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.     

非完整超晶格中电子透射问题的计算机模拟

采用转移矩阵方法,模拟研究了垒高无序和阱宽无序非完整超晶格的电子态问题.计算了垒高无序有限超晶格的透射谱和其局域态波函数以及阱宽无序有限超晶格的透射谱和本征值,直观地给出了垒高无序和阱宽无序非完整有限超晶格其电子态行为的物理图像.模拟结果表明:垒高无序和阱宽无序这两种常见非完整一维有限超晶格的子带带隙间均存在强烈的电子运动定域化,且电子波的布喇格散射对周期性势场更敏感;这两种非完整性引起的局域,通过计算电子局域态波函数和有限系统的本征值得到了证实;对本文讨论的这种类型和周期的超晶格,如果控制阱宽在9.1～10.9nm间随机变化,即阱宽的值最大相差1.8岫时,计算机模拟的结果是,阱宽的这种非周期性开始使子带的带隙消失.     

Controlling potential traps for filtering solitons in Bose-Einstein condensates

We present a controlling potential method for solving the three-dimensional Gross-Pitaevskii equation (GPE), which governs the nonlinear dynamics of the Bose-Einstein condensates (BECs) in an inhomogeneous potential trap. Our method allows one to construct ground and excited matter wave states whose longitudinal profiles can have bright solitons. This method provides the confining potential that filters and controls localized BECs. Moreover, it is predicted that, while the BEC longitudinal soliton profile is controlled and kept unchanged, the transverse profile may exhibit oscillatory breathers (the unmatched case) or move as a rigid body in the form of either coherent states (performing the Lissajous figures) or a Schrödinger cat state (matched case).     

Suppression of the "Quasiclassical" proximity gap in correlated-metal--superconductor structures

We study the energy and spatial dependence of the local density of states in a superconductor--correlated-metal--superconductor Josephson junction, where the correlated metal is a non-Fermi liquid (described by the Falicov-Kimball model). Many-body correlations are treated with dynamical mean-field theory, extended to inhomogeneous systems. While quasiclassical theories predict a minigap in the spectrum of a disordered Fermi liquid which is proximity-coupled within a mesoscopic junction, we find that increasing electron correlations destroy any minigap that might be opened in the absence of many-body correlations.     

Delocalization of quasiparticles in quasi-two-dimensional disordered superconductors with s-wave pairing

We investigate localization behavior of quasiparticles in disordered multi-plane superconductors with s-wave pairing. By introducing disorder with random site energies, the spatial fluctuations of Bogoliubov-de Gennes pairing potential are self-consistently determined. The size dependence of rescaled localization length for a long bar is calculated by using the transfer-matrix method. From the finite-size scaling analysis we show that there exists a critical point of the disorder strength W_c which separates the extended and localized quasiparticle states in such quasi-two-dimensional systems. The associated critical behavior is studied and the relationship of the results to the number of planes is discussed.     

On the possibility of electric transport mediated by long living intrinsic localized solectron modes

We consider a polaron Hamiltonian in which not only the lattice and the electron-lattice interactions, but also the electron hopping term is affected by anharmonicity. We find that the one-electron ground states of this system are localized in a wide range of the parameter space. Furthermore, low energy excited states, generated either by additional momenta in the lattice sites or by appropriate initial electron conditions, lead to states constituted by a localized electron density and an associated lattice distortion, which move together through the system, at subsonic or supersonic velocities. Thus we investigate here the localized states above the ground state which correspond to moving electrons. We show that besides the stationary localized electron states (proper polaron states) there exist moving localized solectron states which can be easily excited. The evolution of these localized states suggests their potential as new carriers for fast electric charge transport.     

Ferromagnetically coupled magnetic impurities in a quantum point contact

We investigate the ground and excited states of interacting electrons in a quantum point contact using an exact diagonalization method. We find that strongly localized states in the point contact appear when a new transverse conductance channel opens and longitudinal resonant level is formed due to momentum mismatch. These localized states form magnetic impurity states which are stable in a finite regime of chemical potential and excitation energy. Interestingly, these magnetic impurities have ferromagnetic coupling, which sheds light on the experimentally observed puzzling coexistence of Kondo correlation and spin filtering in a quantum point contact.     

Conducting properties of classical transmission lines with Ornstein-Uhlenbeck type disorder

In this work we study the behavior of bands of extended states and localized states which appear in classical disordered electrical transmission lines, when we use a ternary map and the Ornstein-Uhlenbeck process to generate the long-range correlated disorder, instead of using the Fourier filtering method. By performing finite-size scaling we obtain the asymptotic value of the map parameter b in the thermodynamic limit in a selected range of values of the parameters γ and C of the Ornstein-Uhlenbeck process. With these data we obtain the phase diagrams which separate the localized states from the extended states. These are the fundamental results of this article.     

Current layers and filaments in a semiconductor model with an impact ionization induced instability

Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.     

Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function f(l). Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function f(l). The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function f(l). Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.Received: 7 July 2003, Published online: 19 November 2003PACS: 63.50. + x Vibrational states in disordered systems - 63.22. + m Phonons or vibrational states in low-dimensional structures and nanoscale materials - 62.30. + d Mechanical and elastic waves; vibrations     

Quantum-state transfer through long-range correlated disordered channels

We study quantum-state transfer in XX spin-1/2 chains where both communicating spins are weakly coupled to a channel featuring disordered on-site magnetic fields. Fluctuations are modeled by long-range correlated sequences with self-similar profile obeying a power-law spectrum. We show that the channel is able to perform almost perfect quantum-state transmissions even in the presence of significant amounts of disorder provided the degree of those correlations is strong enough, with the cost of having long transfer times and unavoidable timing errors. Still, we show that the lack of mirror symmetry in the channel does not affect much the likelihood of having high-quality outcomes. Our results suggest that coexistence between localized and delocalized states can diminish effects of static perturbations in solid-state devices for quantum communication.     

具有p波超流的一维非公度晶格中迁移率边研究

研究了具有p波超流的一维非公度晶格中迁移率边的性质. 发现适当的p波超流可以增加体系中的迁移率边的数目, 并且通过多分形分析确定了迁移率边所在的位置.     

Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.     

Magnetic and charge orders in zigzag nanographene ribbons

We theoretically study the electronic states in graphene ribbons which are strongly affected by the edge states, the peculiar non-bonding molecular orbitals localized along the zigzag edges of the ribbons. New kinds of edge localized electronic states with spin and charge polarizations are found in the mean field solutions of the extended Hubbard model with onsite and nearest-neighbor Coulomb repulsions. These novel states appear due to the interplay between the edge states and the Fermi instabilities. We also examine the competition between the charge polarized state and the spin polarized state to draw a phase diagram depending on Coulomb parameters. The results obtained by the mean field calculations with the extended Hubbard model modified to include Coulomb integrals provide useful insights to understand and functionalize the nanoscale materials.     

Bosonic and fermionic dipoles on a ring

We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gaslike state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.     

Electrostatic Surface Trap for Cold Polar Molecules with a Charged Circular Wire

We propose a novel scheme to trap cold polar molecules on the surface of an insulating substrate （i.e. a chip） by using an inhomogeneous electrostatic field, which is generated by the combination of a circular charged wire （a ring electrode） and a grounded metal plate. The spatial distributions of the electrostatic field from the above charged wire layout and its Stark potentials for CO molecules are calculated. Our study shows that when the voltage applied to the wire is U = 15 kV, a ring radius is R = 5 mm, the thickness of the insulating substrate is b = 5 mm, and a wire radius is r = 1mm, the maximum efficient trapping potential （i.e., as equivalent temperature） for CO molecules is greater than 141.7mK, which is high enough to trap cold polar molecules with a temperature of 50 mK in the low-field-seeking states.     

Multifractal analysis of electronic states on random Voronoi-Delaunay lattices

We consider the transport of non-interacting electrons on two- and three-dimensional random Voronoi-Delaunay lattices. It was recently shown that these topologically disordered lattices feature strong disorder anticorrelations between the coordination numbers that qualitatively change the properties of continuous and first-order phase transitions. To determine whether or not these unusual features also influence Anderson localization, we study the electronic wave functions by multifractal analysis and finite-size scaling. We observe only localized states for all energies in the two-dimensional system. In three dimensions, we find two Anderson transitions between localized and extended states very close to the band edges. The critical exponent of the localization length is about 1.6. All these results agree with the usual orthogonal universality class. Additional generic energetic randomness introduced via random potentials does not lead to qualitative changes but allows us to obtain a phase diagram by varying the strength of these potentials.     

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.     

Energy levels and their correlations in quasicrystals

Quasicrystals can be considered, from the point of view of their electronic properties, as being intermediate between metals and insulators. For example, experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have conductivities far smaller than those of the metals that these alloys are composed from. Wavefunctions in a quasicrystal are typically intermediate in character between the extended states of a crystal and the exponentially localized states in the insulating phase, and this is also reflected in the energy spectrum and the density of states. In the theoretical studies we consider in this review, the quasicrystals are described by a pure hopping tight binding model on simple tilings. We focus on spectral properties, which we compare with those of other complex systems, in particular, the Anderson model of a disordered metal. We discuss ‘strong‘ and ‘weak’ quasicrystals, which are described by different universal laws. We find similarities and universal behaviour, but also significant differences between quasiperiodic models and models with disorder. Like weakly disordered metals, the quasicrystal can be described by the universal level statistics that can be derived from random matrix theory. These level statistics are only one aspect of the energy spectrum, whose very large fluctuations can also be described by a level spacing distribution that is log-normal. An analysis of spectral rigidity shows that electrons diffuse with a bigger exponent (super-diffusion) than in a disordered metal. Adding disorder attenuates the singular properties of the perfect quasicrystal, and leads to improved transport. Spectral properties are also used in computing conductances of such systems, and to attempt to resolve the experimental enigmas such as whether quasicrystals are intrinsically conductors, and if so, how conductances depend on the structure.     

Instanton in disordered Peierls systems

We study disordered Peierls systems described by the fluctuating gap model. We show that the typical electron states with energies lying deep inside the pseudogap are localized near large disorder fluctuations (instantons), which have the form of a soliton-antisoliton pair. Using the “saddle-point” method we obtain the average density of states and the average optical absorption coefficient at small energy.