Angle-resolved photoemission spectroscopy of the insulating NaxWO3: Anderson localization, polaron formation, and remnant Fermi surface

The electronic structure of the insulating sodium tungsten bronze, Na0.025WO3, is investigated by high-resolution angle-resolved photoemission spectroscopy. We find that near-E-F states are localized due to the strong disorder arising from random distribution of Na+ ions in the WO3 lattice, which makes the system insulating. The temperature dependence of photoemission spectra provides direct evidence for polaron formation. The remnant Fermi surface of the insulator is found to be the replica of the real Fermi surface in the metallic system

Chaotic destruction of Anderson localization in a nonlinear lattice

We consider a scattering problem for a nonlinear disordered lattice layer governed by the discrete nonlinear Schrodinger equation. The linear state with exponentially small transparency, due to the Anderson localization, is followed for an increasing nonlinearity, until it is destroyed via a bifurcation. The critical nonlinearity is shown to decay with the lattice length as a power law. We demonstrate that in the chaotic regimes beyond the bifurcation the field is delocalized and this leads to a drastic increase of transparency. Copyright (C) EPLA, 2008

Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Anderson localization and momentum-space entanglement

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical study of Anderson localization of terahertz waves in disordered waveguides

We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO3 waveguides with randomly arranged air-filled circular scatterers exhibit an onset of Anderson localization at experimentally accessible length scales. Results for the average transmission as a function of waveguide length and scatterer density demonstrate a clear crossover from diffusive to localized transport regime. In addition, we find that transmission fluctuations grow dramatically when crossing into the localized regime. Our numerical results are in good quantitative agreement with theory over a wide range of experimentally accessible parameters both in the diffusive and localized regime opening the path towards experimental observation of terahertz wave localization.

Anderson localization in synthetic photonic lattices

We experimentally demonstrate Anderson localization for optical pulses in time domain, using a photonic mesh lattice implemented with coupled optical fiber loops. We also discuss interplay of photonic band-gaps and disorder in such lattices. © OSA 2015.

Anderson localization of light in synthetic photonic lattices

We make an comprehensive experimental and theoretical study of an effect of localization of light in photonic lattices realized in time domain with random optical potential. We show that localization occurs in whole range of disorder strength in full agreement with Anderson localization in 1D model. The disorder influence on modes structure is also discussed.

Intrinsic Electron localization in manganites

We mention here an unusual disorder effect in manganites, namely the ubiquitous hopping behavior for electron transport observed in them over a wide range of doping. We argue that the implied Anderson localization is intrinsic to manganites, because of the existence of polarons in them which are spatially localized, generally at random sites (unless there is polaron ordering). We have developed a microscopic two fluid lb model for manganites, where l denotes lattice site localized l polarons, and b denotes band electrons. Using this, and the self-consistent theory of localization, we show that the occupied b states are Anderson localized in a large range of doping due to the scattering of b electrons from l polarons. Numerical simulations which further include the effect of long range Coulomb interactions support this, as well the existence of a novel polaronic Coulomb glass. A consequence is the inevitable hopping behaviour for electron transport observed in doped insulating manganites.

Localization of light in coherently amplifying random media

We derive and analyze the statistics of reflection coefficient of light backscattered coherently from an amplifying and disordered optical medium modeled by a spatially random refractive index having a uniform imaginary part in one dimension. We find enhancement of reflected intensity owing to a synergy between wave confinement by Anderson localization and coherent amplification by the active medium. This is not the same as that due to enhanced optical path lengths expected from photon diffusion in the random active medium. Our study is relevant to the physical realizability of a mirrorless laser by photon confinement due to Anderson localization.

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess `additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Photon localization in amorphous photonic crystal

The photon localization in disordered two-dimensional photonic crystal is studied theoretically. It is found that the mean transmission coefficient in the photonic band decreases exponentially as the disorder degree increases, reflecting the occurrence of Anderson localization. The strength of photon localization can be controlled by tuning the disorder degree in the photonic crystal. We think the variation regular of the transmission coefficient in our disordered system is equivalent to that of the scaling theory of localization.

Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Matter-wave localization in a random potential

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)