arXiv subjects

Andrei A. Fedorenko

Publications and source records attributed to Andrei A. Fedorenko.

At least 37 records · Page 2Linked to original sources

arXiv2015

Minimal conductivity, topological Berry winding and duality in three-band semimetals

The physics of massless relativistic quantum particles has recently arisen in the electronic properties of solids following the discovery of graphene. Around the accidental crossing of two energy bands, the electronic excitations are described by a Weyl equation initially derived for ultra-relativistic particles. Similar three and four band semimetals have recently been discovered in two and three dimensions. Among the remarkable features of graphene are the characterization of the band crossings by a topological Berry winding, leading to an anomalous quantum Hall effect, and a finite minimal conductivity at the band crossing while the electronic density vanishes. Here we show that these two properties are intimately related: this result paves the way to a direct measure of the topological nature of a semi-metal. By considering three band semimetals with a flat band in two dimensions, we find that only few of them support a topological Berry phase. The same semimetals are the only ones displaying a non vanishing minimal conductivity at the band crossing. The existence of both a minimal conductivity and a topological robustness originates from properties of the underlying lattice, which are encoded not by a symmetry of their Bloch Hamiltonian, but by a duality.

cond-mat.mes-hall↗

arXiv2014

Localization of spin waves in disordered quantum rotors

We study the dynamics of excitations in a system of $O(N)$ quantum rotors in the presence of random fields and random anisotropies. Below the lower critical dimension $d_{\mathrm{lc}}=4$ the system exhibits a quasi-long-range order with a power-law decay of correlations. At zero temperature the spin waves are localized at the length scale $L_{\mathrm{loc}}$ beyond which the quantum tunneling is exponentially suppressed $ c \sim e^{-(L/L_{\mathrm{loc}})^{2(θ+1)}}$. At finite temperature $T$ the spin waves propagate by thermal activation over energy barriers that scales as $L^θ$. Above $d_{\mathrm{lc}}$ the system undergoes an order-disorder phase transition with activated dynamics such that the relaxation time grows with the correlation length $ξ$ as $τ\sim e^{C ξ^θ/T}$ at finite temperature and as $τ\sim e^{C' ξ^{2(θ+1)}/\hbar^2}$ in the vicinity of the quantum critical point.

cond-mat.dis-nn↗

arXiv2013

Non-Gaussian effects and multifractality in the Bragg glass

We study, beyond the Gaussian approximation, the decay of the translational order correlation function for a d-dimensional scalar periodic elastic system in a disordered environment. We develop a method based on functional determinants, equivalent to summing an infinite set of diagrams. We obtain, in dimension d=4-epsilon, the even n-th cumulant of relative displacements as <[u(r)-u(0)]^n>^c = A_n ln r, with A_n = -(ε/3)^n Γ(n-1/2) ζ(2n-3)/π^(1/2), as well as the multifractal dimension x_q of the exponential field e^{q u(r)}. As a corollary, we obtain an analytic expression for a class of n-loop integrals in d=4, which appear in the perturbative determination of Konishi amplitudes, also accessible via AdS/CFT using integrability.

cond-mat.dis-nn↗

arXiv2013

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

We study the influence of disorder on the topological transition from a two-dimensional Dirac semi-metal to an insulating state. This transition is described as a continuous merging of two Dirac points leading to a semi-Dirac spectrum at the critical point. The latter is characterized by a dispersion relation linear in one direction and quadratic in the orthogonal one. Using the self-consistent Born approximation and renormalization group we calculate the density of states above, below and in the vicinity of the transition in the presence of different types of disorder. Beyond the expected disorder smearing of the transition we find an intermediate disordered semi-Dirac phase. On one side this phase is separated from the insulating state by a continuous transition while on the other side it evolves through a crossover to the disordered Dirac phase.

cond-mat.mes-hall↗

arXiv2012

Functional renormalization-group approach to decaying turbulence

We reconsider the functional renormalization-group (FRG) approach to decaying Burgers turbulence, and extend it to decaying Navier-Stokes and Surface-Quasi-Geostrophic turbulence. The method is based on a renormalized small-time expansion, equivalent to a loop expansion, and naturally produces a dissipative anomaly and a cascade after a finite time. We explicitly calculate and analyze the one-loop FRG equations in the zero-viscosity limit as a function of the dimension. For Burgers they reproduce the FRG equation obtained in the context of random manifolds, extending previous results of one of us. Breakdown of energy conservation due to shocks and the appearance of a direct energy cascade corresponds to failure of dimensional reduction in the context of disordered systems. For Navier-Stokes in three dimensions, the velocity-velocity correlation function acquires a linear dependence on the distance, zeta_2=1, in the inertial range, instead of Kolmogorov's zeta_2=2/3; however the possibility remains for corrections at two- or higher-loop order. In two dimensions, we obtain a numerical solution which conserves energy and exhibits an inverse cascade, with explicit analytical results both for large and small distances, in agreement with the scaling proposed by Batchelor. In large dimensions, the one-loop FRG equation for Navier-Stokes converges to that of Burgers.

nlin.CD↗

arXiv2012

Random field and random anisotropy O(N) spin systems with a free surface

We study the surface scaling behavior of a semi-infinite $d$-dimensional O(N) spin system in the presence of quenched random field and random anisotropy disorders. It is known that above the lower critical dimension $d_{\mathrm{lc}}=4$ the infinite models undergo a paramagnetic-ferromagnetic transition for $N>N_c$ ($N_c=2.835$ for random field and $N_c=9.441$ for random anisotropy). For $N d_{\mathrm{lc}}$ and the long-range behavior of spin correlations near the surface in the quasi-long-range ordered phase for $d<d_{\mathrm{lc}}$. The corresponding surface exponents are calculated to one-loop order. The obtained results can be applied to the surface scaling of periodic elastic systems in disordered media and amorphous magnets.

cond-mat.dis-nn↗

arXiv2011

Two dimensional Dirac fermions in the presence of long-range correlated disorder

We consider 2D Dirac fermions in the presence of three types of disorder: random scalar potential, random gauge potential and random mass with long-range correlations decaying as a power law. Using various methods such as the self-consistent Born approximation (SCBA), renormalization group (RG), the matrix Green function formalism and bosonisation we calculate the density of states and study the full counting statistics of fermionic transport at lower energy. The SCBA and RG show that the random correlated scalar potentials generate an algebraically small energy scale below which the density of states saturates to a constant value. For correlated random gauge potential, RG and bosonisation calculations provide consistent behavior of the density of states which diverges at zero energy in an integrable way. In the case of correlated random mass disorder the RG flow has a nontrivial infrared stable fixed point leading to a universal power-law behavior of the density of states and also to universal transport properties. In contrast to uncorrelated case the correlated scalar potential and random mass disorders give rise to deviation from the pseudodiffusive transport already to lowest order in disorder strength.

cond-mat.mes-hall↗

arXiv2010

Density of states in an optical speckle potential

We study the single particle density of states of a one-dimensional speckle potential, which is correlated and non-Gaussian. We consider both the repulsive and the attractive cases. The system is controlled by a single dimensionless parameter determined by the mass of the particle, the correlation length and the average intensity of the field. Depending on the value of this parameter, the system exhibits different regimes, characterized by the localization properties of the eigenfunctions. We calculate the corresponding density of states using the statistical properties of the speckle potential. We find good agreement with the results of numerical simulations.

cond-mat.dis-nn↗

arXiv2010

Non-linear sigma model study of magnetic dephasing in a mesoscopic spin glass

We propose a nonlinear sigma model for the description of quantum transport in a mesoscopic metallic conductor with magnetic impurities frozen in a spin glass phase. It accounts for the presence of both the corresponding scalar and magnetic random potentials. In a spin glass, this magnetic random potential is correlated between different realizations. As the strength of the magnetic potential is varied, this model describes the crossover between orthogonal and unitary universality classes of the nonlinear sigma model. We apply this technique to the calculations of the correlation of conductance between two frozen spin configurations in terms of dephasing rates for the usual low energy modes of weak localization theory.

cond-mat.dis-nn↗

arXiv2008

Field theory conjecture for loop-erased random walks

We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a systematic expansion in epsilon=4-d. Up to two loop, the FRG agrees with rigorous bounds, correctly reproduces the leading logarithmic corrections at the upper critical dimension d=4, and compares well with numerical studies. We obtain the universal subleading logarithmic correction in d=4, which can be used as a further test of the conjecture.

cond-mat.dis-nn↗

arXiv2008

Long-range correlated random field and random anisotropy O(N) models: A functional renormalization group study

We study the long-distance behavior of the O(N) model in the presence of random fields and random anisotropies correlated as ~1/x^{d-sigma} for large separation x using the functional renormalization group. We compute the fixed points and analyze their regions of stability within a double epsilon=d-4 and sigma expansion. We find that the long-range disorder correlator remains analytic but generates short-range disorder whose correlator develops the usual cusp. This allows us to obtain the phase diagrams in (d,sigma,N) parameter space and compute the critical exponents to first order in epsilon and sigma. We show that the standard renormalization group methods with a finite number of couplings used in previous studies of systems with long-range correlated random fields fail to capture all critical properties. We argue that our results may be relevant to the behavior of He-3A in aerogel.

cond-mat.dis-nn↗

arXiv2008

Elastic systems with correlated disorder: Response to tilt and application to surface growth

We study elastic systems such as interfaces or lattices pinned by correlated quenched disorder considering two different types of correlations: generalized columnar disorder and quenched defects correlated as ~ x^{-a} for large separation x. Using functional renormalization group methods, we obtain the critical exponents to two-loop order and calculate the response to a transverse field h. The correlated disorder violates the statistical tilt symmetry resulting in nonlinear response to a tilt. Elastic systems with columnar disorder exhibit a transverse Meissner effect: disorder generates the critical field h_c below which there is no response to a tilt and above which the tilt angle behaves as θ~ (h-h_c)^ϕ with a universal exponent ϕ<1. This describes the destruction of a weak Bose glass in type-II superconductors with columnar disorder caused by tilt of the magnetic field. For isotropic long-range correlated disorder, the linear tilt modulus vanishes at small fields leading to a power-law response θ~ h^ϕ with ϕ>1. The obtained results are applied to the Kardar-Parisi-Zhang equation with temporally correlated noise.

cond-mat.dis-nn↗

arXiv2008

A functional renormalization group approach to systems with long-range correlated disorder

We studied the statics and dynamics of elastic manifolds in disordered media with long-range correlated disorder using functional renormalization group (FRG). We identified different universality classes and computed the critical exponents and universal amplitudes describing geometric and velocity-force characteristics. In contrast to uncorrelated disorder, the statistical tilt symmetry is broken resulting in a nontrivial response to a transverse tilting force. For instance, the vortex lattice in disordered superconductors shows a new glass phase whose properties interpolate between those of the Bragg and Bose glasses formed by pointlike and columnar disorder, respectively. Whereas there is no response in the Bose glass phase (transverse Meissner effect), the standard linear response expected in the Bragg-glass gets modified to a power law response in the presence of disorder correlations. We also studied the long distance properties of the O(N) spin system with random fields and random anisotropies correlated as 1/x^{d-sigma}. Using FRG we obtained the phase diagram in (d,sigma,N)-parameter space and computed the corresponding critical exponents. We found that below the lower critical dimension 4+sigma, there can exist two different types of quasi-long-range-order with zero order-parameter but infinite correlation length.

cond-mat.dis-nn↗

arXiv2007

Statics and dynamics of elastic manifolds in media with long-range correlated disorder

We study the statics and dynamics of an elastic manifold in a disordered medium with quenched defects correlated as r^{-a} for large separation r. We derive the functional renormalization-group equations to one-loop order, which allow us to describe the universal properties of the system in equilibrium and at the depinning transition. Using a double epsilon=4-d and delta=4-a expansion, we compute the fixed points characterizing different universality classes and analyze their regions of stability. The long-range disorder-correlator remains analytic but generates short-range disorder whose correlator exhibits the usual cusp. The critical exponents and universal amplitudes are computed to first order in epsilon and delta at the fixed points. At depinning, a velocity-versus-force exponent beta larger than unity can occur. We discuss possible realizations using extended defects.

cond-mat.dis-nn↗

arXiv2006

Universal distribution of threshold forces at the depinning transition

We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group (FRG) technique, we compute the distribution of pinning forces in the quasi-static limit. This distribution is universal up to two parameters, the average critical force, and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.

cond-mat.dis-nn↗

arXiv2006

Surface segregation of conformationally asymmetric polymer blends

We have generalized the Edwards' method of collective description of dense polymer systems in terms of effective potentials to polymer blends in the presence of a surface. With this method we have studied conformationally asymmetric athermic polymer blends in the presence of a hard wall to the first order in effective potentials. For polymers with the same gyration radius $R_g$ but different statistical segment lengths $l_{A}$ and $l_{B}$ the excess concentration of stiffer polymers at the surface is derived as $% δρ_{A}(z=0)\sim (l_{B}^{-2}-l_{A}^{-2}){\ln (}R_{g}^{2}/l_{c}^{2}{)%}$, where $l_{c}$ is a local length below of which the incompressibility of the polymer blend is violated. For polymer blends differing only in degrees of polymerization the shorter polymer enriches the wall.

cond-mat.soft↗

arXiv2005

Critical aging of a ferromagnetic system from a completely ordered state

We adapt the non-linear $σ$ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in $d=2+ε$ dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behavior almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behavior which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in $ε$ and the relation between transverse and longitudinal fluctuations is discussed.

cond-mat.stat-mech↗

arXiv2004

Nonequilibrium critical relaxation in the presence of extended defects

We study nonequilibrium critical relaxation properties of systems with quenched extended defects, correlated in $ε_d$ dimensions and randomly distributed in the remaining $d-ε_d$ dimensions. Using a field-theoretic renormalization-group approach, we find the scaling behavior of the nonequilibrium response and correlation functions and calculate the initial slip exponents $θ$ and $θ^{\prime}$, which describe the growth of correlations during the initial stage of the critical relaxation, in the two-loop approximation.

cond-mat.dis-nn↗