Strong Localization Regime Research Articles

Electronic states of a disordered two-dimensional quasiperiodic tiling: From critical states to Anderson localization

We consider critical eigenstates in a two dimensional quasicrystal and their evolution as a function of disorder. By exact diagonalization of finite size systems we show that the evolution of properties of a typical wave-function is non-monotonic. That is, disorder leads to states delocalizing, until a certain crossover disorder strength is attained, after which they start to localize. Although this non-monotonic behavior is only present in finite-size systems and vanishes in the thermodynamic limit, the crossover disorder strength decreases logarithmically slowly with system size, and is quite large even for very large approximants. The non-monotonic evolution of spatial properties of eigenstates can be observed in the anomalous dimensions of the wave-function amplitudes, in their multifractal spectra, and in their dynamical properties. We compute the two-point correlation functions of wave-function amplitudes and show that these follow power laws in distance and energy, consistent with the idea that wave-functions retain their multifractal structure on a scale which depends on disorder strength. Dynamical properties are studied as a function of disorder. We find that the diffusion exponents do not reflect the non-monotonic wave-function evolution. Instead, they are essentially independent of disorder until disorder increases beyond the crossover value, after which they decrease rapidly, until the strong localization regime is reached. The differences between our results and earlier studies on geometrically disordered ``phason-flip'' models lead us to propose that the two models are in different universality classes. We conclude by discussing some implications of our results for transport and a proposal for a Mott hopping mechanism between power law localized wave-functions, in moderately disordered quasicrystals.

Anderson localization at the boundary of a two-dimensional topological superconductor

A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topologically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a situation when only a given number of channels ($m$) are topologically protected, while others are not and therefore are subject to Anderson localization in the presence of disorder. We study transport properties of such quasi-one-dimensional quantum wires with broken time-reversal and spin-rotational symmetries (class D) and calculate the average conductance, its variance and the third cumulant, as well as the average shot noise power. The results are obtained for arbitrary wire length, tracing a crossover from the diffusive Drude regime to the regime of strong localization where only $m$ protected channels conduct. Our approach is based on the nonperturbative treatment of the nonlinear supersymmetric sigma model of symmetry class D with two replicas developed in our recent publication [D. S. Antonenko et al., Phys. Rev. B 102, 195152 (2020)]. The presence of topologically protected modes results in the appearance of a topological Wess-Zumino-Witten term in the sigma-model action, which leads to an additional subsidiary series of eigenstates of the transfer-matrix Hamiltonian. The developed formalism can be applied to study the interplay of Anderson localization and topological protection in quantum wires of other symmetry classes.

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.

Localization effects in graphene nanoribbons with quasiperiodic hopping modulation

Graphene nanoribbons present remarkable electronic transport properties which can be tailored to specific applications. We consider a quasiperiodic modulation in the electronic hopping of metallic armchair and zigzag graphene nanoribbons, originating a Fibonacci superlattice with two possible hopping parameters. The electronic conductance for various Fibonacci generations is calculated via the recursive Green's function method. We observe that a quasiperiodic hopping modulation opens a conductance gap at the Fermi level of armchair nanoribbons, leading to a strong electronic localization regime. The localization length initially increases with Fibonacci generation and saturates for high order generations. Considering an energy slightly above the Fermi level, we obtain similar results for the armchair nanoribbon, while the zigzag nanoribbon eventually enters the localization regime for high order Fibonacci generations. Our results demonstrate that a quasiperiodic hopping modulation is a viable way to control the electronic transport in graphene nanoribbons, widening its range of possible application in nanoelectronic devices.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder.

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reinekermodel to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Existence of odd, even, and multi-pulse discrete breathers in infinite Fermi-Pasta-Ulam lattices

Discrete breathers are spatially localized periodic solutions in nonlinear lattices. We prove the existence of odd symmetric, even symmetric, and multi-pulse discrete breathers in strong localization regime in one-dimensional infinite Fermi-Pasta-Ulam lattices with even interaction potentials. The multi-pulse discrete breather consists of an arbitrary number of the odd-like and/or even-like primary discrete breathers located separately on the lattice. The proof applies to both cases of pure attractive and repulsive-attractive interaction potentials.

Stable, multi-mode lasing in the strong localization regime from InP random nanowire arrays at low temperature

Disorder is generally considered an undesired element in lasing action. However, in random lasers whose feedback mechanism is based on random scattering events, disorder plays a very important and critical role. Even though some unique properties in random lasers such as large-angle emission, lasing from different surfaces, large-area manufacturability, and wavelength tunability can be advantageous in certain applications, the applicability of random lasers has been limited due to the chaotic fluctuations and instability of the lasing modes because of weak confinement. To solve this, mode localization could reduce the spatial overlap between lasing modes, thus preventing mode competition and improving stability, leading to laser sources with high quality factors and very low thresholds. Here, by using a random array of III-V nanowires, high-quality-factor localized modes are demonstrated. We present the experimental evidence of strong light localization in multi-mode random nanowire lasers which are temporally stable at low temperatures.

Transmission of waves through a pinned elastic medium

We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian correlations, acting on propagating waves. We find signatures of the correlations in the wave transmission in a wide frequency range, which covers both the weak and strong localization regimes. Our theory elucidates the dynamics of collectively pinned phases occurring in any natural or synthetic elastic medium. The latter one is exemplified by a one-dimensional array of Josephson junctions, for which we specify our results. The obtained results provide benchmarks for the array-enabled quantum simulations addressing the dynamics in broader and as yet unexplored domains of individual pinning and quantum Bose glass.

Piezo-electric fields and state-filling photo-luminescence in natural InP/GaInP2 Wigner molecule structures

We used the measurements of the photo-luminescence spectra vs photon pumping and Coulomb blockade charge tuning together with Kelvin probe microscopy to study piezo-electric fields in self-organized InP/GaInP2 quantum dots (QDs) having a strong Wigner localization regime. These exciton/electron state-filling measurements together with the surface potential imaging and the band structure calculations demonstrate a piezo-electric doping and type-I optical transitions induced in these dots by an atomic ordering (AO) of GaInP2. Our results clarify a critical role of AO in the formation of natural Wigner and anyon molecules and represent an important step for realization of the topological quantum gates using these QDs.

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.

Continuous transition from weakly localized regime to strong localization regime in Nd0.7La0.3NiO3 films

We report an investigation of metal-insulator transition (MIT) using conductivity and magnetoconductance (MC) measurements down to 0.3 K in Nd0.7La0.3NiO3 films grown on crystalline substrates of LaAlO3 (LAO), SrTiO3 (STO), and NdGaO3 (NGO) by pulsed laser deposition. The film grown on LAO experiences a compressive strain and shows metallic behavior with the onset of a weak resistivity upturn below 2 K which is linked to the onset of weak localization contribution. Films grown on STO and NGO show a cross-over from a positive temperature coefficient (PTC) resistance regime to negative temperature coefficient (NTC) resistance regime at definite temperatures. We establish that a cross-over from PTC to NTC on cooling does not necessarily constitute a MIT because the extrapolated conductivity at zero temperature though small (<10 S cm−1) is finite, signaling the existence of a bad metallic state and absence of an activated transport. The value of for films grown on NGO is reduced by a factor of 40 compared to that for films grown on STO. We show that a combination of certain physical factors makes substituted nickelate (that are known to exhibit first-order Mott type transition), undergo a continuous transition as seen in systems undergoing disorder/composition driven Anderson transition. The MC measurement also supports the above observation and shows that at low temperatures, there exists a positive MC that arises from the quantum interference which co-exists with a spin-related negative MC that becomes progressively stronger as the electrons approach a strongly localized state in the film grown on NGO.

Strong Spatial and Spectral Localization of Surface Plasmons in Individual Randomly Disordered Gold Nanosponges.

Porous nanosponges, percolated with a three-dimensional network of 10 nm sized ligaments, recently emerged as promising substrates for plasmon-enhanced spectroscopy and (photo)catalysis. Experimental and theoretical work suggests surface plasmon localization in some hot-spot modes as the physical origin of their unusual optical properties, but so far the existence of such hot-spots has not been proven. Here we use scattering-type scanning near-field nanospectroscopy on individual gold nanosponges to reveal spatially and spectrally confined modes at 10 nm scale by recording local near-field scattering spectra. High quality factors of individual hot-spots of more than 40 are demonstrated, predicting high Purcell factors up to 106. The observed field localization and enhancement make such nanosponges an appealing platform for a variety of applications ranging from nonlinear optics to strong-coupling physics.

Macromolecules with amphiphilic monomer units at interface of two immiscible liquids.

The adsorption of macromolecules with amphiphilic monomer units at the liquid-liquid interface was studied. The amphiphilic structure of monomer units with groups selectively interacting with α and β liquids was described by the A-graft-B dumbbell model. The calculations were performed for the symmetrical interaction of A and B groups with liquids, different selectivity parameters ξ and degree of polymerization N. The simulations indicate a three-step adsorption scenario, including non-adsorbed, weak and strong localization states. It was shown that the adsorption of (A-graft-B)N macromolecules obeys scaling laws developed to describe the adsorption of the alternating (AB)N copolymer at the liquid-liquid interface with critical selectivity parameter ξc of transition into the weak localization state depending on the degree of polymerization as N-1/5; critical selectivity parameter ξ∞ of transition to the strong localization regime non-depending on the degree of polymerization; and relative change of perpendicular Rz radius of gyration varying as a power function of ξN1/5: Rz(ξ)/Rz(0) ∼ (ξN1/5)ρ and ρ = -2ν/(1 - v). Meanwhile, (A-graft-B)N macromolecules have much lower ξc and ξ∞ values and thus are more prospective for practical applications.

Electronic transport in metallic carbon nanotubes with mixed defects within the strong localization regime

We study the electron transport in metallic carbon nanotubes (CNTs) with realistic defects of different types. We focus on large CNTs with many defects in the mesoscopic range. In a recent paper we demonstrated that the electronic transport in those defective CNTs is in the regime of strong localization. We verify by quantum transport simulations that the localization length of CNTs with defects of mixed types can be related to the localization lengths of CNTs with identical defects by taking the weighted harmonic average. Secondly, we show how to use this result to estimate the conductance of arbitrary defective CNTs, avoiding time consuming transport calculations.

Nonequilibrium transport through a disordered molecular nanowire

We investigate the non-equilibrium transport properties of a disordered molecular nanowire. The nanowire is regarded as a quasi-one-dimensional organic crystal composed of self-assembled molecules. One orbital and a single random energy are assigned to each molecule while the intermolecular coupling does not fluctuate. Consequently, electronic states are expected to be spatially localized. We consider the regime of strong localization, namely, the localization length is smaller than the length of the molecular wire. Electron-vibron interaction, taking place in each single molecule, is also taken into account. We investigate the interplay between disorder and electron-vibron interaction in response to either an applied electric bias or a temperature gradient. To this end, we calculate the electric and heat currents when the nanowire is connected to leads, using the Keldysh non-equilibrium Green's function formalism. At intermediate temperature, scattering by disorder dominates both charge and heat transport. We find that the electron-vibron interaction enhances the effect of the disorder on the transport properties due to the exponential suppression of tunneling.

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.

Can 3D light localization be reached in ‘white paint’?

When waves scatter multiple times in 3D random media, a disorder driven phase transition from diffusion to localization may occur (Anderson 1958 Phys. Rev. 109 1492–505; Abrahams et al 1979 Phys. Rev. Lett. 42 673–6). In ‘The question of classical localization: a theory of white paint?’ Anderson suggested the possibility to observe light localization in TiO2 samples (Anderson 1985 Phil. Mag. B 52 505–9). We recently claimed the observation of localization effects measuring photon time of flight (ToF) distributions (Störzer et al 2006 Phys. Rev. Lett. 96 063904) and evaluating transmission profiles (TPs) (Sperling et al 2013 Nat. Photonics 7 48–52) in such TiO2 samples. Here we present a careful study of the long time tail of ToF distributions and the long time behavior of the TP width for very thin samples and different turbidities that questions the localization interpretation. We further show new data that allow an alternative consistent explanation of these previous data by a fluorescence process. An adapted diffusion model including an appropriate exponential fluorescence decay accounts for the shape of the ToF distributions and the TP width. These observations question whether the strong localization regime can be reached with visible light scattering in polydisperse TiO2 samples, since the disorder parameter can hardly be increased any further in such a ‘white paint’ material.

Localization of Charge Carriers in Monolayer Graphene Gradually Disordered by Ion Irradiation

Gradual localization of charge carriers was studied in a series of micro-size samples of monolayer graphene fabricated on the common large scale film and irradiated by different doses of C$^+$ ions with energy 35 keV. Measurements of the temperature dependence of conductivity and magnetoresistance in fields up to 4 T showed that at low disorder, the samples are in the regime of weak localization and antilocalization. Further increase of disorder leads to strong localization regime, when conductivity is described by the variable-range-hopping (VRH) mechanism. A crossover from the Mott regime to the Efros-Shklovskii regime of VRH is observed with decreasing temperature. Theoretical analysis of conductivity in both regimes showed a remarkably good agreement with experimental data.

Electronic transport in graphene with aggregated hydrogen adatoms.

Hydrogen adatoms and other species covalently bound to graphene act as resonant scattering centers affecting the electronic transport properties and inducing Anderson localization. We show that attractive interactions between adatoms on graphene and their diffusion mobility strongly modify the spatial distribution, thus fully eliminating isolated adatoms and increasing the population of larger size adatom aggregates. Such spatial correlation is found to strongly influence the electronic transport properties of disordered graphene. Our scaling analysis shows that such aggregation of adatoms increases conductance by up to several orders of magnitude and results in significant extension of the Anderson localization length in the strong localization regime. We introduce a simple definition of the effective adatom concentration x*, which describes the transport properties of both random and correlated distributions of hydrogen adatoms on graphene across a broad range of concentrations.

Strong localization in defective carbon nanotubes: a recursive Greenʼs function study

We study the transport properties of defective single-walled armchair carbon nanotubes (CNTs) on a mesoscopic length scale. Monovacancies and divancancies are positioned randomly along the CNT. The calculations are based on a fast, linearly scaling recursive Greenʼs function formalism that allows us to treat large systems quantum-mechanically. The electronic structure of the CNT is described by a density-functional-based tight-binding model. We determine the influence of the defects on the transmission function for a given defect density by statistical analysis. We show that the system is in the regime of strong localization (i.e. Anderson localization). In the limit of large disorder the conductance scales exponentially with the number of defects. This allows us to extract the localization length. Furthermore, we study in a systematic and comprehensive way, how the conductance, the conductance distribution, and the localization length depend on defect probability, CNT diameter, and temperature.