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Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model, and an opportunity to validate recently introduced ``purification-based'' error-mitigation strategies. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), on up to $20$ qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques (e.g. post-selection); the gain from error mitigation is seen to increase with the system size. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolating performance from these results allows us to estimate minimum requirements for a beyond-classical simulation of electronic structure. We find that, despite the impressive gains from purification-based error mitigation, significant hardware improvements will be required for classically intractable variational chemistry simulations., Comment: 10 pages, 13 page supplementary material, 12 figures. Experimental data available at https://doi.org/10.5281/zenodo.7225821

I derived Bethe Ansatz equations for two model Periodic Quantum Circuits: 1) XXZ model; 2) Chiral Hubbard Model. I obtained explicit expressions for the spectra of the strings of any length. These analytic results may be useful for calibration and error mitigations in modern engineered quantum platforms., Comment: 44 pages, 6 figures

The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of $\ln2$, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results demonstrate the potential for quantum processors to provide key insights into topological quantum matter and quantum error correction., Comment: 6 pages 4 figures, plus supplementary materials

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to probe fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band-structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors and arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 rad, whereas typical energy scales are of order 1 rad. Insight into this unprecedented algorithm fidelity is gained by highlighting robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 1e-4 rad. Furthermore, we synthesize magnetic flux and disordered local potentials, two key tenets of a condensed-matter system. When sweeping the magnetic flux, we observe avoided level crossings in the spectrum, a detailed fingerprint of the spatial distribution of local disorder. Combining these methods, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits.

Umklapp processes play a fundamental role as the only intrinsic mechanism that allows electrons to transfer momentum to the crystal lattice and, therefore, provide a finite electrical resistance in pure metals. However, umklapp scattering has proven to be elusive in experiment as it is easily obscured by other dissipation mechanisms. Here we show that electron-electron umklapp scattering dominates the transport properties of graphene-on-boron-nitride superlattices over a wide range of temperatures and carrier densities. The umklapp processes cause giant excess resistivity that rapidly increases with increasing the superlattice period and are responsible for deterioration of the room-temperature mobility by more than an order of magnitude as compared to standard, non-superlattice graphene devices. The umklapp scattering exhibits a quadratic temperature dependence accompanied by a pronounced electron-hole asymmetry with the effect being much stronger for holes rather than electrons. Aside from fundamental interest, our results have direct implications for design of possible electronic devices based on heterostructures featuring superlattices.

Monolayers of molybdenum and tungsten dichalcogenides are direct bandgap semiconductors, which makes them promising for opto-electronic applications. In particular, van der Waals heterostructures consisting of monolayers of MoS2 sandwiched between atomically thin hexagonal boron nitride (hBN) and graphene electrodes allows one to obtain light emitting quantum wells (LEQWs) with low-temperature external quantum efficiency (EQE) of 1%. However, the EQE of MoS2 and MoSe2-based LEQWs shows behavior common for many other materials: it decreases fast from cryogenic conditions to room temperature, undermining their practical applications. Here we compare MoSe2 and WSe2 LEQWs. We show that the EQE of WSe2 devices grows with temperature, with room temperature EQE reaching 5%, which is 250x more than the previous best performance of MoS2 and MoSe2 quantum wells in ambient conditions. We attribute such a different temperature dependences to the inverted sign of spin-orbit splitting of conduction band states in tungsten and molybdenum dichalcogenides, which makes the lowest-energy exciton in WSe2 dark.

We show that the Bardeen-Cooper-Schrieffer state (BCS) and the Bose-Einstein condensation (BEC) sides of the BCS-BEC crossover can be rigorously distinguished from each other by the extrema of the spectrum of the fermionic excitations. Moreover, we demonstrate that this formal distinction is realized as a non-equilibrium phase transition under radio frequency radiation. The BEC phase remains translationally invariant, whereas the BCS phase transforms into the supersolid phase. For a two-dimensional system this effect occurs at arbitrary small amplitude of the radiation field., Comment: 4 pages, 4 figures and supplemental material

We consider the many-body localization-delocalization transition for strongly interacting one- dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transitions at any finite temperature when varying the interaction strength. At weak interactions an increase in the interaction strength leads to insulator->fluid transition, and for large interactions one has a reentrance to the insulator regime.

We show that transport and thermodynamic properties of \emph{singly-connected} disordered conductors exhibit quantum Aharonov - Bohm oscillations with the total magnetic flux through the system. The oscillations are associated with the interference contribution from a special class of electron trajectories confined to the surface of the sample., Comment: 5 pages, 2 figures

We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov's hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov's action, which, in particular, allows for weak solutions of the Gross-Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying {\em within} the phonon part of the spectrum, contrary to traditional view., Comment: 45 pages, 8 figures

We consider chiral electrons moving along the 1D helical edge of a 2D topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states., Comment: Minor revisions; 4 pages, 1 figure

We analyze the phase diagram of the Bilayer graphene (BLG) at zero temperature and doping. Assuming that at the high energies the electronic system of BLG can be described within a weak coupling theory (consistent with the experimental evidence), we systematically study the evolution of the couplings with going from high to low energies. The divergences of the couplings at some energies indicates the tendency towards certain symmetry breakings. Carrying out this program, we found that the phase diagram is determined by microscopic couplings defined on the short distances (initial conditions). We explored all plausible space of these initial conditions and found that the three states have the largest phase volume of the initial couplings: nematic, antiferromagnetic and spin flux (a.k.a quantum spin Hall). In addition, ferroelectric and two superconducting phases and appear only near the very limits of the applicability of the weak coupling approach. The paper also contains the derivation and analysis of the renormalization group equations and the group theory classification of all the possible phases which might arise from the symmetry breakings of the lattice, spin rotation, and gauge symmetries of graphene., Comment: 19 pages, 16 figures

In spite of having finite life-time exciton-polaritons in microcavities are known to condense at strong enough pumping of the reservoir. We present an analytical theory of such Bose-condensates on a set of localized one-particle states: condensation centers. To understand physics of these arrays one has to supplement the Josephson coupling by the radiative coupling caused by the interference of the light emitted by different centers. Combination of these couplings with the one-site interaction between the bosons leads to a rich nonlinear dynamics. In particular, a new regime of radiation appears. We call it weak lasing: the centers have macroscopic occupations and radiate coherently, but the coupling alone is sufficient for stabilization. The system can have several stable states and switch between them. Moreover, the time reversal symmetry in this regime is, as a rule, broken. A number of existing experimental puzzles find natural interpretation in the framework of this theory., Comment: 5 pages, 2 figures

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ff=+-4 being the most stable in the quantum Hall effect measurement, instead of ff=+-8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ff=+-4 is, down to very low fields, weakly dependent on the strength of the magnetic field., Comment: 14 single-column pages, 5 figures, more details on material presented in arXiv:1104.5029

We introduce the notion of the strongly correlated band insulator (SCI), where the lowest energy excitations are collective modes (excitons) rather than the single particles. We construct controllable 1/N expansion for SCI to describe their observables properties. A remarkable example of the SCI is bilayer graphene which is shown to be tunable between the SCI and usual weak coupling regime., Comment: 4 pages, 4 figures

We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to existence of long range hops. We found that the critical wavefunctions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T-invariant the states are critical for all values of the parameters. Otherwise, there can be a "metal-insulator" transition between this "ordinary" diffusion and the Levy-flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified non-linear supermatrix $\sigma$-model., Comment: 4.2 pages

We derive the renormalization group equations describing all the short-range interactions in bilayer graphene allowed by symmetry and the long range Coulomb interaction. For certain range of parameters, we predict the first order phase transition to the uniaxially deformed gapless state accompanied by the change of the topology of the electron spectrum., Comment: 4 pages, 3 figures

The superconductor-insulator transition (SIT) in regular arrays of Josephson junctions is studied at low temperatures. Near the transition a Ginzburg-Landau type action containing the imaginary time is derived. The new feature of this action is that it contains a gauge field $\Phi $ describing the Coulomb interaction and changing the standard critical behavior. The solution of renormalization group (RG) equations derived at zero temperature $T=0$ in the space dimensionality $d=3$ shows that the SIT is always of the first order. At finite temperatures, a tricritical point separates the lines of the first and second order phase transitions. The same conclusion holds for $d=2$ if the mutual capacitance is larger than the distance between junctions., Comment: 4.1 pages, 1 figure

It is commonly accepted that there are no phase transitions in one-dimensional (1D) systems at a finite temperature, because long-range correlations are destroyed by thermal fluctuations. Here we demonstrate that the 1D gas of short-range interacting bosons in the presence of disorder can undergo a finite temperature phase transition between two distinct states: fluid and insulator. None of these states has long-range spatial correlations, but this is a true albeit non-conventional phase transition because transport properties are singular at the transition point. In the fluid phase the mass transport is possible, whereas in the insulator phase it is completely blocked even at finite temperatures. We thus reveal how the interaction between disordered bosons influences their Anderson localization. This key question, first raised for electrons in solids, is now crucial for the studies of atomic bosons where recent experiments have demonstrated Anderson localization in expanding very dilute quasi-1D clouds., Comment: 8 pages, 5 figures

We argue that giant jumps of current at finite voltages observed in disordered samples of InO, TiN and YSi manifest a bistability caused by the overheating of electrons. One of the stable states is overheated and thus low-resistive, while the other, high-resistive state is heated much less by the same voltage. The bistability occurs provided that cooling of electrons is inefficient and the temperature dependence of the equilibrium resistance, R(T), is steep enough. We use experimental R(T) and assume phonon mechanism of the cooling taking into account its strong suppression by disorder. Our description of details of the I-V characteristics does not involve adjustable parameters and turns out to be in a quantitative agreement with the experiments. We propose experiments for more direct checks of this physical picture., Comment: Final version, as published; 4 pages, 3 figures

We consider mutual effect of the electron-phonon and strong Coulomb interactions on each other by summing up leading logarithmic corrections via the renormalization group approach. We find that the Coulomb interaction enhances electron coupling to the intervalley A1 optical phonons, but not to the intravalley E2 phonons.

Application of the magnetic field parallel to the plane of the graphene sheet leads to the formation of electron- and hole-like Fermi surfaces. Such situation is shown to be unstable with respect to the formation of an excitonic condensate even for an arbitrary weak magnetic field and interaction strength. At temperatures lower than the mean-field temperature the order parameter amplitude is formed. The order parameter itself is a U(2) matrix allowing for the combined rotations in the spin and valley spaces. These rotations smoothly interpolate between site and bond centered spin density waves and spin flux states. The trigonal warping, short range interactions, and the three particle Umklapp processes freeze some degrees of freedom at temperatures much smaller than the mean-field transition temperature and make either Berezinskii-Kosterlitz-Thouless (driven either by vortices or half-vortices) or Ising type transitions possible. Strong logarithmic renormalization for the coupling constants of these terms by the Coulomb interaction are calculated within one-loop renormalization group. It is found that in the presence of the Coulomb interaction some short range interaction terms become much greater than one might expect from the naive dimensionality counting., Comment: 28 pages, 20 figures; Supersedes arXiv:cond-mat/0611251

Transport in undoped graphene is related to percolating current patterns in the networks of {\em N-} and {\em P}-type regions reflecting the strong bipolar charge density fluctuations. Transmissions of the {\em P-N} junctions, though small, are vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate., Comment: 4 pages, 3 figures

Recently, it was predicted that if all one-electron states in a non-interacting disordered system are localized, the interaction between electrons in the absence of coupling to phonons leads to a finite-temperature metal-insulator trnasition. Here we show that even in the presence of a weak coupling to phonons the transition manifests itself (i) in the nonlinear conduction, leading to a bistable $I$-$V$ curve, (ii) by a dramatic enhancement of the nonequilibrium current noise near the transition., Comment: misprints corrected

We study a polarized Fermi gas and demonstrate that Fano-Feshbach (FF) resonances lead to the pairing of fermions and holes into long living massive bosonic modes (bifermions and biholes), which can be viewed as signatures of a first order quantum phase transition. These modes, which are neither conventional Cooper pairs nor closed channel bosonic dimers, have a peculiar dispersion relation and appear already in the weak coupling limit, i.e. for large FF detunings. Our result is in accord with claims of Schunck \emph{et al.} [cond-mat/0702066] that by stabilizing the normal state the population imbalance still allows effect of s-wave fermionic pairing., Comment: 5 pages, 4 figures

We predict a nonequilibrium critical phenomenon in the space-time density evolution of a fermionic gas above the temperature of transition into the superfluid phase. On the BCS side of the BEC-BCS crossover, the evolution of a localized density disturbance exhibits a negative echo at the point of the initial inhomogeneity. Approaching the BEC side, this effect competes with the slow spreading of the density of bosonic molecules. However, even here the echo dominates for large enough times. This effect may be used as an experimental tool to locate the position of the transition., Comment: 4 pages, 2 figures

We develop a theory of nonlinear response to an electric field of a two-dimensional electron gas (2DEG) placed in a classically strong magnetic field. The latter leads to a non-linear current-voltage characteristic at a relatively weak electric field. The origin of the non-linearity is two-fold: the formation of a non-equilibrium electron distribution function, and the geometrical resonance in the inter-Landau-levels transitions rates. We find the dependence of the current-voltage characteristics on the electron relaxation rates in the 2DEG., Comment: 4 pages, 2 figures

We discuss a recent bosonization method developed to study clean Fermi gases with a repulsion in any dimensions. The method enables one to consider both density and spin excitations. It is demonstrated that due to a non-abelian structure of the effective theory, the spin excitations interact with each other, which leads to new logarithmic in temperature corrections to physical quantities. Using a renormalization group scheme constructed for the effective low energy field theory these logarithms are summed up in all orders. Temperature dependent corrections to the specific heat and spin susceptibility are obtained for all dimensions d=1,2,3., Comment: A talk given at the conference "Mott's Physics in Nanowires and Quantum Dots", Cambridge, UK, 2006; corrected typos

Quenched disorder in graphene is characterized by 5 constants and experiences the logarithmic renormalization even from the spatial scales smaller than the Fermi wavelength. We derive and solve renormalization group equations (RGEs) describing the system at such scales. At larger scales, we derive a non-linear supermatrix $\sigma $-model completely describing localization and crossovers between different ensembles. The parameters of this $\sigma $% -model are determined by the solutions of the RGEs., Comment: 4+ pages

We review recent progress in the study of transport properties of interacting electrons subject to a disordered potential which is strong enough to localize all single-particle states. This review may also serve as a guide to the recent paper by the authors [Annals of Physics (2006), in press]. Here we skip most of the technical details and make an attempt to discuss the physical grounds of the final-temperature metal-insulator transition described in the above-mentioned paper., Comment: contribution to the book "Problems of condensed matter physics"

We suggest a new method of calculations for a clean Fermi gas with a repulsion in any dimension. This method is based on writing equations for quasiclassical Green functions and reducing them to equations for collective spin and charge excitations. The spin excitations interact with each other and this leads to non-trivial physics. Writing the solution of the equations and the partition function in terms of a functional integral over supervectors and averaging over fluctuating fields we come to an effective field theory describing the spin excitations. In some respects, the theory is similar to bosonization but also includes the ``ghost'' excitations which prevents overcounting of the degrees of freedom. Expansion in the interaction reveals logarithmic in temperature corrections. This enables us to suggest a renormalization group scheme and derive renormalization group equations. Solving these equations and using their solutions for calculating thermodynamic quantities we obtain explicit expression for the specific heat containing only an effective amplitude of the backward scattering. This amplitude has a complicated dependence on the logarithm of temperature, which leads to a non-trivial temperature dependence of the specific heat.

We study the effect of spin-orbit scattering on the statistics of the conductance of a quantum dot for Coulomb blockade peaks and valleys. We find the distribution function of the peak heights for strong spin-orbit scattering in the presence and absence of time reversal symmetry. We find that the application of a magnetic field suppresses the average peak height, similar to the antilocalizaion in the bulk systems. For the valleys, we consider the elastic cotunneling contribution to the conductance and calculate its moments at the crossover between ensembles of various symmetries., Comment: 4 pages, 2 figures

We study the interaction corrections to the transport coefficients in open quantum dots (i.e. dots connected to leads of large conductance $G \gg e^2/\pi\hbar$), via a quantum kinetic equation approach. The effects of all the channels of the universal (in the Random Matrix Theory sense) interaction Hamiltonian are accounted for at one loop approximation. For the electrical conductance we find that even though the magnitude of the triplet channel interaction is smaller than the charging energy, the differential conductance at small bias is greatly affected by this interaction. Furthermore, the application of a magnetic field can significantly change the conductance due to the Zeeman splitting, producing finite bias anomalies. For the thermal conductance we find that the Wiedemann-Franz law is violated by the interaction corrections, and we investigated the effect of magnetic field on the Lorentz ratio for contacts of finite reflection. The charge and triplet channel corrections to the electrical and thermal conductance vanish for reflectionless contacts. In the latter case the temperature and magnetic field dependence of the conductance is determined by the Maki-Thompson correction in the Cooper channel., Comment: 27 pages, 8 figures

We consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperatute $T$ does not exceed some finite value $T_c$. At the same time, it can be also proven that at high enough $T$ the conductivity is finite. These two statements imply that the system undergoes a finite temperature Metal-to-Insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in the Fock space. Metallic and insulating states are not different from each other by any spatial or discrete symmetries. We formulate the effective Hamiltonian description of the system at low energies (of the order of the level spacing in the single-particle localization volume). In the metallic phase quantum Boltzmann equation is valid, allowing to find the kinetic coefficients. In the insulating phase, $T

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., Comment: Extended version of cond-mat/0310668. 12 pages, 4 figures. V2: published version (minor changes, Fig. 4 corrected, references added)

A resonant level strongly coupled to a local phonon under nonequilibrium conditions is investigated. The nonequilibrium Hartree-Fock approximation is shown to correspond to approximating the steady state density matrix by delta functions at field values to which the local dynamics relaxes in a semiclassical limit. If multiple solutions exist, all are shown to make nonvanishing contributions to physical quantities: multistability does not exist. Nonequilibrium effects are shown to produce decoherence, causing the standard expansions to converge and preventing the formation of a polaron feature in the spectral function. The formalism also applies to the nonequilibrium Kondo problem., Comment: 5 pages, 3 figures

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., Comment: v2: analysis of the wave-vector dependence of the compressibility added; discussion of the Hall conductivity removed (shifted to cond-mat/0409590 in a revised form)

We consider the singular electron-electron interaction corrections to the transport coefficients in disordered metals to test the validity of the Wiedemann-Franz law. We develop a local, quantum kinetic equation approach in which the charge and energy conservation laws are explicitly obeyed. To obtain the local description, we introduce bosonic distribution functions for the neutral, low-energy collective modes (electron-hole pairs). The resulting system of kinetic equations enables us to distinguish between the different physical processes involved in the charge and energy transport: elastic electron scattering affects both, while the inelastic processes influence only the latter. Moreover, the neutral bosons, though incapable of transporting charge, contribute significantly to the energy transport. In our approach we calculate on equal footing the electrical and thermal conductivities and the specific heat in any dimension. We found that the Wiedemann-Franz law is always violated by the interaction corrections; the violation is larger for one- and two-dimensional systems in the diffusive regime $T\tau \ll \hbar$ and it is due to the energy transported by the neutral bosons. For two-dimensional systems in the quasi-ballistic regime $T\tau \gg \hbar$ the inelastic scattering of the electron on the bosons also contributes to the violation., Comment: 4 figures, 35 pages

We observe a new type of magneto-oscillations in the photovoltage and the longitudinal resistance of a two-dimensional electron system. The oscillations are induced by microwave irradiation and are periodic in magnetic field. The period is determined by the microwave frequency, the electron density, and the distance between potential probes. The phenomenon is accounted for by coherent excitation of edge magnetoplasmons in the regions near the contacts and offers perspectives for the development of new tunable microwave and terahertz detection schemes and spectroscopic techniques., Comment: 5 pages, 5 figures

We present a comprehensive theoretical treatment of the effect of electron-phonon interactions in molecular transistors, including both quantal and classical limits and we study both equilibrated and out of equilibrium phonons. We present detailed results for conductance, noise and phonon distribution in two regimes. One involves temperatures large as compared to the rate of electronic transitions on and off the dot; in this limit our approach yields classical rate equations, which are solved numerically for a wide range of parameters. The other regime is that of low temperatures and weak electron-phonon coupling where a perturbative approximation in the Keldysh formulation can be applied. The interplay between the phonon-induced renormalization of the density of states on the quantum dot and the phonon-induced renormalization of the dot-lead coupling is found to be important. Whether or not the phonons are able to equilibrate in a time rapid compared to the transit time of an electron through the dot is found to affect the conductance. Observable signatures of phonon equilibration are presented. We also discuss the nature of the low-T to high-T crossover., Comment: 20 pages, 19 figures. Minor changes, version accepted for publication in Phys. Rev. B

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., Comment: 4 pages, 3 figures

We establish the consistency of the Fermi liquid description and find a relation between Fermi liquid constants for the two dimensional electron system near the point of full polarization due to a parallel magnetic field $H$. Our results enable us to predict connections between different thermodynamic properties of the system. In particular, we find that near the point of full polarization $H_c$, the thermodynamic compressibility of the system experiences a jump with the subleading $(H_c-H)^{1/2}$ dependence on the magnetic field. Also, the magnetization has a cusp with the dependence of the type $(H-H_c) + (H_c-H)^{3/2}$ at $H

We evaluate a typical value of higher order cumulants (irreducible moments) of conductance fluctuations that could be extracted from magneto-conductance measurements in a single sample when an external magnetic field is swept over an interval $B_0$. We find that the n-th cumulant has a sample-dependent random part $\pm \gN 2^{n/2}\sqrt{a_{n}B_{c}/B_{0}}$, where $\gN 2$ is the variance of conductance fluctuations, $B_{c}$ is a correlation field, and $a_{n}\sim n!$. This means that an apparent deviation of the conductance distribution from a Gaussian shape, manifested by non-vanishing higher cumulants, can be a spurious result of correlations of conductances at different values of the magnetic field., Comment: 4 pages, no figures, submitted to Phys. Rev. B

We derive the quantum Boltzmann equation for the two-dimensional electron gas in a magnetic field such that the filling factor $\nu \gg 1$. This equation describes all of the effects of the external fields on the impurity collision integral including Shubnikov-de Haas oscillations, smooth part of the magnetoresistance, and non-linear transport. Furthemore, we obtain quantitative results for the effect of the external microwave radiation on the linear and non-linear $dc$ transport in the system. Our findings are relevant for the description of the oscillating resistivity discovered by Zudov {\em et al.}, zero-resistance state discovered by Mani {\em et al.} and Zudov {\em et al.}, and for the microscopic justification of the model of Andreev {\em et al.}. We also present semiclassical picture for the qualitative consideration of the effects of the applied field on the collision integral., Comment: 28 pages, 19 figures; The discussion of the role of the effect of the microwave field on the distribution function is revised (see also cond-mat/0310668). Accepted in Phys. Rev. B

A rate equation formalism is used to determine the effect of electron-phonon coupling on the conductance of a molecule. Interplay between the phonon-induced renormalization of the density of states on the quantum dot and the phonon-induced renormalization of the dot-lead coupling is found to be important. Whether or not the phonons are able to equilibrate in a time rapid compared to the transit time of an electron through the dot is found to affect the conductance. Observable signatures of phonon equilibration are presented., Comment: 4 pages, 4 figures

Under a strong $ac$ drive the zero-frequency linear response dissipative resistivity $\rho_{d}(j=0)$ of a homogeneous state is allowed to become negative. We show that such a state is absolutely unstable. The only time-independent state of a system with a $\rho_{d}(j=0)<0$ is characterized by a current which almost everywhere has a magnitude $j_{0}$ fixed by the condition that the nonlinear dissipative resistivity $\rho_{d}(j_{0}^{2})=0$. As a result, the dissipative component of the $dc$ electric field vanishes. The total current may be varied by rearranging the current pattern appropriately with the dissipative component of the $dc$-electric field remaining zero. This result, together with the calculation of Durst \emph{et. al.}, indicating the existence of regimes of applied $ac$ microwave field and $dc$ magnetic field where $\rho_{d}(j=0)<0$, explains the zero-resistance state observed by Mani \emph{et. al.} and Zudov \emph{et. al.}., Comment: Published version

We point out that the structure of the self-energy suggested in cond-mat/0208140 as a result of a ``non-perturbative analysis'' by ``purely mathematical means'' is incompatible with the very definition of the self-energy., Comment: 3/2 pages, 1 figure