We present a theory of the finite temperature thermo-electric response functions of graphene in t... more We present a theory of the finite temperature thermo-electric response functions of graphene in the hydrodynamic regime where electron-electron collisions dominate the scattering. In moderate magnetic fields, the Dirac particles undergo a collective cyclotron motion with a temperaturedependent relativistic cyclotron frequency proportional to the net charge density of the Dirac plasma. In contrast to the undamped cyclotron pole in Galilean-invariant systems (Kohn's theorem), here there is a finite damping induced by collisions between the counter-propagating particles and holes. This cyclotron motion shows up as a damped pole in the frequency dependent conductivities, and should be readily detectable in microwave measurements at room temperature. We also compute the large Nernst signal in the hydrodynamic regime which is significantly bigger than in ordinary metals.
We study the temperature-dependent corrections to the conductance due to electron-electron (ee) i... more We study the temperature-dependent corrections to the conductance due to electron-electron (ee) interactions in clean two-dimensional conductors, such as lightly doped graphene or other Dirac matter. We use semiclassical Boltzmann kinetic theory to solve the problem of collision-dominated transport between reflection-free contacts. Time-reversal symmetry and the kinematic constraints of scattering in two dimensions (2D) ensure that inversion-odd and inversion-even distortions of the quasiparticle distribution relax with parametrically different rates at low temperature. This entails the surprising result that at lowest temperatures the conductance of very long samples tends to the noninteracting, ballistic conductance, despite the relaxation of the quasiparticle distribution to a drifting equilibrium. The relative correction to the conductance depends on the ratio of relaxation rates of even and odd modes and scales as δG/G ballistic ∼ (T /εF) log ε F T , in stark contrast to the behavior in other dimensionalities. This holds generally in 2D systems with simply connected and convex but otherwise arbitrary Fermi surfaces, as long as e-e scattering processes are dominant and umklapp scattering is negligible. These results are especially relevant to the bulk of wide and long suspended high-mobility graphene sheets.
We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in pa... more We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in particular the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focuses on the dichotomy MBL versus ETH (eigenstate thermalization hypothesis). We show that a few natural assumptions imply that the system is localized with probability one at criticality. On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition. On the MBL side, the typical localization length tends to a finite universal value at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean field approximation analytically illustrates these results and predicts as a power-law distribution for thermal inclusions at criticality.
We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains... more We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains, initialized in a fully magnetized state. Its long time limit is an order parameter for the localization transition, which is readily accessible by standard experimental probes in magnets. We analytically calculate its value in the strong-disorder regime exploiting the explicit construction of quasi-local conserved quantities of the localized phase. We discuss analogies in cold atomic systems.
We study the role of dipolar interactions in the standard protocol used to achieve dynamic nuclea... more We study the role of dipolar interactions in the standard protocol used to achieve dynamic nuclear polarization (DNP). In the so-called spin-temperature regime, where the interactions establish an effective thermodynamic behavior in the out-of-equilibrium stationary state, we provide numerical predictions for the level of hyperpolarization. We show that nuclear spins equilibrate to the effective spin-temperature established among the electron spins of radicals, as expected from the quantum theory of thermalization. Moreover, we present an analytical technique to estimate the spin temperature, and thus, the nuclear hyperpolarization in the steady state, as a function of interaction strength and quenched disorder. This reproduces both our numerical data and experimental results. Our central finding is that the nuclear hyperpolarization increases steadily upon reducing the interaction strength (by diluting the radical density). Interestingly, the highest polarization is reached at a point where the establishment of a spin temperature is just about to break down due to the incipient many-body localization transition in the electron spin system. I. GENERAL INTRODUCTION
We study the relaxation dynamics of strongly interacting quantum systems that display a kind of m... more We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation invariant Hamiltonian. We show that dynamics starting from a random initial configuration are non-perturbatively slow in the hopping strength, and potentially genuinely non-ergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, that are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonant configurations. We suggest experimental realizations and ways how to observe the discussed non-ergodic dynamics.
We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the ma... more We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.
We propose a new analytic approach to study the phase diagram of random heteropolymers, based on ... more We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered.
Motivated by recent neutron scattering experiments, we study the ordering of spins in the ironbas... more Motivated by recent neutron scattering experiments, we study the ordering of spins in the ironbased superconductors La(O1−xFx)FeAs, assuming them in proximity to a Mott insulator in the phase diagram. The ground state of the parent system with x = 0 is a spin density wave with ordering wave vector Q = (0, π) or (π, 0). Upon raising the temperature, we find the system to restore SU(2) symmetry, while an Ising symmetry remains broken, explaining the experimentally observed lattice distortion to a monoclinic crystal structure. Upon further temperature increase, the spins finally disorder at a second transition. The phase transition driven by doping with charge carriers similarly splits into an O(3) transition, and an Ising transition with z = 3 at larger doping.
We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at... more We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick model we present a detailed derivation of the density ρ(∆M) of the magnetization jumps ∆M. It is obtained by introducing a multi-component generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that ρ(∆M) ∼ ∆M −τ with an avalanche exponent τ = 1 for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size 1 ∆M < N 1/2 being provoked by changes of the external field by δH = O(N −1/2) where N is the total number of spins. Our general formula also suggests that the density of overlap q between initial and final state in an avalanche is ρ(q) ∼ 1/(1 − q). These results show interesting similarities with numerical simulations for the out-ofequilibrium dynamics of the SK model. For finite-range models, using droplet arguments, we obtain the prediction τ = (d f +θ)/dm where d f , dm and θ are the fractal dimension, magnetization exponent and energy exponent of a droplet, respectively. This formula is expected to apply to other glassy disordered systems, such as the random-field model and pinned interfaces. We make suggestions for further numerical investigations, as well as experimental studies of the Barkhausen noise in spin glasses.
We study the interplay of superfluidity and glassy ordering of hard core bosons with random, frus... more We study the interplay of superfluidity and glassy ordering of hard core bosons with random, frustrating interactions. This is motivated by bosonic systems such as amorphous supersolid, disordered superconductors with preformed pairs and helium in porous media. We analyze the fully connected mean field version of this problem, which exhibits three low temperature phases, separated by two continuous phase transitions: an insulating, glassy phase with an amorphous frozen density pattern, a non-glassy superfluid phase and an intermediate phase, in which both types of order coexist. We elucidate the nature of the phase transitions, highlighting in particular the role of glassy correlations across the superfluid-insulator transition. The latter suppress superfluidity down to T = 0, due to the depletion of the low energy density of states, unlike in the standard BCS scenario. Further, we investigate the properties of the coexistence (superglass) phase. We find anticorrelations between the local order parameters and a non-monotonous superfluid order parameter as a function of T. The latter arises due to the weakening of the glassy correlation gap with increasing temperature. Implications of the mean field phenomenology for finite dimensional bosonic glasses with frustrating Coulomb interactions are discussed.
Motivated by evidence of local electron-electron attraction in experiments on disordered insulati... more Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range interelectron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further study variable-range hopping transport in such systems by extending the standard resistor network approach to include the motion of both single electrons and local pairs. In certain parameter regimes the competition between these two types of carriers results in a distinct peak in resistance as a function of the local attraction strength, which can be tuned by a magnetic field.
We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a ... more We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a crossover from collisionless transport at frequencies larger than k B T / (T is the temperature) to collision-dominated transport at lower frequencies. The d.c. conductivity is computed by the solution of a quantum Boltzmann equation. Due to a logarithmic singularity in the collinear scattering amplitude (a consequence of relativistic dispersion in two dimensions) quasi-particles and-holes moving in the same direction tend to an effective equilibrium distribution whose parameters depend on the direction of motion. This property allows us to find the non-equilibrium distribution functions and the quantum critical conductivity exactly to leading order in 1/| log(α)| where α is the coupling constant characterizing the Coulomb interactions.
Many condensed matter experiments explore the finite temperature dynamics of systems near quantum... more Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport coefficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport coefficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.
We characterize the low temperature phase of a simple model for RNA secondary structures by deter... more We characterize the low temperature phase of a simple model for RNA secondary structures by determining the typical energy scale E(l) of excitations involving l bases. At low enough temperatures, including T = 0, we find a scaling law E(l) ∼ l θ with a small exponent θ. Above a critical temperature, there is a different phase characterized by a relatively flat free energy landscape resembling that of a homopolymer with a scaling exponent θ = 1. These results strengthen the evidence in favour of the existence of a glass phase at low temperatures.
We establish the connection between the presence of a glass phase and the appearance of a Coulomb... more We establish the connection between the presence of a glass phase and the appearance of a Coulomb gap in disordered materials with strongly interacting electrons. Treating multiparticle correlations in a systematic way, we show that in the case of strong disorder a continuous glass transition takes place whose Landau expansion is identical to that of the Sherrington-Kirkpatrick spin glass. We show that the marginal stability of the glass phase controls the physics of these systems: it results in slow dynamics and leads to the formation of a Coulomb gap.
We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the ch... more We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunnelling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ −1 (B) − ξ −1 (0) ∼ B 4/5. The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the non-trivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.
We report on the reinforcement of superconductivity in a system consisting of a narrow supercondu... more We report on the reinforcement of superconductivity in a system consisting of a narrow superconducting wire weakly coupled to a diffusive metallic film. We analyze the effective phase-only action of the system by a perturbative renormalization group and a self-consistent variational approach to obtain the critical points and phases at T = 0. We predict a quantum phase transition toward a superconducting phase with long-range order as a function of the wire stiffness and coupling to the metal. We discuss implications for the dc resistivity of the wire.
We investigate the temperature dependence of the conductivity in ballistic graphene using Landaue... more We investigate the temperature dependence of the conductivity in ballistic graphene using Landauer transport theory. We obtain results which are qualitatively in agreement with many features recently observed in transport measurements on high mobility suspended graphene. The conductivity σ at high temperature T and low density n grows linearly with T , while at high n we find σ ∼ p |n| with negative corrections at small T due to the T-dependence of the chemical potential. At moderate densities the conductivity is a non-monotonic function of T and n, exhibiting a minimum at T = 0.693 v p |n| where v is the Fermi velocity. We discuss two kinds of Fabry-Perot oscillations in short nanoribbons and their stability at finite temperatures.
We present a theory of the finite temperature thermo-electric response functions of graphene in t... more We present a theory of the finite temperature thermo-electric response functions of graphene in the hydrodynamic regime where electron-electron collisions dominate the scattering. In moderate magnetic fields, the Dirac particles undergo a collective cyclotron motion with a temperaturedependent relativistic cyclotron frequency proportional to the net charge density of the Dirac plasma. In contrast to the undamped cyclotron pole in Galilean-invariant systems (Kohn's theorem), here there is a finite damping induced by collisions between the counter-propagating particles and holes. This cyclotron motion shows up as a damped pole in the frequency dependent conductivities, and should be readily detectable in microwave measurements at room temperature. We also compute the large Nernst signal in the hydrodynamic regime which is significantly bigger than in ordinary metals.
We study the temperature-dependent corrections to the conductance due to electron-electron (ee) i... more We study the temperature-dependent corrections to the conductance due to electron-electron (ee) interactions in clean two-dimensional conductors, such as lightly doped graphene or other Dirac matter. We use semiclassical Boltzmann kinetic theory to solve the problem of collision-dominated transport between reflection-free contacts. Time-reversal symmetry and the kinematic constraints of scattering in two dimensions (2D) ensure that inversion-odd and inversion-even distortions of the quasiparticle distribution relax with parametrically different rates at low temperature. This entails the surprising result that at lowest temperatures the conductance of very long samples tends to the noninteracting, ballistic conductance, despite the relaxation of the quasiparticle distribution to a drifting equilibrium. The relative correction to the conductance depends on the ratio of relaxation rates of even and odd modes and scales as δG/G ballistic ∼ (T /εF) log ε F T , in stark contrast to the behavior in other dimensionalities. This holds generally in 2D systems with simply connected and convex but otherwise arbitrary Fermi surfaces, as long as e-e scattering processes are dominant and umklapp scattering is negligible. These results are especially relevant to the bulk of wide and long suspended high-mobility graphene sheets.
We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in pa... more We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in particular the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focuses on the dichotomy MBL versus ETH (eigenstate thermalization hypothesis). We show that a few natural assumptions imply that the system is localized with probability one at criticality. On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition. On the MBL side, the typical localization length tends to a finite universal value at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean field approximation analytically illustrates these results and predicts as a power-law distribution for thermal inclusions at criticality.
We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains... more We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains, initialized in a fully magnetized state. Its long time limit is an order parameter for the localization transition, which is readily accessible by standard experimental probes in magnets. We analytically calculate its value in the strong-disorder regime exploiting the explicit construction of quasi-local conserved quantities of the localized phase. We discuss analogies in cold atomic systems.
We study the role of dipolar interactions in the standard protocol used to achieve dynamic nuclea... more We study the role of dipolar interactions in the standard protocol used to achieve dynamic nuclear polarization (DNP). In the so-called spin-temperature regime, where the interactions establish an effective thermodynamic behavior in the out-of-equilibrium stationary state, we provide numerical predictions for the level of hyperpolarization. We show that nuclear spins equilibrate to the effective spin-temperature established among the electron spins of radicals, as expected from the quantum theory of thermalization. Moreover, we present an analytical technique to estimate the spin temperature, and thus, the nuclear hyperpolarization in the steady state, as a function of interaction strength and quenched disorder. This reproduces both our numerical data and experimental results. Our central finding is that the nuclear hyperpolarization increases steadily upon reducing the interaction strength (by diluting the radical density). Interestingly, the highest polarization is reached at a point where the establishment of a spin temperature is just about to break down due to the incipient many-body localization transition in the electron spin system. I. GENERAL INTRODUCTION
We study the relaxation dynamics of strongly interacting quantum systems that display a kind of m... more We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation invariant Hamiltonian. We show that dynamics starting from a random initial configuration are non-perturbatively slow in the hopping strength, and potentially genuinely non-ergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, that are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonant configurations. We suggest experimental realizations and ways how to observe the discussed non-ergodic dynamics.
We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the ma... more We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.
We propose a new analytic approach to study the phase diagram of random heteropolymers, based on ... more We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered.
Motivated by recent neutron scattering experiments, we study the ordering of spins in the ironbas... more Motivated by recent neutron scattering experiments, we study the ordering of spins in the ironbased superconductors La(O1−xFx)FeAs, assuming them in proximity to a Mott insulator in the phase diagram. The ground state of the parent system with x = 0 is a spin density wave with ordering wave vector Q = (0, π) or (π, 0). Upon raising the temperature, we find the system to restore SU(2) symmetry, while an Ising symmetry remains broken, explaining the experimentally observed lattice distortion to a monoclinic crystal structure. Upon further temperature increase, the spins finally disorder at a second transition. The phase transition driven by doping with charge carriers similarly splits into an O(3) transition, and an Ising transition with z = 3 at larger doping.
We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at... more We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick model we present a detailed derivation of the density ρ(∆M) of the magnetization jumps ∆M. It is obtained by introducing a multi-component generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that ρ(∆M) ∼ ∆M −τ with an avalanche exponent τ = 1 for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size 1 ∆M < N 1/2 being provoked by changes of the external field by δH = O(N −1/2) where N is the total number of spins. Our general formula also suggests that the density of overlap q between initial and final state in an avalanche is ρ(q) ∼ 1/(1 − q). These results show interesting similarities with numerical simulations for the out-ofequilibrium dynamics of the SK model. For finite-range models, using droplet arguments, we obtain the prediction τ = (d f +θ)/dm where d f , dm and θ are the fractal dimension, magnetization exponent and energy exponent of a droplet, respectively. This formula is expected to apply to other glassy disordered systems, such as the random-field model and pinned interfaces. We make suggestions for further numerical investigations, as well as experimental studies of the Barkhausen noise in spin glasses.
We study the interplay of superfluidity and glassy ordering of hard core bosons with random, frus... more We study the interplay of superfluidity and glassy ordering of hard core bosons with random, frustrating interactions. This is motivated by bosonic systems such as amorphous supersolid, disordered superconductors with preformed pairs and helium in porous media. We analyze the fully connected mean field version of this problem, which exhibits three low temperature phases, separated by two continuous phase transitions: an insulating, glassy phase with an amorphous frozen density pattern, a non-glassy superfluid phase and an intermediate phase, in which both types of order coexist. We elucidate the nature of the phase transitions, highlighting in particular the role of glassy correlations across the superfluid-insulator transition. The latter suppress superfluidity down to T = 0, due to the depletion of the low energy density of states, unlike in the standard BCS scenario. Further, we investigate the properties of the coexistence (superglass) phase. We find anticorrelations between the local order parameters and a non-monotonous superfluid order parameter as a function of T. The latter arises due to the weakening of the glassy correlation gap with increasing temperature. Implications of the mean field phenomenology for finite dimensional bosonic glasses with frustrating Coulomb interactions are discussed.
Motivated by evidence of local electron-electron attraction in experiments on disordered insulati... more Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range interelectron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further study variable-range hopping transport in such systems by extending the standard resistor network approach to include the motion of both single electrons and local pairs. In certain parameter regimes the competition between these two types of carriers results in a distinct peak in resistance as a function of the local attraction strength, which can be tuned by a magnetic field.
We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a ... more We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a crossover from collisionless transport at frequencies larger than k B T / (T is the temperature) to collision-dominated transport at lower frequencies. The d.c. conductivity is computed by the solution of a quantum Boltzmann equation. Due to a logarithmic singularity in the collinear scattering amplitude (a consequence of relativistic dispersion in two dimensions) quasi-particles and-holes moving in the same direction tend to an effective equilibrium distribution whose parameters depend on the direction of motion. This property allows us to find the non-equilibrium distribution functions and the quantum critical conductivity exactly to leading order in 1/| log(α)| where α is the coupling constant characterizing the Coulomb interactions.
Many condensed matter experiments explore the finite temperature dynamics of systems near quantum... more Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport coefficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport coefficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance.
We characterize the low temperature phase of a simple model for RNA secondary structures by deter... more We characterize the low temperature phase of a simple model for RNA secondary structures by determining the typical energy scale E(l) of excitations involving l bases. At low enough temperatures, including T = 0, we find a scaling law E(l) ∼ l θ with a small exponent θ. Above a critical temperature, there is a different phase characterized by a relatively flat free energy landscape resembling that of a homopolymer with a scaling exponent θ = 1. These results strengthen the evidence in favour of the existence of a glass phase at low temperatures.
We establish the connection between the presence of a glass phase and the appearance of a Coulomb... more We establish the connection between the presence of a glass phase and the appearance of a Coulomb gap in disordered materials with strongly interacting electrons. Treating multiparticle correlations in a systematic way, we show that in the case of strong disorder a continuous glass transition takes place whose Landau expansion is identical to that of the Sherrington-Kirkpatrick spin glass. We show that the marginal stability of the glass phase controls the physics of these systems: it results in slow dynamics and leads to the formation of a Coulomb gap.
We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the ch... more We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunnelling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ −1 (B) − ξ −1 (0) ∼ B 4/5. The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the non-trivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.
We report on the reinforcement of superconductivity in a system consisting of a narrow supercondu... more We report on the reinforcement of superconductivity in a system consisting of a narrow superconducting wire weakly coupled to a diffusive metallic film. We analyze the effective phase-only action of the system by a perturbative renormalization group and a self-consistent variational approach to obtain the critical points and phases at T = 0. We predict a quantum phase transition toward a superconducting phase with long-range order as a function of the wire stiffness and coupling to the metal. We discuss implications for the dc resistivity of the wire.
We investigate the temperature dependence of the conductivity in ballistic graphene using Landaue... more We investigate the temperature dependence of the conductivity in ballistic graphene using Landauer transport theory. We obtain results which are qualitatively in agreement with many features recently observed in transport measurements on high mobility suspended graphene. The conductivity σ at high temperature T and low density n grows linearly with T , while at high n we find σ ∼ p |n| with negative corrections at small T due to the T-dependence of the chemical potential. At moderate densities the conductivity is a non-monotonic function of T and n, exhibiting a minimum at T = 0.693 v p |n| where v is the Fermi velocity. We discuss two kinds of Fabry-Perot oscillations in short nanoribbons and their stability at finite temperatures.
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Papers by MARKUS MUELLER