Periodic oscillations in transmission decay of anderson localized one-dimensional dielectric systems

It is well recognized that the transmittance of Anderson localized systems decays exponentially on average with sample size, showing large fluctuations brought up by extremely rare occurrences of necklaces of resonantly coupled states, possessing almost unity transmission. We show here that in a one-dimensional (1D) random photonic system with resonant layers these fluctuations appear to be very regular and have a period defined by the localization length xi of the system. We stress that necklace states are the origin of these well-defined oscillations. We predict that in such a random system efficient transmission channels form regularly each time the increasing sample length fits so-called optimal-order necklaces and demonstrate the phenomenon through numerical experiments. Our results provide new insight into the physics of Anderson localization in random systems with resonant units.     

Dynamical study of the necklace states

Based on finite-difference-time domain methods (FDTD), we have numerically directly investigated the dynamical effects of necklace states on the transmission for one-dimensional (1D) random systems with pulsed incidence in time domain. The necklace state propagation property, which is faster than the common localized modes, is demonstrated directly. From the instantaneous decay coefficient κ(t) and the instantaneous transmittance spectrum T(τ,ω), we have constructed a dynamical picture for the random systems with necklace states. In the picture, we have explained the high plateau on the κ(t) curves by the properties of necklace states, and then defined the time range of high plateau as the “effective time range” of necklace states effects. Further more, we have confirmed the dynamical picture by the ensemble study of random configurations. For the different length, we show that the effects of necklace states will be stronger if the system is longer. Besides these, we also introduce the instantaneous decay coefficient and the instantaneous transmittance spectrum to study the dynamical effects of necklace states. This theoretical study of necklace states can be helpful not only for the deeper physical understanding of necklace states, but also for the experimental observation of necklace states.     

Localized mode hybridization by fine tuning of two-dimensional random media

We study numerically the interaction of spatially localized modes in strongly scattering two-dimensional (2D) media. We move eigenvalues in the complex plane by changing gradually the index of a single scatterer. When spatial and spectral overlap is sufficient, localized states couple, and avoided level crossing is observed. We show that local manipulation of the disordered structure can couple several localized states to form an extended chain of hybridized modes crossing the entire sample, thus changing the nature of certain modes from localized to extended in a nominally localized disordered system. We suggest such a chain in 2D random systems is the analog of one-dimensional necklace states, the occasional open channels predicted by Pendry [Physics 1, 20 (2008).] through which the light can sneak through an opaque medium.     

Non-Hermitian topological Anderson insulators

Non-Hermitian systems can exhibit exotic topological and localization properties.Here we elucidate the non-Hermitian effects on disordered topological systems using a nonreciprocal disordered Su-Schrieffer-Heeger model.We show that the non-Hermiticity can enhance the topological phase against disorders by increasing bulk gaps.Moreover,we uncover a topological phase which emerges under both moderate non-Hermiticity and disorders,and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes.Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators.We reveal that the system has unique non-monotonous localization behavior and the topological transition is accompanied by an Anderson transition.These properties are general in other non-Hermitian models.     

Higher-order solitons in amplitude-disordered waveguide arrays

We investigate the existence and stability of different families of spatial solitons in optical waveguide arrays whose amplitudes obey a disordered distribution. The competition between focusing nonlinearity and linearly disordered refractive index modulation results in the formation of spatial localized nonlinear states. Solitons originating from Anderson modes with few nodes are robust during propagation. While multi-peaked solitons with in-phase neighboring components are completely unstable, multipole-mode solitons whose neighboring components are out-of-phase can propagate stably in wide parameter regions provided that their power exceeds a critical value. Our findings, thus, provide the first example of stable higher-order nonlinear states in disordered systems.     

Coupling and level repulsion in the localized regime: from isolated to quasiextended modes

We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply peaked quasiextended modes. Level repulsion is observed experimentally and explained within a model of coupled resonators. The spectral and spatial evolution of the coupled modes is described in terms of the coupling coefficient and Q factors of resonators.     

Quantum coherent effects in Anderson insulators

During the last two decades quantum interference effects have been extensively studied in the transport properties of diffusive systems such as metals and semiconductors. When the spatial disorder in these systems exceeds a critical value the electronic wavefunctions are localized and their ground state is insulating (the Anderson transition). At finite temperatures charge transport in this phase involves phonon-assisted tunnelling between localized states. This mode of transport is purely quantum mechanical and has no classical analogue. Anderson insulators are therefore the paradigmatic system for studying interference phenomena of electron waves in random media. In this paper we discuss the question of quantum coherence in Anderson insulators and review some of the experimental manifestations of interference phenomena in their transport properties.     

Emergence of Anderson localization in plasmonic waveguides

The propagation of surface plasmon polaritons in dielectric loaded waveguides with randomly placed scatterers is studied using both numerical simulations and a simplified transfer matrix framework. Despite the importance of losses in this system, we find fingerprints of the localized behavior of one-dimensional disordered systems. Furthermore, losses amplify the impact of the necklace states on the transport properties for systems not much larger than the localization length. The system presented here also offers the possibility to use localization effects for engineering purposes by means of deliberately introduced disorder.     

一维无公度系统Aubry模型的Anderson转变

数值计算结果表明,一维无公度系统Aubry模型存在扩展态、中间态和局域态。由扩展态向局域态的转变,要经过处于势强度v=2t附近的一段过渡区。这个新的结果不同于用对偶性理论证明给出的结论,即当势强度V<2t时都是扩展态,而当V>2t时都是局域态,在V=2t存在Anderson转变。 关键词：     

Localized and extended states in a disordered trap

We study Anderson localization in a disordered potential combined with an inhomogeneous trap. We show that the spectrum displays both localized and extended states, which coexist at intermediate energies. In the region of coexistence, we find that the extended states result from confinement by the trap and are weakly affected by the disorder. Conversely, the localized states correspond to eigenstates of the disordered potential, which are only affected by the trap via an inhomogeneous energy shift. These results are relevant to disordered quantum gases and we propose a realistic scheme to observe the coexistence of localized and extended states in these systems.     

Enhanced infrared transmission through subwavelength coaxial metallic arrays

We report the observation of enhanced near-infrared transmission through arrays of subwavelength coaxial metallic structures compared with that through comparable diameter hole arrays as a result of localized electromagnetic modes supported by the complex coaxial unit cell. Polarization and angle-dependent transmission measurements clearly demonstrate the coupling between this localized mode and delocalized surface plasmon modes. A generalized, multiple discrete states Fano line shape provides a good fit to the experimental results.     

Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △ U² are less than, equal to, and greater than uncertainties △ V² for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities, for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.     

Specific heat of 1T-Ta0.93Ti0.07S2 in the Anderson localized states

The specific heat of 1T-Ta_0.93Ti_0.07S₂ in the Anderson localized states has been measured from 0.2 to 5.0 K in magnetic fields up to 60 kOe. Below 3.5 K, a Schottky type excess specific heat was observed, depending on the magnetic field. This excess specific heat is explained on the basis of both the Coulomb interactions between different Anderson localized states as well as in the same state.     

Anderson localization in a two-dimensional random gap model

We study the properties of the spinor wavefunction in a strongly disordered environment on a two-dimensional lattice. By employing a transfer-matrix calculation we find that there is a transition from delocalized to localized states at a critical value of the disorder strength. We prove that there exists an Anderson localized phase with exponentially decaying correlations for sufficiently strong scattering. Our results indicate that suppressed backscattering is not sufficient to prevent Anderson localization of surface states in topological insulators.     

Bethe ansatz results for the 4f-electron spectra of a degenerate Anderson model

We show that the density of states for localized 4f electrons coupled to a conduction band calculated in the framework of Bethe ansatz solution for the degenerate Anderson model qualitatively disagree with the well-known results obtained for the same model but using a variational approach. The scales of parameters used in our Bethe ansatz calculations to fit the experiments disagree with the commonly accepted values from other studies. This implies narrower conduction bands hybridized with 4f orbitals or questions the applicability of the Bethe ansatz for a degenerate Anderson model for the high-energy characteristics of some rare-earth systems.     

Critical transport and anomalously localized states at the Anderson transition

The effect of anomalously localized states (ALS) for electron transport at the critical point of the Anderson transition is numerically investigated for two-dimensional symplectic systems. Defining ALS quantitatively, it is found that a probability of finding ALS at criticality increases with the system size, and saturates in an infinite system. This remarkable feature influences transport properties at criticality.     

Constructive proof of localization in the Anderson tight binding model

We prove that, for large disorder or near the band tails, the spectrum of the Anderson tight binding Hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues. The corresponding eigenfunctions are exponentially well localized. These results hold in arbitrary dimension and with probability one. In one dimension, we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder. Our techniques extend to other physical systems which exhibit localization phenomena, such as infinite systems of coupled harmonic oscillators, or random Schrödinger operators in the continuum.Work supported in part by National Science Foundations grant MCS-8108814 (A03).Work supported in part by National Science Foundation grant DMR 81-00417.     

Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder

We investigate theoretically the nature of the states and the localization properties in a one-dimensional Anderson model with long-range correlated disorder and weak nonlinearity. Using the stationary discrete nonlinear Schrödinger equation, we calculate the disorder-averaged logarithm of the transmittance and the localization length in the fixed input case in a numerically exact manner. Unlike in many previous studies, we strictly fix the intensity of the incident wave and calculate the localization length as a function of other parameters. We also calculate the wave functions in a given disorder configuration. In the linear case, flat phased localized states appear near the bottom of the band and staggered localized states appear near the top of the band, while a continuum of extended states appears near the band center. We find that the focusing Kerr-type nonlinearity enhances the Anderson localization of flat phased states and suppresses that of staggered states. We observe that there exists a perfect symmetry relationship for the localization length between focusing and defocusing nonlinearities. Above a critical value of the strength of nonlinearity, delocalization due to the long-range correlations of disorder is destroyed and all states become localized.     

Dynamical susceptibility of intermediate valence systems

The transverse susceptibility if magnetic systems described by the Anderson model is calculated evaluating the self energy for the two particle Green function. The results are applied to semiconductors and metals. In the first case a shift in the resonance frequency is obtained as well as a continuum of excitations corresponding to the promotion of electrons from the localized state to the conduction band states. In the metallic case a Korringa relation for the relaxation time in the magnetic limit is obtained. The real and imaginary parts of the self energy are given as functions of the distance from the localized level to the Fermi level.     

Anderson Localization Enhanced Spin Selective Transport of Electrons in DNA

Recent experiments revealed the unusual strong spin effects with high spin selective transmission of electrons in double-stranded DNA. We propose a new mechanism that the strong spin effects could be understood in terms of the combination of the ehiral structure, spin-orbit coupling, and especially spin-dependent Anderson localization. The presence of chiral structure and spin-orbit coupling of DNA induce weak Fermi energy splitting between two spin polarization states. The intrinsic Anderson localization in generic DNA molecules may result in remarkable enhancement of the spin selective transport. In particular, these two spin states with energy splitting have different localization lengths. Spin up/down channel may have shorter/longer localization length so that relatively less/more spin up/down electrons may tunnel through the system. In addition, the strong length dependence of spin selectivity observed in experiments can be naturally understood. Anderson localization enhanced spin selectivity effect may provide a deeper understanding of spin-selective processes in molecular spintronics and biological systems.