation of the adiabaticity of the electron dynamics in a slowly varying magnetic field. We formulate and solve exactly a non-adiabatic scattering problem. In particular, we consider scattering on a magnetic field inhomogeneity which models scatterers in the composite-fermion theory of the half-filled Landau level. The calculated non-adiabatic shift of the guiding center is exponentially small and exhibits an oscillatory behavior related to the "self-commensurability"...

Source: http://arxiv.org/abs/cond-mat/9807213v1

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28

Sep 23, 2013
09/13

by
I. A. Dmitriev; M. Khodas; A. D. Mirlin; D. G. Polyakov

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We study transport in the domain state, the so-called zero-resistance state, that emerges in a two-dimensional electron system in which the combined action of microwave radiation and magnetic field produces a negative absolute conductivity. We show that the voltage-biased system has a rich phase diagram in the system size and voltage plane, with second- and first-order transitions between the domain and homogeneous states for small and large voltages, respectively. We find the residual negative...

Source: http://arxiv.org/abs/1305.1028v1

38
38

Sep 23, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov; M. A. Zudov

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Developments in the physics of 2D electron systems during the last decade have revealed a new class of nonequilibrium phenomena in the presence of a moderately strong magnetic field. The hallmark of these phenomena is magnetoresistance oscillations generated by the external forces that drive the electron system out of equilibrium. The rich set of dramatic phenomena of this kind, discovered in high mobility semiconductor nanostructures, includes, in particular, microwave radiation-induced...

Source: http://arxiv.org/abs/1111.2176v3

35
35

Jul 20, 2013
07/13

by
D. A. Bagrets; I. V. Gornyi; A. D. Mirlin; D. G. Polyakov

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The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part...

Source: http://arxiv.org/abs/0804.4887v1

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36

Sep 18, 2013
09/13

by
F. Dahlem; F. Evers; A. D. Mirlin; D. G. Polyakov; P. Woelfle

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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...

Source: http://arxiv.org/abs/cond-mat/0105552v1

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29

Sep 21, 2013
09/13

by
A. G. Yashenkin; I. V. Gornyi; A. D. Mirlin; D. G. Polyakov

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We study the influence of spin on the quantum interference of interacting electrons in a single-channel disordered quantum wire within the framework of the Luttinger liquid (LL) model. The nature of the electron interference in a spinful LL is particularly nontrivial because the elementary bosonic excitations that carry charge and spin propagate with different velocities. We extend the functional bosonization approach to treat the fermionic and bosonic degrees of freedom in a disordered spinful...

Source: http://arxiv.org/abs/0808.1093v1

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44

Sep 21, 2013
09/13

by
A. D. Mirlin; J. Wilke; F. Evers; D. G. Polyakov; P. Woelfle

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We calculate the semiclassical magnetoresistivity $\rho_{xx}(B)$ 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 $\rho_{xx}(B)$ becomes parametrically much larger than its B=0 value.

Source: http://arxiv.org/abs/cond-mat/9905364v1

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43

Sep 19, 2013
09/13

by
J. Wilke; A. D. Mirlin; D. G. Polyakov; F. Evers; P. Woelfle

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We study the low-frequency behavior of the {\it ac} conductivity $\sigma(\omega)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|\omega|$ correction to ${\rm Re} \sigma$, 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 $|\omega|$-term is positive and...

Source: http://arxiv.org/abs/cond-mat/9912366v1

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48

Sep 19, 2013
09/13

by
J. T. Chalker; D. G. Polyakov; F. Evers; A. D. Mirlin; P. Woelfle

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We discuss the behaviour of a quantum Hall system when two Landau levels with opposite spin and combined filling factor near unity are brought into energetic coincidence using an in-plane component of magnetic field. We focus on the interpretation of recent experiments under these conditions [Zeitler et al, Phys. Rev. Lett. 86, 866 (2001); Pan et al, Phys. Rev. B 64, 121305 (2001)], in which a large resistance anisotropy develops at low temperatures. Modelling the systems involved as Ising...

Source: http://arxiv.org/abs/cond-mat/0208024v1

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33

Sep 22, 2013
09/13

by
I. A. Dmitriev; M. Khodas; A. D. Mirlin; D. G. Polyakov; M. G. Vavilov

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We present a systematic study of the microwave-induced oscillations in the magnetoresistance of a 2D electron gas for mixed disorder including both short-range and long-range components. The obtained photoconductivity tensor contains contributions of four distinct transport mechanisms. We show that the photoresponse depends crucially on the relative weight of the short-range component of disorder. Depending on the properties of disorder, the theory allows one to identify the temperature range...

Source: http://arxiv.org/abs/0908.2130v1

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49

Sep 20, 2013
09/13

by
M. G. Vavilov; I. A. Dmitriev; I. L. Aleiner; A. D. Mirlin; D. G. Polyakov

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Microwave irradiation of a two-dimensional electron gas (2DEG) produces a non-equilibrium distribution of electrons, and leads to oscillations in the dissipative part of the conductivity. We show that the same non-equilibrium electron distribution induces strong oscillations in the 2DEG compressibility measured by local probes. Local measurements of the compressibility are expected to provide information about the domain structure of the zero resistance state of a 2DEG under microwave radiation.

Source: http://arxiv.org/abs/cond-mat/0405377v2

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33

Sep 22, 2013
09/13

by
I. A. Dmitriev; M. G. Vavilov; I. L. Aleiner; A. D. Mirlin; D. G. Polyakov

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We develop a theory of magnetooscillations in the photoconductivity of a two-dimensional electron gas observed in recent experiments. The effect is governed by a change of the electron distribution function induced by the microwave radiation. We analyze a nonlinearity with respect to both the dc field and the microwave power, as well as the temperature dependence determined by the inelastic relaxation rate.

Source: http://arxiv.org/abs/cond-mat/0409590v2

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43

Sep 22, 2013
09/13

by
I. A. Dmitriev; M. G. Vavilov; I. L. Aleiner; A. D. Mirlin; D. G. Polyakov

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We develop a theory of magnetooscillations in the photoconductivity of a two-dimensional electron gas observed in recent experiments. The effect is governed by a change of the electron distribution function induced by the microwave radiation. We analyze a nonlinearity with respect to both the dc field and the microwave power, as well as the temperature dependence determined by the inelastic relaxation rate.

Source: http://arxiv.org/abs/cond-mat/0310668v1

99
99

Sep 17, 2013
09/13

by
I. A. Dmitriev; F. Evers; I. V. Gornyi; A. D. Mirlin; D. G. Polyakov; P. Wölfle

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Recent theoretical results on magnetotransport of electrons in a 2D system in the range of moderately strong transverse magnetic fields are reviewed. The phenomena discussed include: quasiclassical memory effects in systems with various types of disorder, transport in lateral superlattices, interaction-induced quantum magnetoresistance, quantum magnetooscillations in dc and ac transport, and oscillatory microwave photoconductivity.

Source: http://arxiv.org/abs/0711.4234v1

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41

Sep 23, 2013
09/13

by
D. N. Aristov; A. P. Dmitriev; I. V. Gornyi; V. Yu. Kachorovskii; D. G. Polyakov; P. Wölfle

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We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced break up of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the...

Source: http://arxiv.org/abs/1006.4844v2