arXiv subjects

A. D. Mirlin

Publications and source records attributed to A. D. Mirlin.

At least 73 records · Page 4Linked to original sources

arXiv2013

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.

cond-mat.mes-hall↗

arXiv2013

Nonequilibrium phenomena in high Landau levels

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.

cond-mat.mes-hall↗

arXiv2013

Quantum magnetooscillations in the ac conductivity of disordered graphene

The dynamic conductivity σ(ω) of graphene in the presence of diagonal white noise disorder and quantizing magnetic field B is calculated. We obtain analytic expressions for σ(ω) in various parametric regimes ranging from the quasiclassical Drude limit corresponding to strongly overlapping Landau levels (LLs) to the extreme quantum limit where the conductivity is determined by the optical selection rules of the clean graphene. The nonequidistant LL spectrum of graphene renders its transport characteristics quantitatively different from conventional 2D electron systems with parabolic spectrum. Since the magnetooscillations in the semiclassical density of states are anharmonic and are described by a quasi-continuum of cyclotron frequencies, both the ac Shubnikov-de Haas oscillations and the quantum corrections to σ(ω) that survive to higher temperatures manifest a slow beating on top of fast oscillations with the local energy-dependent cyclotron frequency.Both types of quantum oscillations possess nodes whose index scales as ω^2. In the quantum regime of separated LLs, we study both the cyclotron resonance transitions, which have a rich spectrum due to the nonequidistant spectrum of LLs, and disorder-induced transitions which violate the clean selection rules of graphene. We identify the strongest disorder-induced transitions in recent magnetotransmission experiments. We also compare the temperature- and chemical potential-dependence of σ(ω) in various frequency ranges from the dc limit allowing intra-LL transition only to the universal high-frequency limit where the Landau quantization provides a small B-dependent correction to the universal value of the interband conductivity σ=e^2/4 \hbar of the clean graphene.

cond-mat.mes-hall↗

arXiv2012

Correlations in non-equilibrium 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 ${\rm det}(1+\hat{A}\hat{B})$, where $A(ε)$ and $B(t)$ have multiple discontinuities in energy and time spaces. Such determinants are a generalization of Toeplitz determinants with Fisher-Hartwig singularities. 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 non-equilibrium power-law singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing correlations between left- and right-moving fermions that have left the interaction region.

cond-mat.str-el↗

arXiv2012

Classification and symmetry properties of scaling dimensions at Anderson transitions

We develop a classification of composite operators without gradients at Anderson-transition critical points in disordered systems. These operators represent correlation functions of the local density of states (or of wave-function amplitudes). Our classification is motivated by the Iwasawa decomposition for the field of the pertinent supersymmetric σ-model: the scaling operators are represented by "plane waves" in terms of the corresponding radial coordinates. We also present an alternative construction of scaling operators by using the notion of highest-weight vector. We further argue that a certain Weyl-group invariance associated with the σ-model manifold leads to numerous exact symmetry relations between the scaling dimensions of the composite operators. These symmetry relations generalize those derived earlier for the multifractal spectrum of the leading operators.

cond-mat.dis-nn↗

arXiv2012

Conductivity of suspended graphene at the Dirac point

We study transport properties of clean suspended graphene at the Dirac point. In the absence of the electron-electron interaction, the main contribution to resistivity comes from interaction with flexural (out-of-plane deformation) phonons. We find that the phonon-limited conductivity scales with the temperature as $T^{-η}, $ where $η$ is the critical exponent (equal to $\approx 0.7$ according to numerical studies) describing renormalization of the flexural phonon correlation functions due to anharmonic coupling with the in-plane phonons. The electron-electron interaction induces an additional scattering mechanism and also affects the electron-phonon scattering by screening the deformation potential. We demonstrate that the combined effect of both interactions results in a conductivity that can be expressed as a dimensionless function of two temperature-dependent dimensionless constants, $G[T]$ and $G_e[T]$ which characterize the strength of electron-phonon and electron-electron interaction, respectively. We also discuss the behavior of conductivity away from the Dirac point as well as the role of the impurity potential and compare our predictions with available experimental data.

cond-mat.mes-hall↗

arXiv2012

Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion

We explore dynamics of a density pulse induced by a local quench in a one-dimensional electron system. The spectral curvature leads to an "overturn" (population inversion) of the wave. We show that beyond this time the density profile develops strong oscillations with a period much larger than the Fermi wave length. The effect is studied first for the case of free fermions by means of direct quantum simulations and via semiclassical analysis of the evolution of Wigner function. We demonstrate then that the period of oscillations is correctly reproduced by a hydrodynamic theory with an appropriate dispersive term. Finally, we explore the effect of different types of electron-electron interaction on the phenomenon. We show that sufficiently strong interaction [$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatial scale] determines the dominant dispersive term in the hydrodynamic equations. Hydrodynamic theory reveals crucial dependence of the density evolution on the relative sign of the interaction and the density perturbation.

cond-mat.str-el↗

arXiv2012

Symmetries and weak (anti)localization of Dirac fermions in HgTe quantum wells

We perform a symmetry analysis of a 2D electron system in HgTe/HgCdTe quantum wells in the situation when the chemical potential is outside of the gap, so that the bulk of the quantum well is conducting. In order to investigate quantum transport properties of the system, we explore symmetries of the low-energy Hamiltonian which is expressed in terms of two flavors of Dirac fermions, and physically important symmetry-breaking mechanisms. This allows us to predict emerging patterns of symmetry breaking that control the weak localization and antilocalization showing up in transverse-field magnetoresistance.

cond-mat.mes-hall↗

arXiv2012

Coulomb drag in graphene near the Dirac point

We study Coulomb drag in double-layer graphene near the Dirac point. A particular emphasis is put on the case of clean graphene, with transport properties dominated by the electron-electron interaction. Using the quantum kinetic equation framework, we show that the drag becomes $T$-independent in the clean limit, $Tτ\to \infty$, where $T$ is temperature and $1/τ$ impurity scattering rate. For stronger disorder (or lower temperature), $Tτ\ll 1/α^2$, where $α$ is the interaction strength, the kinetic equation agrees with the leading-order ($α^2$) perturbative result. At still lower temperatures, $Tτ\ll 1$ (diffusive regime) this contribution gets suppressed, while the next-order ($α^3$) contribution becomes important; it yields a peak centered at the Dirac point with a magnitude that grows with lowering $Tτ$.

cond-mat.mes-hall↗

arXiv2012

Metal-insulator transition in 2D random fermion systems of chiral symmetry classes

Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite lattices at the band center. As was found by Gade and Wegner two decades ago within the sigma-model formalism, quantum interference effects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum localization effects emerge when the theory is treated non-perturbatively. Specifically, they are controlled by topological vortex-like excitations of the sigma models. We derive renormalization group equations including these non-perturbative contributions. Analyzing them, we find that the 2D disordered systems of chiral classes undergo a metal-insulator transition driven by topologically induced Anderson localization. We also show that the Wess-Zumino and Z_2 theta terms on surfaces of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.

cond-mat.mes-hall↗

arXiv2012

Luttinger liquids with multiple Fermi edges: Generalized Fisher-Hartwig conjecture and numerical analysis of Toeplitz determinants

It has been shown that solutions of a number of many-body problems out of equilibrium can be expressed in terms of Toeplitz determinants with Fisher-Hartwig (FH) singularities. In the present paper, such Toeplitz determinants are studied numerically. Results of our numerical calculations fully agree with the FH conjecture in an extended form that includes a summation over all FH representations (corresponding to different branches of the logarithms). As specific applications, we consider problems of Fermi edge singularity and tunneling spectroscopy of Luttinger liquid with multiple-step energy distribution functions, including the case of population inversion. In the energy representation, a sum over FH branches produces power-law singularities at multiple edges.

cond-mat.str-el↗

arXiv2011

Cold bosons in the Landauer setup

We consider one dimensional potential trap that connects two reservoirs containing cold Bose atoms. The thermal current and single-particle bosonic Green functions are calculated under non-equilibrium conditions. The bosonic statistics leads to Luttinger liquid state with non-linear spectrum of collective modes. This results in suppression of thermal current at low temperatures and affects the single-particle Green functions.

cond-mat.quant-gas↗

arXiv2011

Symmetries of multifractal spectra and field theories of Anderson localization

We uncover field-theoretic underpinnings 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 non-linear $σ$-model with respect to the Weyl group of the target space of the model.

cond-mat.dis-nn↗

arXiv2011

Negative conductivity and anomalous screening in two-dimensional electron systems subjected to microwave radiation

A 2D electron system in a quantized magnetic field can be driven by microwave radiation into a non-equilibrium state with strong magnetooscillations of the dissipative conductivity. We demonstrate that in such system a negative conductivity can coexist with a positive diffusion coefficient. In a finite system, solution of coupled electrostatic and linear transport problems shows that the diffusion can stabilize a state with negative conductivity. Specifically, this happens when the system size is smaller than the absolute value of the non-equilibrium screening length that diverges at the point where the conductivity changes sign. We predict that a negative resistance can be measured in such a state. Further, for a non-zero difference between the work functions of two contacts, we explore the distribution of the electrostatic potential and of the electron density in the sample. We show that in the diffusion-stabilized regime of negative conductivity the system splits into two regions with opposite directions of electric field. This effect is a precursor of the domain structure that has been predicted to emerge spontaneously in the microwave-induced zero-resistance states.

cond-mat.mes-hall↗

arXiv2011

Many-particle correlations in non-equilibrium Luttinger liquid

We develop an operator-based approach to the problem of Luttinger liquid conductor in a non-equilibrium stationary state. We show that the coherent-state many-body fermionic density matrix as well as all fermionic correlation functions out of equilibrium are given by one-dimensional functional determinants of the Fredholm type. Thus, the model constitutes a remarkable example of a many-body problem where all the correlation functions can be evaluated exactly. On the basis of the general formalism we investigate four-point correlation functions of the fermions coming out of the Luttinger liquid wire. Obtained correlations in the fermionic distribution functions represent the combined effect of interaction and non-equilibrium conditions.

cond-mat.mes-hall↗

arXiv2011

Enhancement of superconductivity by Anderson localization

Influence of disorder on the temperature of superconducting transition (T_c) is studied within the sigma-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 the Anderson localization leads to strong enhancement of T_c related to the multifractal character of wave functions.

cond-mat.mes-hall↗

arXiv2010

Coulomb interaction in graphene: Relaxation rates and transport

We analyze the inelastic electron-electron scattering in undoped graphene within the Keldysh diagrammatic approach. We demonstrate that finite temperature strongly affects the screening properties of graphene, which, in turn, influences the inelastic scattering rates as compared to the zero-temperature case. Focussing on the clean regime, we calculate the quantum scattering rate which is relevant for dephasing of interference processes. We identify an hierarchy of regimes arising due to the interplay of a plasmon enhancement of the scattering and finite-temperature screening of the interaction. We further address the energy relaxation and transport scattering rates in graphene. We find a non-monotonic energy dependence of the inelastic relaxation rates in clean graphene which is attributed to the resonant excitation of plasmons. Finally, we discuss the temperature dependence of the conductivity at the Dirac point in the presence of both interaction and disorder. Our results complement the kinetic-equation and hydrodynamic approaches for the collision-limited conductivity of clean graphene and can be generalized to the treatment of physics of inelastic processes in strongly non-equilibrium setups.

cond-mat.str-el↗

arXiv2010

Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions

We analyze the critical behavior of the dephasing rate induced by short-range electron-electron interaction near an Anderson transition of metal-insulator or quantum Hall type. The corresponding exponent characterizes the scaling of the transition width with temperature. Assuming no spin degeneracy, the critical behavior can be studied by performing the scaling analysis in the vicinity of the non-interacting fixed point, since the latter is stable with respect to the interaction. We combine an analytical treatment (that includes the identification of operators responsible for dephasing in the formalism of the non-linear sigma-model and the corresponding renormalization-group analysis in $2+ε$ dimensions) with numerical simulations on the Chalker-Coddington network model of the quantum Hall transition. Finally, we discuss the current understanding of the Coulomb interaction case and the available experimental data.

cond-mat.mes-hall↗