Anomalous Hydrodynamics in a One-Dimensional Electronic Fluid

We construct multimode viscous hydrodynamics for one-dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In the four-mode regime, all modes are ballistic and acquire Kardar-Parisi-Zhang (KPZ)-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to ω^{-1/3} scaling of its real part. In the three-mode regime, the system is in the universality class of a classical viscous fluid [O. Narayan and S. Ramaswamy, Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems, Phys. Rev. Lett. 89, 200601 (2002).PRLTAO0031-900710.1103/PhysRevLett.89.200601, H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014).JSTPBS0022-471510.1007/s10955-014-0933-y]. Self-interaction of the sound modes results in a KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to ω^{-1/3} scaling of heat conductivity.

Thermal Transport in One-Dimensional Electronic Fluids

We study thermal conductivity for one-dimensional electronic fluids. The many-body Hilbert space is partitioned into bosonic and fermionic sectors that carry the thermal current in parallel. For times shorter than the bosonic umklapp time, the momenta of Bose and Fermi components are separately conserved, giving rise to the ballistic heat propagation and imaginary heat conductivity proportional to T/iω. The real part of thermal conductivity is controlled by decay processes of fermionic and bosonic excitations, leading to several regimes in frequency dependence. At lowest frequencies or longest length scales, the thermal transport is dominated by Lévy flights of low-momentum bosons that lead to a fractional scaling, ω^{-1/3} and L^{1/3}, of heat conductivity with the frequency ω and system size L, respectively.

Lévy Flights due to Anisotropic Disorder in Graphene

We study transport properties of graphene with anisotropically distributed on-site impurities (adatoms) that are randomly placed on every third line drawn along carbon bonds. We show that stripe states characterized by strongly suppressed backscattering are formed in this model in the direction of the lines. The system reveals Lévy-flight transport in the stripe direction such that the corresponding conductivity increases as the square root of the system length. Thus, adding this type of disorder to clean graphene near the Dirac point strongly enhances the conductivity, which is in stark contrast with a fully random distribution of on-site impurities, which leads to Anderson localization. The effect is demonstrated both by numerical simulations using the Kwant code and by an analytical theory based on the self-consistent T-matrix approximation.

Density of states in a two-dimensional chiral metal with vacancies

We study quantum interference effects in a two-dimensional chiral metal (bipartite lattice) with vacancies. We demonstrate that randomly distributed vacancies constitute a peculiar type of chiral disorder leading to strong modifications of critical properties at zero energy as compared to those of conventional chiral metals. In particular, the average density of states diverges as ρ∝E(-1)|lnE|(-3/2) and the correlation length L(c)∝√[|lnE|] in the limit E→0. When the average density of vacancies is different in the two sublattices, a finite concentration of zero modes emerges and a gap in the quasiclassical density of states opens around zero energy. Interference effects smear this gap, resulting in exponentially small tails at low energies.

Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point

We explore the longitudinal conductivity of graphene at the Dirac point in a strong magnetic field with two types of short-range scatterers: adatoms that mix the valleys and "scalar" impurities that do not mix them. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample as a function of impurity coordinates; an averaging over impurity positions is then performed numerically. The conductivity σ is equal to the ballistic value 4e2/πh for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point with σ≃4×0.4e2/h at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is also obtained at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes: remarkably, all key manifestations of Anderson localization and criticality in two dimensions are observed numerically in a single setup.

Emergence of domains and nonlinear transport in the zero-resistance state

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.

Giant magnetodrag in graphene at charge neutrality

We report experimental data and theoretical analysis of Coulomb drag between two closely positioned graphene monolayers in a weak magnetic field. Close enough to the neutrality point, the coexistence of electrons and holes in each layer leads to a dramatic increase of the drag resistivity. Away from charge neutrality, we observe nonzero Hall drag. The observed phenomena are explained by decoupling of electric and quasiparticle currents which are orthogonal at charge neutrality. The sign of magnetodrag depends on the energy relaxation rate and geometry of the sample.

Multifractality at Anderson transitions with Coulomb interaction

We explore mesoscopic fluctuations and correlations of the local density of states (LDOS) near localization transition in a disordered interacting electronic system. It is shown that the LDOS multifractality survives in the presence of the Coulomb interaction. We calculate the spectrum of multifractal dimensions in 2+ϵ spatial dimensions and show that it differs from that in the absence of interaction. The multifractal character of fluctuations and correlations of the LDOS can be studied experimentally by scanning tunneling microscopy of two-dimensional and three-dimensional disordered structures.

Correlations in nonequilibrium Luttinger liquid and singular Fredholm determinants

We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants det(1+ÂB[over ^]), where A(ε) and B(t) have multiple discontinuities in energy and time spaces. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region.

Coulomb drag in graphene near the Dirac point

We study Coulomb drag in graphene near the Dirac point, focusing on the regime of interaction-dominated transport. We establish a novel, graphene-specific mechanism of Coulomb drag based on fast interlayer thermalization, inaccessible by standard perturbative approaches. Using the quantum kinetic equation framework, we derive a hydrodynamic description of transport in double-layer graphene in terms of electric and energy currents. In the clean limit the drag becomes temperature independent. In the presence of disorder the drag coefficient at the Dirac point remains nonzero due to higher-order scattering processes and interlayer disorder correlations. At low temperatures (diffusive regime) these contributions manifest themselves in the peak in the drag coefficient centered at the neutrality point with a magnitude that grows with lowering temperature.

Enhancement of the critical temperature of superconductors by Anderson localization

The influence of disorder on the temperature of superconducting transition (T{c}) is studied within the σ-model renormalization-group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short range. Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. It is shown that in all these regimes Anderson localization leads to strong enhancement of T{c} related to the multifractality of wave functions. Screening of the long-range Coulomb interaction thus opens a promising direction for searching novel materials for high-T{c} superconductivity.

Symmetries of multifractal spectra and field theories of Anderson localization

We uncover the field-theoretical origin of symmetry relations for multifractal spectra at Anderson transitions and at critical points of other disordered systems. We show that such relations follow from the conformal invariance of the critical theory, which implies their general character. We also demonstrate that for the Anderson localization problem the entire probability distribution for the local density of states possesses a symmetry arising from the invariance of correlation functions of the underlying nonlinear σ model with respect to the Weyl group of the target space of the model.

Diffusion and criticality in undoped graphene with resonant scatterers

A general theory is developed to describe graphene with an arbitrary number of isolated impurities. The theory provides a basis for an efficient numerical analysis of the charge transport and is applied to calculate the Dirac-point conductivity σ of graphene with resonant scatterers. In the case of smooth resonant impurities the symmetry class is identified as DIII and σ grows logarithmically with increasing impurity concentration. For vacancies (or strong on-site potential impurities, class BDI) σ saturates at a constant value that depends on the vacancy distribution among two sublattices.

Full counting statistics of a Luttinger liquid conductor

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.

Interaction-induced criticality in Z(2) topological insulators

We study interaction effects in topological insulators with strong spin-orbit coupling. We find that the interplay of nontrivial topology and Coulomb repulsion induces a novel critical state on the surface of a three-dimensional topological insulator. Remarkably, this interaction-induced criticality, characterized by a universal value of conductivity, emerges without any adjustable parameters. Further, we predict a direct quantum-spin-Hall transition in two dimensions that occurs via a similar critical state.

Charge transport in graphene with resonant scatterers

The full counting statistics for the charge transport through an undoped graphene sheet in the presence of strong potential impurities is studied. Treating the scattering off the impurity in the s-wave approximation, we calculate the impurity correction to the cumulant generating function. This correction is universal provided the impurity strength is tuned to a resonant value. In particular, the conductance of the sample acquires a correction of 16e{2}/(pi{2}h) per resonant impurity.

Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left and right movers yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.

Multifractality at the quantum Hall transition: beyond the parabolic paradigm

We present an ultrahigh-precision numerical study of the spectrum of multifractal exponents Deltaq characterizing anomalous scaling of wave function moments |psi|2q at the quantum Hall transition. The result reads Deltaq=2q(1-q)[b0+b1(q-1/2)2+cdots, three dots, centered], with b0=0.1291+/-0.0002 and b1=0.0029+/-0.0003. The central finding is that the spectrum is not exactly parabolic: b1 not equal0. This rules out a class of theories of the Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.

Nonequilibrium zero-bias anomaly in disordered metals

We extend the theory of a zero-bias anomaly (ZBA) in the tunneling density of states of a diffusive metallic film to out-of-equilibrium conditions. An effective action describing virtual fluctuations out of equilibrium is derived. The singular behavior of the equilibrium ZBA is smoothed out by real processes of inelastic scattering.

Theory of fractional microwave-induced resistance oscillations

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 disorder-broadened Landau levels becomes important.

Transport of charge-density waves in the presence of disorder: classical pinning versus quantum localization

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 quantum localization sets in at a temperature much smaller than the pinning temperature, whereas the quantum localization length is much smaller than the pinning length.

Quantum criticality and minimal conductivity in graphene with long-range disorder

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.

Exact relations between multifractal exponents at the Anderson transition

Two exact relations between mutlifractal exponents are shown to hold at the critical point of the Anderson localization transition. The first relation implies a symmetry of the multifractal spectrum linking the exponents with indices q<1/2 to those with q>1/2. The second relation connects the wave-function multifractality to that of Wigner delay times in a system with a lead attached.

Surface criticality and multifractality at localization transitions

We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.

Interacting electrons in disordered wires: Anderson localization and low-T transport

We study the conductivity sigma(T) of interacting electrons in a low-dimensional disordered system at low temperature T. 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 T = T(c), so that sigma(T < T(c)) = 0. The critical behavior of sigma(T) above T(c) is ln sigma(T) proportional to -(T - T(c))(-1/2). The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space.

Dephasing and weak localization in disordered Luttinger liquid

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 interaction and disorder, thus vanishing in the clean limit.

Cyclotron-resonance harmonics in the ac response of a 2D electron gas with smooth disorder

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 et al. and Mani et al. is discussed.

Loschmidt echo and Lyapunov exponent in a quantum disordered system

We investigate the sensitivity of a disordered system with diffractive scatterers to a weak external perturbation. Specifically, we calculate the fidelity M(t) (also called the Loschmidt echo) characterizing a return probability after a propagation for a time t followed by a backward propagation governed by a slightly perturbed Hamiltonian. For short-range scatterers, we perform a diagrammatic calculation showing that the fidelity decays first exponentially according to the golden rule, and then follows a power law governed by the diffusive dynamics. For long-range disorder (when the diffractive scattering is of small-angle character), an intermediate regime emerges where the diagrammatics is not applicable. Using the path-integral technique, we derive a kinetic equation and show that M(t) decays exponentially with a rate governed by the classical Lyapunov exponent.

Interaction-induced magnetoresistance: from the diffusive to the ballistic regime

We study interaction-induced quantum correction deltasigma(alphabeta) to the conductivity tensor of electrons in two dimensions for arbitrary Ttau, where T is the temperature and tau the transport mean free time. A general formula is derived, expressing deltasigma(alphabeta) in terms of classical propagators ("ballistic diffusons"). The formalism is used to calculate the interaction contribution to the magnetoresistance in a classically strong transverse field and smooth disorder in the whole range of temperatures from the diffusive (Ttau<<1) to the ballistic (Ttau greater, similar 1) regime.

Wave function correlations on the ballistic scale: exploring quantum chaos by quantum disorder

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry [J. Phys. A 10, 2083 (1977)] and generalized by Hortikar and Srednicki [Phys. Rev. Lett. 80, 1646 (1998); Phys. Rev. E 57, 7313 (1998)] is proven to hold on sufficiently short distances, while it is found to be strongly violated on larger scales. This also resolves the conflict between the above conjecture and the wave function normalization. The method is further used to study ballistic correlations of wave functions in a random magnetic field.

Counting statistics for arbitrary cycles in quantum pumps

We study noise-related properties of current in adiabatic pumps. A symmetry of the problem allows us to relate the statistics of charge transport in the case of one-channel leads to the geometry of loops on a sphere (for many channels on a higher-dimensional manifold). This provides a unifying framework, which simplifies analysis of transport in various realizations of pumps. For each pumping cycle, the average current and its minimal variance are given by the areas enclosed by the corresponding loop on the sphere and on a minimal surface (soap film) spanned by this loop. We formulate conditions for quantization of the pumped charge.

Quasiclassical negative magnetoresistance of a 2D electron gas: interplay of strong scatterers and smooth disorder

We study the quasiclassical magnetotransport of noninteracting 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 relevance to the transport in semiconductor heterostructures is discussed.

Fluctuations of the inverse participation ratio at the anderson transition

Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale invariant, with a power-law asymptotic "tail." This scale invariance implies that the fractal dimensions D(q) are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2 and the spectral compressibility chi is violated in the regime of strong multifractality, with chi-->1 in the limit D2-->0.