We formulate a general framework to study the flow of the electron liquid in two dimensions past a random array of impenetrable obstacles in the presence of a magnetic field. We derive a linear-response formula for the resistivity tensor $\hat\rho$ in hydrodynamics with obstacles, which expresses $\hat\rho$ in terms of the vorticity and its harmonic conjugate, both on the boundary of obstacles. In the limit of rare obstacles, in which we calculate $\hat\rho$, the contributions of the flow-induced electric field to the dissipative resistivity from the area covered by the liquid and the area inside obstacles are shown to be equal to each other. We demonstrate that the averaged electric fields outside and inside obstacles are rotated by Hall viscosity from the direction of flow. For the diffusive boundary condition on the obstacles, this effect exactly cancels in $\hat\rho$. By contrast, for the specular boundary condition, the total electric field is rotated by Hall viscosity, which means the emergence of a Hall-viscosity-induced effective -- proportional to the obstacle density -- magnetic field. Its effect on the Hall resistivity is particularly notable in that it leads to a deviation of the Hall constant from its universal value. We show that the applied magnetic field enhances hydrodynamic lubrication, giving rise to a strong negative magnetoresistance. We combine the hydrodynamic and electrostatic perspectives by discussing the distribution of charges that create the flow-induced electric field around obstacles. We provide a connection between the tensor $\hat\rho$ and the disorder-averaged electric dipole induced by viscosity at the obstacle. This establishes a conceptual link between the resistivity in hydrodynamics with obstacles and the notion of the Landauer dipole. We show that the viscosity-induced dipole is rotated from the direction of flow by Hall viscosity.

We study electron transport through a multichannel fractional quantum Hall edge in the presence of both interchannel interaction and random tunneling between channels, with emphasis on the role of contacts. The prime example in our discussion is the edge at filling factor 2/3 with two counterpropagating channels. Having established a general framework to describe contacts to a multichannel edge as thermal reservoirs, we particularly focus on the line-junction model for the contacts and investigate incoherent charge transport for an arbitrary strength of interchannel interaction beneath the contacts and, possibly different, outside them. We show that the conductance does not explicitly depend on the interaction strength either in or outside the contact regions (implicitly, it only depends through renormalization of the tunneling rates). Rather, a long line-junction contact is characterized by a single parameter which defines the modes that are at thermal equilibrium with the contact and is determined by the interplay of various types of scattering beneath the contact. This parameter-playing the role of an effective interaction strength within an idealized model of thermal reservoirs-is generically nonzero and affects the conductance. We formulate a framework of fractionalization-renormalized tunneling to describe the effect of disorder on transport in the presence of interchannel interaction. Within this framework, we give a detailed discussion of charge equilibration for arbitrarily strong interaction in the bulk of the edge and arbitrary effective interaction characterizing the line-junction contacts.

We study charge transport through N-lead junctions (N >= 3) of spinless Luttinger-liquid wires with bias voltages applied to Fermi-liquid reservoirs. In particular, we consider a Y junction, which is a setup characteristic of the tunneling experiment. In this setup, the strength of electron-electron interactions in one of the arms ("tunneling tip") is different from that in the other two arms (which form together the "main wire"). For a generic single-particle S matrix of the junction, we find that the bias voltage V applied, even symmetrically, to the main wire generates a current proportional to vertical bar V vertical bar in the tip wire. We identify two mechanisms of this nonequilibrium-induced "emergent chirality" in a setup characterized by the time-reversal- and parity-symmetric Hamiltonian of the junction. These are (i) the emergence of an effective magnetic flux, which breaks time-reversal symmetry, and (ii) the emergence of parity-breaking asymmetry of the setup, both proportional to the interaction strength and the sign of the voltage. The current in the tip wire generated by mechanism (i) is reminiscent of the Hall current in the linear response of a system the Hamiltonian of which breaks time-reversal symmetry; however, in the absence of any magnetic field or a local magnetic moment. Similarly, mechanism (ii) can be thought of as an emergent "photogalvanic effect," however, in the presence of inversion symmetry within the main wire. The nonequilibrium chirality implies a rectification of the current in the tip when the main wire is biased by ac voltage.

We analyze the role of spectral diffusion in the problem of many-body delocalization in quantum dots and in extended systems. The spectral diffusion parametrically enhances delocalization, modifying the scaling of the delocalization threshold with the interaction coupling constant.

We calculate the conductances of a three-way junction of spinless Luttinger-liquid wires as functions of bias voltages applied to three independent Fermi-liquid reservoirs. In particular, we consider the setup that is characteristic of a tunneling experiment, in which the strength of electron-electron interactions in one of the arms of the junction ("tunneling tip") is different from that in the other two arms (which together form a "main wire"). The scaling dependence of the two independent conductances on bias voltages is determined within a fermionic renormalization-group approach in the limit of weak interactions. The solution shows that, in general, the conductances scale with the bias voltages in an essentially different way compared to their scaling with the temperature T. Specifically, unlike in the two-terminal setup, the nonlinear conductances cannot be generically obtained from the linear ones by simply replacing T with the "corresponding" bias voltage or the largest one. Remarkably, a finite tunneling bias voltage prevents the interaction-induced breakup of the main wire into two disconnected pieces in the limit of zero T and a zero source-drain voltage.

We study manifestations of spin-charge separation (SCS) in transport through a tunnel-coupled interacting single-channel quantum ring. We focus on the high-temperature case (temperature T larger than the level spacing Delta) and discuss both the classical (flux-independent) and interference contributions to the tunneling conductance of the ring in the presence of magnetic flux. We demonstrate that the SCS effects, which arise solely from the electron-electron interaction, lead to the appearance of a peculiar fine structure of the electron spectrum in the ring. Specifically, each level splits into a series of sublevels, with their spacing governed by the interaction strength. In the high-T limit, the envelope of the series contains of the order of T/Delta sublevels. At the same time, SCS suppresses the tunneling width of the sublevels by a factor of Delta/T. As a consequence, the classical transmission through the ring remains unchanged compared to the noninteracting case: the suppression of tunneling is compensated by the increase of the number of tunneling channels. On the other hand, the flux-dependent contribution to the conductance depends on the interaction-induced dephasing rate which is known to be parametrically increased by SCS in an infinite system. We show, however, that SCS is not effective for dephasing in the limit of weak tunneling. Moreover, generically, in the almost closed ring, the dephasing rate does not depend on the interaction strength and is determined by the tunneling coupling to the leads. In certain special symmetric cases, dephasing is further suppressed. Similarly to the spinless case, the high-T conductance shows, as a function of magnetic flux, a sequence of interaction-induced sharp negative peaks on top of the classical contribution.

We consider an extended electronic system with localized single-particle states coupled by short-range interactions, in the absence of coupling to an external bath. We show that many-body localization, which exists in tight-binding models, is unstable in a continuum. Irrespective of the dimensionality of the system, many-body localization does not survive the unbounded growth of the single-particle localization length with increasing energy that is characteristic of the continuum limit. The system remains delocalized down to arbitrarily small temperature T, although its dynamics slows down as T decreases. Remarkably, the conductivity vanishes with decreasing T faster than in the Arrhenius law. The system can be characterized by an effective T-dependent single-particle mobility edge which diverges in the limit of T0. Delocalization is driven by interactions between hot electrons above the mobility edge and the bath of thermal electrons in the vicinity of the Fermi level.

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 dependence on the temperature T. In the limit of low T, rho(D) vanishes with decreasing T as a power law if intraedge interactions are not too strong. This is in stark contrast to Coulomb drag in conventional quantum wires, where rho(D) diverges at T -> 0 irrespective of the strength of repulsive interactions. Another unusual property of Coulomb drag between the helical edges concerns higher T for which, unlike in the Luttinger liquid model, drag is mediated by plasmons. The special type of plasmon-mediated drag can be viewed as a distinguishing feature of the helical liquid-because it requires peculiar umklapp scattering only available in the presence of a Dirac point in the electron spectrum.

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 interaction). We also analyze the temporal relaxation of quantum states of various types (a "hot-electron state", a "typical" many-body state, and a single-electron excitation added to a "thermal state") with energies below, at, and above the transition.

We overview transport properties of an Aharonov-Bohm interferometer made of a single-channel quantum ring. Remarkably, in this setup, essentially quantum effects survive thermal averaging: the high-temperature tunneling conductance G of a ring shows sharp dips (antiresonances) as a function of magnetic flux. We discuss effects of the electron-electron interaction, disorder, and spin-orbit coupling on the Aharonov-Bohm transport through the ring. The interaction splits the dip into series of dips broadened by dephasing. The physics behind this behavior is the persistent-current-blockade: the current through the ring is blocked by the circular current inside the ring. Dephasing is then dominated by tunneling-induced fluctuations of the circular current. The short-range disorder broadens antiresonances, while the long-range one induces additional dips. In the presence of a spin-orbit coupling, G exhibits two types of sharp antiresonances: Aharonov-Bohm and Aharonov-Casher ones. In the vicinity of the antiresonances, the tunneling electrons acquire spin polarization, so that the ring serves as a spin polarizer.

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 dissipative resistance in the stable domain state.

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 resistance oscillations and zero-resistance states, as well as Hall field-induced resistance oscillations and associated zero-differential resistance states. We review the experimental manifestations of these phenomena and the unified theoretical framework for describing them in terms of a quantum kinetic equation. The survey contains also a thorough discussion of the magnetotransport properties of 2D electrons in the linear response regime, as well as an outlook on future directions, including related nonequilibrium phenomena in other 2D electron systems.

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 the vicinity of the Fermi surface alone is not sufficient to produce a nonzero dc drag resistivity $\rho_{\rm D}$, in contrast to a number of works that have studied Coulomb drag due to this mechanism of scattering before. We show that slow equilibration between two subsystems of electrons of opposite chirality, "bottlenecked" by inelastic collisions involving cold electrons near the bottom of the conduction band, leads to a strong suppression of Coulomb drag, which results in an activation dependence of $\rho_{\rm D}$ on temperature---instead of the conventional power law. We demonstrate the emergence of a drag regime in which $\rho_{\rm D}$ does not depend on the strength of interwire interactions, while depending strongly on the strength of interactions inside the wires.

We study the effect of electron-electron interaction on transport through a tunnel-coupled single-channel ring. We find that the conductance as a function of magnetic flux shows a series of interaction-induced resonances that survive thermal averaging. The period of the series is given by the interaction strength α. The physics behind this behavior is the blocking of the tunneling current by the circular current. The main mechanism of dephasing is due to circular-current fluctuations. The dephasing rate is proportional to the tunneling rate and does not depend on α.

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 breakup of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.

We present a systematic study of the microwave-induced oscillations in the magnetoresistance of a two-dimensional 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 within which the photoresponse is dominated by one of the mechanisms analyzed in the paper.

Recent results on nonequilibrium magnetotransport of electrons in irradiated quantum Hall systems are reviewed. The phenomena discussed include integer and fractional microwave-induced resistance oscillations as well as quantum magnetooscillations in DC and AC conductivity and in local compressibility of a 2D electron gas.

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 rate gamma: the ratio gamma(E)/gamma similar to 1 is independent of the strength of electron-electron interaction, temperature, and bias.

Submitted for the MAR09 Meeting of The American Physical Society Photoconductivity of a 2D electron gas at large filling factors IVAN DMITRIEV, Karlsruhe, Germany, MAXIM KHODAS, Brookhaven National Laboratory, A.D. MIRLIN, D.G. POLYAKOV, Karlsruhe, Germany, MAXIM VAVILOV, Wisconsin, Madison, USA — We study non-equilibrium dc conductivity of a 2D electron gas, placed in a classically strong perpendicular magnetic field in the presence of in-plane microwave field and generic Gaussian disorder potential. Focusing the consideration on the bilinear response in the microwave field, we identify four different mechanisms essential for the linear dc resistance. We employ two specific models of the disorder relevant for ultra-high mobility samples and show that the relative strength of the above mechanisms strongly depends on the spatial range of the disorder potential. In particular, when large angle scattering dominates the transport and temperature is sufficiently high, the contribution of the “displacement” mechanism can overcome the “inelastic” contribution, which is dominant at low temperature. For smooth disorder, characterized by small angle scattering, the “displacement” contribution is strongly suppressed. Other contributions are responsible for the microwave-induced corrections to the non-diagonal part of the conductivity tensor and only weakly depend on the nature of the disorder. We discuss the ways to distinguish experimentally the contributions of the above mechanisms according to their different polarization and temperature dependence. Maxim Khodas Brookhaven National Laboratory Date submitted: 21 Nov 2008 Electronic form version 1.4