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 electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder. We show that the transport properties of the system depend strongly on the character of disorder. Away from half filling, the concentration dependence of conductivity is linear in the case of strong scatterers, in line with recent experimental observations, and logarithmic for weak scatterers. At half filling the conductivity is of the order of e^2/h if the randomness preserves one of the chiral symmetries of the clean Hamiltonian; otherwise, the conductivity is strongly affected by localization effects.Comment: 21 pages, 9 figure

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 consider the conductivity sigma of graphene with negligible intervalley scattering at half filling. We derive the effective field theory, which, for the case of a potential disorder, is a symplectic-class sigma model including a topological term with theta=pi. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e(2)/h. When the effective time-reversal symmetry is broken, the symmetry class becomes unitary, and sigma acquires the value characteristic for the quantum Hall transition.

We develop a hydrodynamic description of transport properties in graphene-based systems, which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this "three-mode" approximation, we evaluate transport coefficients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magnetoresistance is strongly sensitive to the interplay between the sample geometry and leading relaxation processes. In small, mesoscopic samples, the macroscopic currents are inhomogeneous, which leads to a linear magnetoresistance in classically strong fields. Applying our theory to double-layer graphene-based systems, we provide a microscopic foundation for a phenomenological description of giant magnetodrag at charge neutrality and find the magnetodrag and Hall drag in doped graphene.