Giant fluctuations of local magnetoresistance of organic spin valves and the non-Hermitian 1D Anderson model.

Motivated by recent experiments, where the tunnel magnetoresitance (TMR) of a spin valve was measured locally, we theoretically study the distribution of TMR along the surface of magnetized electrodes. We show that, even in the absence of interfacial effects (like hybridization due to donor and acceptor molecules), this distribution is very broad, and the portion of area with negative TMR is appreciable even if on average the TMR is positive. The origin of the local sign reversal is quantum interference of subsequent spin-rotation amplitudes in the course of incoherent transport of carriers between the source and the drain. We find the distribution of local TMR exactly by drawing upon formal similarity between evolution of spinors in time and of the reflection coefficient along a 1D chain in the Anderson model. The results obtained are confirmed by the numerical simulations.

Localization properties of random-mass Dirac fermions from real-space renormalization group.

Localization properties of random-mass Dirac fermions for a realization of mass disorder, commonly referred to as the Cho-Fisher model, are studied on the D-class chiral network. We show that a simple renormalization group (RG) description captures accurately a rich phase diagram: thermal metal and two insulators with quantized σ(xy), as well as transitions (including critical exponents) between them. Our main finding is that, even with small transmission of nodes, the RG block exhibits a sizable portion of perfect resonances. Delocalization occurs by proliferation of these resonances to larger scales. Evolution of the thermal conductance distribution towards a metallic fixed point is synchronized with evolution of signs of transmission coefficients, so that delocalization is accompanied with sign percolation.

Fermi-edge singularity in the vicinity of the resonant scattering condition.

Fermi-edge absorption theory predicting the spectrum A(ω) ∝ ω(-2δ(0)/π+δ(0)92)/π2) relies on the assumption that scattering phase δ(0) is frequency independent. The dependence of δ(0) on ω becomes crucial near the resonant condition, where the phase changes abruptly by π. In this limit, because of the finite time spent by electron on a resonant level, the scattering is dynamic. We incorporate the finite time delay into the theory, solve the Dyson equation with a modified kernel, and find that, near the resonance, A(ω) behaves as ω(-3/4)|lnω|. Scattering off the core hole becomes resonant in 1D and 2D in the presence of an empty subband above the Fermi level; then a deep hole splits off a level from the bottom of this subband. Fermi-edge absorption in the regime when resonant level transforms into a Kondo peak is discussed.

Microscopic description of a quantum Hall transition without landau levels.

By restricting the motion of a high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum mechanically, the interplay of backscattering, and of the bending action of a weak magnetic field. Backscattering limits the mobility, while bending initiates quantization of the Hall conductivity. We demonstrate that, in restricted geometry, electron motion reduces to two Chalker-Coddington networks, with opposite directions of propagation along the links, which are weakly coupled by disorder. The interplay of backscattering and bending results in the quantum Hall transition in a nonquantizing magnetic field, which decreases with increasing mobility. This is in accord with the scenario of floating up delocalized states.

Scattering of plasmons at the intersection of two metallic nanotubes: implications for tunneling.

We study theoretically the plasmon scattering at the intersection of two metallic carbon nanotubes. We demonstrate that, for a small angle of crossing theta<<1, the transmission coefficient is an oscillatory function of lambda/theta, where lambda is the interaction parameter of the Luttinger liquid in an individual nanotube. We calculate the tunnel density of states nu(omega,x) as a function of energy omega and distance x from the intersection. In contrast with a single nanotube, we find that, in the geometry of crossed nanotubes, conventional "rapid" oscillations in nu(omega,x) due to the plasmon scattering acquire an aperiodic "slow-breathing" envelope which has lambda/theta nodes.

Crossover from weak localization to Shubnikov-de Haas oscillations in a high-mobility 2D electron gas.

We study the magnetoresistance deltarho(xx)(B)/rho(0) of a high-mobility 2D electron gas in the domain of magnetic fields B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where deltarho(xx)(B)/rho(0) is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the second order in the interaction parameter lambda a linear B dependence, deltarho(xx)(B)/rho(0) approximately lambda(2)omega(c)/E(F) with a temperature-independent slope, emerges in this domain of B (here omega(c) and E(F) are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is unrelated to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B dependence of the phase of the impurity-induced Friedel oscillations.

Electron-pair resonance in the coulomb blockade.

We study many-body corrections to the cotunneling current via a localized state with energy epsilon(d) at large bias voltages V. We show that the transfer of electron pairs, enabled by the Coulomb repulsion in the localized level, results in ionization resonance peaks in the third derivative of the current with respect to V, centered at eV=+/-2epsilon(d)/3. Our results predict the existence of previously unnoticed structure within Coulomb-blockade diamonds.

Magneto-oscillations due to electron-electron interactions in the ac conductivity of a two-dimensional electron gas.

Electron-electron interactions give rise to the correction, deltasigma(int)(omega), to the ac magnetoconductivity, sigma(omega), of a clean 2D electron gas that is periodic in omega_(c)(-1), where omega_(c) is the cyclotron frequency. Unlike conventional harmonics of the cyclotron resonance, which are periodic with omega, this correction is periodic with omega(3/2). Oscillations in deltasigma(int)(omega) develop at low magnetic fields, omega_(c)<

Smearing of the two-dimensional Kohn anomaly in a nonquantizing magnetic field: implications for interaction effects.

Thermodynamic and transport characteristics of a clean two-dimensional interacting electron gas are shown to be sensitive to the weak perpendicular magnetic field even at temperatures much higher than the cyclotron energy, when the quantum oscillations are completely washed out. We demonstrate this sensitivity for two interaction-related characteristics: electron lifetime and the tunnel density of states. The origin of the sensitivity is traced to the field-induced smearing of the Kohn anomaly; this smearing is the result of curving of the semiclassical electron trajectories in magnetic field.

Zero-bias tunneling anomaly in a clean 2D electron gas caused by smooth density variations.

We show that smooth variations, delta n(r), of the local electron concentration in a clean 2D electron gas give rise to a zero-bias anomaly in the tunnel density of states, nu(omega), even in the absence of scatterers, and thus, without the Friedel oscillations. The energy width, omega 0, of the anomaly scales with the magnitude, delta n, and characteristic spatial extent, D, of the fluctuations as (delta n/D)2/3, while the relative magnitude delta nu/nu scales as (delta n/D). With increasing omega, the averaged delta nu oscillates with omega. We demonstrate that the origin of the anomaly is a weak curving of the classical electron trajectories due to the smooth inhomogeneity of the gas. This curving suppresses the corrections to the electron self-energy which come from the virtual processes involving two electron-hole pairs.

Two-electron linear intersubband light absorption in a biased quantum well.

We point out a novel manifestation of many-body correlations in the linear optical response of electrons confined in a quantum well. Namely, we demonstrate that along with the conventional absorption peak at a frequency omega close to the intersubband energy delta, there exists an additional peak at frequency h omega approximately = 2delta. This new peak is solely due to electron-electron interactions, and can be understood as excitation of two electrons by a single photon. The actual peak line shape is comprised of a sharp feature, due to excitation of pairs of intersubband plasmons, on top of a broader band due to absorption by two single-particle excitations. The two-plasmon contribution allows us to infer intersubband plasmon dispersion from linear absorption experiments.

Pair Tunneling through Single Molecules.

By a polaronic energy shift, the effective charging energy of molecules can become negative, favoring ground states with even numbers of electrons. Here we show that charge transport through such molecules near ground-state degeneracies is dominated by tunneling of electron pairs which coexists with (featureless) single-electron cotunneling. Because of the restricted phase space for pair tunneling, the current-voltage characteristics exhibit striking differences from the conventional Coulomb blockade. In asymmetric junctions, pair tunneling can be used for gate-controlled current rectification and switching.

Full counting statistics of strongly non-ohmic transport through single molecules.

We study analytically the full counting statistics of charge transport through single molecules, strongly coupled to a weakly damped vibrational mode. The specifics of transport in this regime--a hierarchical sequence of avalanches of transferred charges, interrupted by "quiet" periods--make the counting statistics strongly non-Gaussian. We support our findings for the counting statistics as well as for the frequency-dependent noise power by numerical simulations, finding excellent agreement.

Disorder-induced resistive anomaly near ferromagnetic phase transitions.

We show that the resistivity rho(T) of disordered ferromagnets near, and above, the Curie temperature T(c) generically exhibits a stronger anomaly than the scaling-based Fisher-Langer prediction. Treating transport beyond the Boltzmann description, we find that within mean-field theory, drho/dT exhibits a |T - T(c)|(-1/2) singularity near T(c). Our results, being solely due to impurities, are relevant to ferromagnets with low T(c), such as SrRuO(3) or diluted magnetic semiconductors, whose mobility near T(c) is limited by disorder.

Incomplete photonic band gap as inferred from the speckle pattern of scattered light waves.

Motivated by recent experiments on intensity correlations of the waves transmitted through disordered media, we demonstrate that the speckle pattern from disordered photonic crystal with incomplete band gap represents a sensitive tool for determination of the stop-band width. We establish the quantitative relation between this width and the angular anisotropy of the intensity correlation function.

Anomalously localized states in the Anderson model.

It is demonstrated that anomalously localized states (ALS) in the Anderson model, being lattice specific, are not related to any of the continuous theories. We identify the spatial structure of ALS on a lattice and calculate their likelihood. Analytical results explain peculiarities in previous numerical simulations.

Strongly localized mode at the intersection of the phase slips in a photonic crystal without band gap.

A two-dimensional photonic crystal with a rectangular symmetry and low contrast (<1) of the dielectric constant is considered. We demonstrate that, despite the absence of a band gap, strong localization of a photon can be achieved for certain "magic" geometries of a unit cell by introducing two pi/2 phase slips along the major axes. The long-living photon mode is bound to the intersection of the phase slips. We calculate analytically the lifetime of this mode for the simplest geometry-a square lattice of cylinders of a radius, r. We find the magic radius r(c) of a cylinder to be 43.10% of the lattice constant. For this value of r, the quality factor of the bound mode exceeds 10(6). A small ( approximately 1%) deviation of r from r(c) results in a drastic damping of the bound mode.

Localization length in anderson insulator with Kondo impurities.

The localization length, xi, in a two-dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, tau(-1)(s). For antiferromagnetic sign of the exchange, the time tau(s) is itself a function of xi, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, n(M), is smaller than a critical value, n(c). For n(M)>n(c), the dependence of xi on the dimensionless conductance, g, is reentrant, crossing over to unitary, and back to orthogonal behavior upon increasing g. Sensitivity of Kondo correlations to a weak parallel magnetic field results in a giant parallel magnetoresistance.

Crossover between universality classes in the statistics of rare events in disordered conductors.

The crossover from orthogonal to the unitary universality classes in the distribution of the anomalously localized states (ALS) in two-dimensional disordered conductors is traced as a function of magnetic field. We demonstrate that the microscopic origin of the crossover is the change in the symmetry of the underlying disorder configurations that are responsible for ALS. These disorder configurations are of weak magnitude (compared to the Fermi energy) and of small size (compared to the mean free path). We find their shape explicitly by means of the direct optimal fluctuation method.

Coulomb drag for strongly localized electrons: a pumping mechanism.

The mutual influence of two layers with strongly localized electrons is exercised though the random Coulomb shifts of site energies in one layer caused by electron hops in the other layer. We trace how these shifts give rise to a voltage drop in the passive layer, when a current is passed through the active layer. We find that the microscopic origin of drag lies in the time correlations of the occupation numbers of the sites involved in a hop. These correlations are neglected within the conventional Miller-Abrahams scheme for calculating the hopping resistance.