Disorder scattering in magnetic tunnel junctions: theory of nonequilibrium vertex correction

We report a first principles formalism and its numerical implementation for treating quantum transport properties of nanoelectronic devices with atomistic disorder. We develop a nonequilibrium vertex correction (NVC) theory to handle the configurational average of random disorder at the density matrix level so that disorder effects to nonlinear and nonequilibrium quantum transport can be calculated from atomic first principles in a self-consistent and efficient manner. We implement the NVC into a Keldysh nonequilibrium Green's function (NEGF) -based density functional theory (DFT) and apply the NEGF-DFT-NVC formalism to Fe/vacuum/Fe magnetic tunnel junctions with interface roughness disorder. Our results show that disorder has dramatic effects on the nonlinear spin injection and tunnel magnetoresistance ratio.     

Critical currents at the bragg glass to vortex glass transition

We present simulations of the transport properties of superconductors at the transition from the Bragg glass (BG) to the vortex glass (VG) phase. We study the frustrated anisotropic 3D XY model with point disorder, which has been shown to have a first-order transition as a function of the intensity of disorder. We add an external current to the model, and we obtain current-voltage curves as a function of disorder at a low temperature. We find that the in-plane critical current has a steep increase at the BG-VG transition, while the c-axis critical current has a discontinuous jump down, this later result in agreement with the first-order character of the transition.     

Quantum phase slips in the presence of finite-range disorder

To study the effect of disorder on quantum phase slips (QPSs) in superconducting wires, we consider the plasmon-only model where disorder can be incorporated into a first-principles instanton calculation. We consider weak but general finite-range disorder and compute the form factor in the QPS rate associated with momentum transfer. We find that the system maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the wave (plasmon) impedance Z of the wire and with a superconductor-insulator transition at Z = 6.5 k. We speculate that the system will remain in this universality class after resistive effects at the QPS core are taken into account.     

A colloidal model system with tunable disorder: Solid-fluid transition and discontinuities in the limit of zero disorder

We study a colloidal model system where disorder can be continuously tuned from no disorder --corresponding to a system that can crystallize-- to large disorder where geometrical frustration occurs. The model system consists of colloidal particles with screened electrostatic repulsion. They can only move on single lines which are parallel and equidistant to each other. We introduce disorder by modulating the particle line density. The system exhibits a solid-to-fluid transition which we study by the structure factor and the temporal evolution of the mean-square distance of nearest neighbors on neighboring lines. A determining feature is the occurrence of discontinuities when disorder is tuned to zero. We observe that the peak height of the pair correlation function in the solid phase does not extrapolate to the value of the perfect crystal. Similarly, the mean interaction energy and the screening length at which the solid-fluid transition occurs seem to be discontinuous when the limit of zero disorder is approached.     

Disorder induced transition into a one-dimensional wigner glass

The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe glasslike behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the ac conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.     

Destruction of bulk ordering by surface randomness

We demonstrate that the arbitrarily weak quenched disorder on the surface of a system of continuous symmetry destroys long-range order in the bulk, and, instead, quasi-long-range order emerges. Correlation functions are calculated exactly for the two- and three-dimensional XY models with surface randomness via the functional renormalization group. Even at strong quenched disorder the three-dimensional XY model possesses topological order. We also determine roughness of a domain wall in the presence of surface disorder.     

Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators

In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.     

The dynamics of a polariton dimer in a disordered coupled array of cavities

We investigate the effect of disorder in the laser intensity on the dynamics of dark-state polaritons in an array of 20 cavities, each containing an ensemble of four-level atoms that is described by a Bose-Hubbard Hamiltonian. We examine the evolution of the polariton number in the cavities starting from a state with either one or two polaritons in one of the cavities. For the case of a single polariton without disorder in the laser intensity, we calculate the wavefunction of the polariton and find that it disperses away from the initial cavity with time. The addition of disorder results in minimal suppression of the dispersal of the wavefunction. In the case of two polaritons with an on-site repulsion to hopping strength ratio of 20, we find that the polaritons form a repulsively bound state or dimer. Without disorder the dimer wavefunction disperses similarly to the single polariton wavefunction but over a longer time period. The addition of sufficiently strong disorder results in localization of the polariton dimer. The localization length is found to be described by a power law with exponent ? 1.31. We also find that we can localise the dimer at any given time by switching on the disorder.     

Finding universal correlations between cationic disorder and low field magnetoresistance in FeMo double perovskite series

We search for general patterns that explain the low field magnetoresistance at low temperatures in the system A(2-x)A'xFeMoO6. The observed linear dependence of the low field magnetoresistance with the saturation magnetization for the series is related to the antisite disorder at the Fe and Mo sites. This is explained in terms of a spin dependent crossing of intragranular barriers originated from the presence of antiferromagnetic SrFeO3 patches that naturally develop when antisite disorder occurs in the double perovskite. The presence of a moderate level of antisite disorder is at the very root of low field magnetoresistance although effects such as disorder distribution, connectivity, or morphology add their contribution.     

Persistent current in finite-width ring with surface disorder

We explore the surface disorder effect on the persistent current in a finite-width ring. In the strong disorder regime, the persistent current increases with surface disorder strength, while it decreases in the weak disorder regime. The result is at variance with the observation in bulk-disordered ring. Also, it is shown that the disorder-induced changes in the persistent current strongly depend on both the ring width and radius, which show up a singular quantum size effect.     

Edge states versus diffusion in disordered graphene flakes

We study the localization properties of the wavefunctions in graphene flakes with short range disorder, via the numerical calculation of the inverse participation ratio (IPR) and its scaling which provides the fractal dimension D ₂. We show that the edge states which exist at the Dirac point of ballistic graphene (no disorder) with zig-zag edges survive in the presence of weak disorder with wavefunctions localized at the boundaries of the flakes. We argue, that there is a strong interplay between the underlying destructive interference mechanism of the honeycomb lattice of graphene leading to edge states and the diffusive interference mechanism introduced by the short-range disorder. This interplay results in a highly abnormal behavior, wavefunctions are becoming progressively less localized as the disorder is increased, indicated by the decrease of the average ?IPR? and the increase of D ₂. We verify, that this abnormal behavior is absent for graphene flakes with armchair edges which do not provide edge states.     

Conductivity of disordered graphene at half filling

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity 4e²/πh in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is a symplectic-class sigma-model including a topological term with θ=π. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e²/h. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and the conductivity acquires the value characteristic for the quantum Hall transition.     

Level statistics in disordered linear networks

We consider a linear electrical impedance network, and study its frequency of nearest level statistics, P(s). We find that this probability density evolves from a sum of gaussians at small disorder, to a linear combination of Poisson and gaussian orthogonal ensemble for large values of the disorder.     

Disorder-Assisted Error Correction in Majorana Chains

It was recently realized that quenched disorder may enhance the reliability of topological qubits by reducing the mobility of anyons at zero temperature. Here we compute storage times with and without disorder for quantum chains with unpaired Majorana fermions ?? the simplest toy model of a quantum memory. Disorder takes the form of a random site-dependent chemical potential. The corresponding one-particle problem is a one-dimensional Anderson model with disorder in the hopping amplitudes. We focus on the zero-temperature storage of a qubit encoded in the ground state of the Majorana chain. Storage and retrieval are modeled by a unitary evolution under the memory Hamiltonian with an unknown weak perturbation followed by an error-correction step. Assuming dynamical localization of the one-particle problem, we show that the storage time grows exponentially with the system size. We give supporting evidence for the required localization property by estimating Lyapunov exponents of the one-particle eigenfunctions. We also simulate the storage process for chains with a few hundred sites. Our numerical results indicate that in the absence of disorder, the storage time grows only as a logarithm of the system size. We provide numerical evidence for the beneficial effect of disorder on storage times and show that suitably chosen pseudorandom potentials can outperform random ones.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Scaling with respect to disorder in time-to-failure

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of time-to-rupture and of the amplitude of the disorder, which allows us to collapse neatly the numerical simulations over more than five decades in time and more than one decade in disorder amplitude onto a single master curve. We thus conclude that, at least in this model, dynamical rupture in systems with long-range elasticity is a genuine critical phenomenon occurring as soon as the disorder is non-vanishing. Received: 11 July 1997 / Revised: 6 November 1997 / Accepted: 10 November 1997     

Effect of disorder on the critical temperature of a dilute hard-sphere Gas

We have performed path integral Monte Carlo calculations to determine the effect of quenched disorder on the superfluid density of a dilute 3D hard-sphere gas. The disorder was introduced by locating hard cylinders randomly inside the simulation cell. Our results indicate that the disorder does not strongly affect the superfluid critical temperature. There is a reduction of rho(s)/rho with increasing disorder and with excluded volume for similar disorders and a possible change of universality class (as evidenced by the correlation length exponent) at high disorder. Comparison to experiments of helium in Vycor is made.