We study transport of interacting electrons in a low-dimensional disordered system at low temperature T . In view of localization by disorder, the conductivity σ(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 σ(T ), inducing a transition at T = Tc, so that σ(T < Tc) = 0. The critical behavior of σ(T ) above Tc is ln σ(T ) ∝ −(T − Tc) −1/2 . The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space. 72.15.Rn, 71.30.+h, In a pathbreaking paper [1] Anderson demonstrated that a quantum particle may become localized by a random potential. In particular, in non-interacting systems of one-dimensional (1D) or two-dimensional (2D) geometry even weak disorder localizes all electronic states [2], thus leading to the exactly zero conductivity, σ(T ) = 0, whatever temperature T . A non-zero σ(T ) in such systems may only occur due to inelastic scattering processes leading to dephasing of electrons. Two qualitatively different sources of dephasing are possible: (i) scattering of electrons by external excitations (in practice, phonons) and (ii) electron-electron (e-e) scattering. In either case, at sufficiently high temperatures, the dephasing rate τ −1 φ is high, so that the localization effects are reduced to a weak-localization (WL) correction to the Drude conductivity. This correction behaves as ln τ φ in 2D and as τ 1/2 φ in quasi-1D (many-channel wire) systems [3], and thus diverges with lowering T , signaling the occurrence of the strong localization (SL) regime. This prompts a question as to how the system conducts at low T .For the case of electron-phonon scattering the answer is well known. The conductivity is then governed by Mott's variable-range hopping (VRH) [4], yielding σ(T ) ∝ exp{−(T 0 /T ) µ } with µ = 1/(d+1), where d is the spatial dimensionality. In the presence of a long-range Coulomb interaction, the Coulomb gap in the tunneling density of states modifies the VRH exponent, µ = 1 2 [5]. But what is the low-T behavior of σ(T ) if the electronphonon coupling is negligibly weak and the only source of the inelastic scattering is the e-e interaction? Our purpose here is to solve this long-standing fundamental problem, which is also of direct experimental relevance; see, e.g., Refs.[6] and [7,8], where the crossover from WL to SL with lowering T was studied for 1D and 2D systems, respectively. For definiteness, we concentrate on the case of a many-channel 1D system with a short-range interaction. Our results are, however, more general (including single-channel wires, 2D systems, Coulomb interaction), as we discuss in the end of the paper.It was proposed in [9] that the e-e interaction by itself is sufficient to induce VRH at low T . This idea was widely used for interpretation of experimental [8,10] and numerical [11] results on ...

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 electronelectron interaction and disorder, thus vanishing in the clean limit.PACS numbers: 71.10. Pm, 73.20.Jc Mesoscopics of strongly correlated electron systems has emerged as an area of great interest to both experimental and theoretical communities working in the field of nanoscale physics. Recently, progress in manufacturing of nanodevices has paved the way for systematic transport measurements on narrow quantum wires with a few or single conducting channels. Most prominent examples of these are semiconductor cleaved-edge quantum wires [1], carbon nanotubes [2], and quantum Hall edges running in opposite directions and interconnected by means of tunneling [3,4]. On the theoretical side, the challenge is to expand the ideas that have been developed for mesoscopic disordered systems on one side and for strongly correlated clean systems on the other.Much attention has been focused on the interplay between the interaction effects and disorder-induced localization in diffusive systems of low dimensionality D [5]. A key concept in the localization theory of a disordered Fermi liquid is that of the dephasing rate τ −1 φ due to electron-electron (e-e) inelastic scattering. It has been established that a weak-localization (WL) correction to the Drude conductivity of a diffusive system behaves as τ (2−D)/2 φ (ln τ φ for D = 2) and thus diverges with lowering T for D ≤ 2, leading to strong Anderson localization. This paper is concerned with transport in one dimension (1D), where e-e correlations drive a clean system into the non-Fermi liquid state known as Luttinger liquid (LL) [6]. One more peculiarity of the single-channel 1D system is that the ballistic motion on short scales crosses over in the absence of interaction directly to the localization regime, with no diffusive dynamics on intermediate scales. The main question we address is how the conductivity σ(T ) behaves in a disordered LL. It appears that a key piece of transport theory as regards the WL and the interaction-induced dephasing in a strongly correlated 1D system is missing. Most authors to date (e.g., [7,8]) have suggested that the dephasing length that controls localization effects in a disordered LL is L T = u/T (throughout the paper = 1), where u is the plasmon velocity. According to this approach, the interference effects get strong with lowering T at L T ∼ ξ, where ξ is the localization length. An alternative approach [9, 10] is predicated on the assumption that the dephasing rate is determined by the single-particle properties of a clean LL. On top of that, one might think tha...

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.

Developments in the physics of 2D electron systems during the last decade 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. The experimental manifestations of these phenomena and the unified theoretical framework for describing them in terms of a quantum kinetic equation are reviewed. This survey also contains 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.

The frequency-dependent conductivity σxx(ω) 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 76.40.+b The magnetotransport properties of a high-mobility 2D electron gas (2DEG) in semiconductor heterostructures are of great importance from the point of view of both fundamental physics and applications. Important information about the dynamical and spectral properties of the system is provided by its response to a microwave field. Within the quasiclassical Boltzmann theory, the dissipative ac conductivity σ xx (ω) = σ + (ω) + σ − (ω) of a non-interacting 2DEG in a magnetic field B is given by the Drude formula (we neglect spin for simplicity),where v F is the Fermi velocity, ν 0 = m/2π (withh = 1) the density of states (DOS), τ tr,0 the transport relaxation time at B = 0, ω c = eB/mc the cyclotron frequency, and m is the electron effective mass. For a sufficiently clean sample, ωτ tr,0 ≫ 1, Eq.(1) predicts a sharp cyclotron resonance (CR) peak at ω c = ω. It has been shown by Ando [1,2] that the Landau quantization of the orbital electron motion leads, in combination with disorder, to the emergence of harmonics of the CR at ω = nω c , n = 2, 3, . . .. Indeed, such a structure was experimentally observed [3]. The analytical calculations of Ref.[1] were performed, however, only for fully separated Landau levels with point-like scatterers [4].Very recently, great interest in the transport properties of a 2DEG in a microwave field has been caused by experiments on photoconductivity of exceptionally-highmobility samples by Zudov et al. [5] and Mani et al. [6], where oscillations controlled by the ratio ω/ω c were observed. Remarkably, these oscillations persisted down to magnetic fields as low as B ∼ 10 mT, an order of magnitude smaller than the field at which the Shubnikov-de Haas oscillations were damped. The experiments [5,6] triggered an outbreak of theoretical activity. Durst et al. [7] proposed (see also Refs. [8,9]) that the oscillations are governed by the following mechanism: an electron is excited by absorbing a photon with energy ω close to nω c and is scattered by disorder. In view of the oscillatory structure of the DOS, this leads to an extra contribution to the dc conductivity. In fact, a very similar mechanism of oscillatory photoconductivity was proposed long ago [10] for the case of a strong dc electric field.While the proposal of Ref.[7] is very appealing, calculations presented there involve a number of assumptions and approximations, which complicates a comparison with experiment. First, the consideration of Ref. [7] is restricted to the case of white-noise disorder with τ tr,0 = τ s,0 , where τ s,0 is the single-particle relaxation time at B = 0. On the other hand, the experiments are performed on high-mobility samples with smooth disorder, τ tr,0 /τ ...