Strong Anderson Localization Research Articles

Fredholm Homotopies for Strongly-Disordered 2D Insulators

We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between certain Fredholm operators arising in the context of these systems. We use this technique to prove the bulk-edge correspondence for mobility-gapped 2D topological insulators possessing a (Fermionic) time-reversal symmetry (class AII) and provide an alternative route to a theorem by Elgart-Graf-Schenker (Commun Math Phys 259(1):185–221, 2005) about the bulk-edge correspondence for strongly-disordered integer quantum Hall systems. We furthermore provide a proof of the stability of the $$\mathbb {Z}_2$$ index in the mobility gap regime. These two-dimensional results serve as a model for the study of higher dimensional $$\mathbb {Z}_2$$ indices.

Transport and spectral features in non-Hermitian open systems

We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their distribution is either the usual rectangular one or a binary pair-correlated one possessing, in its Hermitian version, delocalized states, and unusual transport properties. Contrary to the Hermitian case, all states in our non-Hermitian system are localized. In addition, the eigenvalue spectrum, for the binary pair-correlated case, exhibits an unexpected intricate fractallike structure on the complex plane and with increasing non-Hermitian disorder, the eigenvalues tend to coalesce in particular small areas of the complex plane, a feature termed "eigenvalue condensation". Despite the strong Anderson localization of all eigenstates, the system appears to exhibit transport not by diffusion but by a new mechanism through sudden jumps between states located even at distant sites. This seems to be a general feature of open non-Hermitian random systems. The relation of our findings to recent experimental results is also discussed.

Quantum transport in a combined kicked rotor and quantum walk system

We present a theoretical and numerical study of the competition between two opposite interference effects, namely interference-induced ballistic transport on one hand, and strong (Anderson) localization on the other. While the former effect allows for resistance free transport, the latter brings the transport to a complete halt. As a model system, we consider the quantum kicked rotor, where strong localization is observed in the discrete momentum coordinate. In this model, we introduce the ballistic transport in the form of a Hadamard quantum walk in that momentum coordinate. The two transport mechanisms are combined by alternating the corresponding Floquet operators. Extending the corresponding calculation for the kicked rotor, we estimate the classical diffusion coefficient for the combined dynamics. Another argument, based on the introduction of an effective Heisenberg time should then allow to estimate the localization time and the localization length. While this is known to work reasonably well in the kicked rotor case, we find that it fails in our case. While the combined dynamics still shows localization, it takes place at much larger times and shows much larger localization lengths than predicted. Finally, we combine the kicked rotor with other types of quantum walks, namely diffusive and localizing quantum walks. In the diffusive case, the localizing dynamics of the kicked rotor is completely canceled and we get pure diffusion. In the case of the localizing quantum walk, the combined system remains localized, but with a larger localization length.

Room-temperature negative magnetoresistance of helium-ion-irradiated defective graphene in the strong Anderson localization regime

Anderson localization (AL), a major topic in condensed matter physics, has been extensively studied. Since the discovery of graphene, its unique AL in Dirac materials, particularly weak localization (WL), has been studied intensively. Strong localization (SL) has also been investigated in graphene with intentionally introduced defects. The precise control of spacing/strength of defects using conventional methods is challenging; thus, He-ion-irradiation is a promising technology. However, magnetotransport, a sensitive tool to probe AL, has not yet been studied for He-ion-irradiated graphene. Herein, we systematically investigate the magnetotransport of He-ion-irradiated graphene. We observe negative magnetoresistance (MR) due to SL-dominated hopping transport. By systematically tuning the device parameters, negative MR at room temperature is first revealed for graphene field-effect transistor devices. Our study reveals carrier localization via searching in the multidimensional parameter space of Dirac materials, contributing to the development of fundamental AL physics and magnetoelectronic device applications.

Observation of optical nonlinearities in an all-solid transverse Anderson localizing optical fiber

An all-solid transverse Anderson localizing optical fiber (TALOF) was fabricated using a novel combination of the stack-and-draw and molten core methods. Strong Anderson localization is observed in multiple regions of the fiber cross section associated with the higher index strontium aluminosilicate phases randomly arranged within a pure silica matrix. Further, to the best of our knowledge, nonlinear four-wave mixing is reported for the first time in a TALOF.

Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices

We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the on-site potential. We calculate the averaged participation number, the Shannon entropy and the structural entropy as a function of other parameters. We show that, in the presence of an imaginary random potential, all eigenstates are localized in the thermodynamic limit and strong anomalous Anderson localization occurs at the band center. In contrast to the usual localization anomalies where a weaker localization is observed, the localization of the eigenstates near the band center is strongly enhanced in the present non-Hermitian model. This phenomenon is associated with the occurrence of a large number of strongly-localized states with pure imaginary energy eigenvalues.

Anderson Localization in 2D Amorphous MoO3‐x Monolayers for Electrochemical Ammonia Synthesis

AbstractTwo‐dimensional amorphous semiconductor (2DAS) monolayers can be regarded as a new phase of 2D monolayers materials and will serve as a promising field for the various electronic and optoelectronic applications. Here, together with the first‐principles calculations within density functional theory, we experimentally demonstrate that the 2DAS MoO3‐x monolayers can enhance the electrochemical nitrogen reduction reaction (NRR). To be specific, the NH3 yield and faradaic efficiency (FE) reach 35.83 ug h−1 mg−1cat at −0.40 V and 12.01 % at −0.20 V vs. reversible hydrogen electrode (RHE), respectively, and which can be dramatically improved than that of reported defective MoO3 nanosheets. Further theoretical calculations reveal that the high electrochemical performance in NH3 yield is contributed to the strong Anderson localization and electron confinement dimensionally. And such Anderson tail states can resonate effectively with the states of intermediate HNNH, playing the critical role in the rate limiting step of NRR. Integrated experimental findings and theoretical understanding, a new concept of Anderson confinement catalysis is put forward, and could be extended to other 2DAS for potential catalytic reactions.

Parity-Induced Thermalization Gap in Disordered Ring Lattices.

The gaps separating two different states widely exist in various physical systems: from the electrons in periodic lattices to the analogs in photonic, phononic, plasmonic systems, and even quasicrystals. Recently, a thermalization gap, an inaccessible range of photon statistics, was proposed for light in disordered structures [Nat. Phys. 11, 930 (2015)NPAHAX1745-247310.1038/nphys3482], which is intrinsically induced by the disorder-immune chiral symmetry and can be reflected by the photon statistics. The lattice topology was further identified as a decisive role in determining the photon statistics when the chiral symmetry is satisfied. Being very distinct from one-dimensional lattices, the photon statistics in ring lattices are dictated by its parity, i.e., odd or even sited. Here, we for the first time experimentally observe a parity-induced thermalization gap in strongly disordered ring photonic structures. In a limited scale, though the light tends to be localized, we are still able to find clear evidence of the parity-dependent disorder-immune chiral symmetry and the resulting thermalization gap by measuring photon statistics, while strong disorder-induced Anderson localization overwhelms such a phenomenon in larger-scale structures. Our results shed new light on the relation among symmetry, disorder, and localization, and may inspire new resources and artificial devices for information processing and quantum control on a photonic chip.

High Electrical Conductivity of Single Metal-Organic Chains.

Molecular wires are essential components for future nanoscale electronics. However, the preparation of individual long conductive molecules is still a challenge. MMX metal-organic polymers are quasi-1D sequences of single halide atoms (X) bridging subunits with two metal ions (MM) connected by organic ligands. They are excellent electrical conductors as bulk macroscopic crystals and as nanoribbons. However, according to theoretical calculations, the electrical conductance found in the experiments should be even higher. Here, a novel and simple drop-casting procedure to isolate bundles of few to single MMX chains is demonstrated. Furthermore, an exponential dependence of the electrical resistance of one or two MMX chains as a function of their length that does not agree with predictions based on their theoretical band structure is reported. This dependence is attributed to strong Anderson localization originated by structural defects. Theoretical modeling confirms that the current is limited by structural defects, mainly vacancies of iodine atoms, through which the current is constrained to flow. Nevertheless, measurable electrical transport along distances beyond 250 nm surpasses that of all other molecular wires reported so far. This work places in perspective the role of defects in 1D wires and their importance for molecular electronics.

Light localization in cold and dense atomic ensemble

We report on results of theoretical analysis of possibilities of light strong (Anderson) localization in a cold atomic ensemble. We predict appearance of localization in dense atomic systems in strong magnetic field. We prove that in absence of the field the light localization is impossible.

Spectral correlations in finite-size Anderson insulators

We investigate spectral correlations in quasi one-dimensional Anderson insulators with broken time-reversal symmetry. While energy levels are uncorrelated in the thermodynamic limit of infinite wire-length, some correlations remain in finite-size Anderson insulators. Asymptotic behaviors of level-level correlations in these systems are known in the large- and small-frequency limits, corresponding to the regime of classical diffusive dynamics and the deep quantum regime of strong Anderson localization. Employing non-perturbative methods and a mapping to the Coulomb-scattering problem, recently introduced by {\it M.~A.~Skvortsov} and {\it P.~M.~Ostrovsky}, we derive a closed analytical expression for the spectral statistics in the classical-to-quantum region bridging the known asymptotic behaviors. We further discuss how Poisson statistics at large energies develop into Wigner-Dyson statistics as the wire-length decreases.

Controlling transmission eigenchannels in random media by edge reflection

Transmission eigenchannels and associated eigenvalues, that give a full account of wave propagation in random media, have recently emerged as a major theme in theoretical and applied optics. Here we demonstrate, both analytically and numerically, that in quasi one-dimensional ($1$D) diffusive samples, their behavior is governed mostly by the asymmetry in the reflections of the sample edges rather than by the absolute values of the reflection coefficients themselves. We show that there exists a threshold value of the asymmetry parameter, below which high transmission eigenchannels exist, giving rise to a singularity in the distribution of the transmission eigenvalues, $\rho({\cal T}\rightarrow 1)\sim(1-{\cal T})^{-\frac{1}{2}}$. At the threshold, $\rho({\cal T})$ exhibits critical statistics with a distinct singularity $\sim(1-{\cal T})^{-\frac{1}{3}}$; above it the high transmission eigenchannels disappear and $\rho({\cal T})$ vanishes for ${\cal T}$ exceeding a maximal transmission eigenvalue. We show that such statistical behavior of the transmission eigenvalues can be explained in terms of effective cavities (resonators), analogous to those in which the states are trapped in $1$D strong Anderson localization. In particular, the $\rho ( \mathcal{T}) $-transition can be mapped onto the shuffling of the resonator with perfect transmittance from the sample center to the edge with stronger reflection. We also find a similar transition in the distribution of resonant transmittances in $1$D layered samples. These results reveal a physical connection between high transmission eigenchannels in diffusive systems and $1$D strong Anderson localization. They open up a fresh opportunity for practically useful application: controlling the transparency of opaque media by tuning their coupling to the environment.

Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions

We study numerically the frequency modulated kicked nonlinear rotator with effective dimension . We follow the time evolution of the model up to 109 kicks and determine the exponent α of subdiffusive spreading which changes from 0.35 to 0.5 when the dimension changes from d = 1 to 4. All results are obtained in a regime of relatively strong Anderson localization well below the Anderson transition point existing for d = 3, 4. We explain that this variation of the exponent is different from the usual dimensional Anderson models with local nonlinearity where α drops with increasing d. We also argue that the renormalization arguments proposed by Cherroret N et al (arXiv:1401.1038) are not valid for this model and the Anderson model with local nonlinearity in d = 3.

Strong Anderson Localization in Cold Atom Quantum Quenches

Signatures of Anderson localization in the momentum distribution of a cold atom cloud after a quantum quench are studied. We consider a quasi-one-dimensional cloud initially prepared in a well-defined momentum state, and expanding for some time in a disorder speckle potential. Quantum interference generates a peak in the forward scattering amplitude which, unlike the common weak localization backscattering peak, is a signature of strong Anderson localization. We present a nonperturbative, and fully time resolved description of the phenomenon, covering the entire diffusion-to-localization crossover. Our results should be observable by present day experiments.

From Fixed-Energy Localization Analysis to Dynamical Localization: An Elementary Path

We review several techniques initiated by a remarkable work written by Spencer (J Stat Phys 51:1009–1019, 1988) a quarter of century ago, used and further developed in numerous subsequent researches. We also describe a fairly general, elementary derivation of spectral and strong dynamical Anderson localization from the fixed-energy analysis of the Green’s functions on locally finite graphs of polynomial growth, obtained either by the multi-scale analysis or by the fractional-moment method. This derivation goes in the same direction as the Simon–Wolf method (Commun Pure Appl Math 39:75–90, 1986), but provides more quantitative estimates, can be adapted to multi-particle models and, combined with a simplified variant of the Germinet–Klein argument (Commun Math Phys 222:415–448, 2001), results in an elementary proof of strong dynamical localization on arbitrary graphs of polynomial growth.

Invariance principle for Mott variable range hopping and other walks on point processes

We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the A-power of the jump length and depend on the energy marks via a Boltzmann--like factor. The case A=1 corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with arbitrary start point, converges to a Brownian motion whose diffusion matrix is positive definite, and independent of the environment. Finally, we extend the above result to other point processes including diluted lattices.

Order to disorder optical phase transition in random photonic crystals

Transition process of optical modal properties induced by the introduction of randomness into random photonic crystals is investigated by a computational method. We analyze an impulse response of two-dimensional triangular photonic crystals, in which the positions of the air holes are slightly deviated to random directions. It is shown that the appropriate degree of random departure from a perfect crystal state gives rise to multiple scattering of low group velocity band-edge modes and supports their strong Anderson localization. The achieved confinement efficiency of light exceeds the one obtained in the perfect photonic crystal state.

Quantum chaos in weakly disordered graphene

We have studied numerically the statistics for electronic states (level-spacings and participation ratios) from disordered graphene of finite size, described by the aspect ratio $W/L$ and various geometries, including finite or torroidal, chiral or achiral carbon nanotubes. Quantum chaotic Wigner energy level-spacing distribution is found for weak disorder, even infinitesimally small disorder for wide and short samples ($W/L>>1$), while for strong disorder Anderson localization with Poisson level-statistics always sets in. Although pure graphene near the Dirac point corresponds to integrable ballistic statistics chaotic diffusive behavior is more common for realistic samples.

Isoperimetric inequalities and mixing time for a random walk on a random point process

We consider the random walk on a simple point process on ℝd, d≥2, whose jump rates decay exponentially in the α-power of jump length. The case α=1 corresponds to the phonon-induced variable-range hopping in disordered solids in the regime of strong Anderson localization. Under mild assumptions on the point process, we show, for α∈(0, d), that the random walk confined to a cubic box of side L has a.s. Cheeger constant of order at least L−1 and mixing time of order L2. For the Poisson point process, we prove that at α=d, there is a transition from diffusive to subdiffusive behavior of the mixing time.

Mott Law as Lower Bound for a Random Walk in a Random Environment

We consider a random walk on the support of an ergodic stationary simple point process on ℝd, d≥2, which satisfies a mixing condition w.r.t. the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the point process is furnished with independent random bounded energy marks. The transition rates of the random walk decay exponentially in the jump distances and depend on the energies through a factor of the Boltzmann-type. This is an effective model for the phonon-induced hopping of electrons in disordered solids within the regime of strong Anderson localization. We show that the rescaled random walk converges to a Brownian motion whose diffusion coefficient is bounded below by Mott's law for the variable range hopping conductivity at zero frequency. The proof of the lower bound involves estimates for the supercritical regime of an associated site percolation problem.