Delocalization Transition Research Articles

Inducing Fe 3d Electron Delocalization and Spin-State Transition of FeN4 Species Boosts Oxygen Reduction Reaction for Wearable Zinc–Air Battery

HighlightsThe strong interaction between Ti3C2Sx and FeN4 species induces the central metal Fe(II) in FeN4 species with intermediate spin state transferred to high spin state, in which the latter is favorable to initiate the reduction of oxygen.This strong interaction induces a remarkable Fe 3d electron delocalization with d band center upshift, boosting oxygen-containing groups adsorption on FeN4 species and oxygen reduction reaction kinetics.The resulting FeN4–Ti3C2Sx with FeN4 moieties in high spin state exhibits high half-wave potential of 0.89 V vs. RHE and high limiting current density of 6.5 mA cm−2, enabling wearable zinc–air battery showing a good discharge performance with a maximum power density of 133.6 mW cm−2.

Dynamical many-body delocalization transition of a Tonks gas in a quasi-periodic driving potential

The quantum kicked rotor is well-known for displaying dynamical (Anderson) localization. It has recently been shown that a periodically kicked Tonks gas will always localize and converge to a finite energy steady-state. This steady-state has been described as being effectively thermal with an effective temperature that depends on the parameters of the kick. Here we study a generalization to a quasi-periodic driving with three frequencies which, without interactions, has a metal-insulator Anderson transition. We show that a quasi-periodically kicked Tonks gas goes through a dynamical many-body delocalization transition when the kick strength is increased. The localized phase is still described by a low effective temperature, while the delocalized phase corresponds to an infinite-temperature phase, with the temperature increasing linearly in time. At the critical point, the momentum distribution of the Tonks gas displays different scaling at small and large momenta (contrary to the non-interacting case), signaling a breakdown of the one-parameter scaling theory of localization.

Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra.

We study a classical model of thermally fluctuating polymers confined to two dimensions, experiencing a grooved periodic potential, and subject to pulling forces both along and transverse to the grooves. The equilibrium polymer conformations are described by a mapping to a quantum system with a non-Hermitian Hamiltonian and with fermionic statistics generated by noncrossing interactions among polymers. Using molecular dynamics simulations and analytical calculations, we identify a localized and a delocalized phase of the polymer conformations, separated by a delocalization transition which corresponds (in the quantum description) to the breakdown of a band insulator when driven by an imaginary vector potential. We calculate the average tilt of the many-body system, at arbitrary shear values and filling density of polymer chains, in terms of the complex-valued non-Hermitian band structure. We find the critical shear value, the localization length, and the critical exponent by which the shear modulus diverges in terms of the branch points (exceptional points) in the band structure at which the bandgap closes. We also investigate the combined effects of non-Hermitian delocalization and localization due to both periodicity and disorder, uncovering preliminary evidence that while disorder favors localization at high values, it encourages delocalization at lower values.

Theoretical insights into the two-dimensional gallium oxide monolayer for adsorption and gas sensing of C4F7N decomposition products

A new descriptor w is provided to explain the different gas sensitivity. Displacement of local atoms and an electron localization–delocalization transition caused by biaxial strain can regulate the gas sensing behavior.

Delocalization and re-entrant localization of flat-band states in non-Hermitian disordered lattice models with flat bands

Abstract We present a numerical study of Anderson localization in disordered non-Hermitian lattice models with flat bands. Specifically, we consider 1D stub and 2D kagome lattices that have a random scalar potential and a uniform imaginary vector potential and calculate the spectra of the complex energy, the participation ratio, and the winding number as a function of the strength of the imaginary vector potential, h. The flat-band states are found to show a double transition from localized to delocalized and back to localized states with h, in contrast to the dispersive-band states going through a single delocalization transition. When h is sufficiently small, all flat-band states are localized. As h increases above a certain critical value h1, some pairs of flat-band states become delocalized. The participation ratio associated with them increases substantially and their winding numbers become nonzero. As h increases further, more and more flat-band states get delocalized until the fraction of the delocalized states reaches a maximum. For larger h values, a re-entrant localization takes place and, at another critical value h2, all flat-band states return to compact localized states with very small participation ratios and zero winding numbers. This re-entrant localization transition, which is due to the interplay among disorder, non-hermiticity, and the flat band, is a phenomenon occurring in many models having an imaginary vector potential and a flat band simultaneously. We explore the spatial characteristics of the flat-band states by calculating the local density distribution.

Excited-eigenstate entanglement properties of XX spin chains with random long-range interactions

Quantum information theoretical measures are useful tools for characterizing quantum dynamical phases. However, employing them to study excited states of random spin systems is a challenging problem. Here, we report results for the entanglement entropy (EE) scaling of excited eigenstates of random XX antiferromagnetic spin chains with long-range (LR) interactions decaying as a power law with distance with exponent $\alpha$. To this end, we extend the real-space renormalization group technique for excited states (RSRG-X) to solve this problem with LR interaction. For comparison, we perform numerical exact diagonalization (ED) calculations. From the distribution of energy level spacings, as obtained by ED for up to $N\sim 18$ spins, we find indications of a delocalization transition at $\alpha_c \approx 1$ in the middle of the energy spectrum. With RSRG-X and ED, we show that for $\alpha>\alpha^*$ the entanglement entropy (EE) of excited eigenstates retains a logarithmic divergence similar to the one observed for the ground state of the same model, while for $\alpha<\alpha^*$ EE displays an algebraic growth with the subsystem size $l$, $S_l\sim l^{\beta}$, with $0<\beta<1$. We find that $\alpha^* \approx 1$ coincides with the delocalization transition $\alpha_c$ in the middle of the many-body spectrum. An interpretation of these results based on the structure of the RG rules is proposed, which is due to {\it rainbow} proliferation for very long-range interactions $\alpha\ll 1$. We also investigate the effective temperature dependence of the EE allowing us to study the half-chain entanglement entropy of eigenstates at different energy densities, where we find that the crossover in EE occurs at $\alpha^* < 1$.

Many-body localization of 1D disordered impenetrable two-component fermions

We study effects of disorder on eigenstates of 1D two-component fermions with infinitely strong Hubbard repulsion. We demonstrate that the spin-independent (potential) disorder reduces the problem to the one-particle Anderson localization taking place at arbitrarily weak disorder. In contrast, a random magnetic field can cause reentrant many-body localization–delocalization transitions. Surprisingly weak magnetic field destroys one-particle localization caused by not too strong potential disorder, whereas at much stronger fields the states are many-body localized. We present numerical support of these conclusions.

Publisher's Note: “Modulated structure and hopping transport mechanism involving a defect-induced localization–delocalization transition in a Ca–Ce(La)–Nb–W–O system” [Appl. Phys. Lett. 120, 112106 (2022)

Publisher's Note: “Modulated structure and hopping transport mechanism involving a defect-induced localization–delocalization transition in a Ca–Ce(La)–Nb–W–O system” [Appl. Phys. Lett. <b>120</b>, 112106 (2022)

Mobility edges generated by the non-Hermitian flatband lattice

We study the cross-stitch flatband lattice subject to the quasiperiodic complex potential exp(ix). We firstly identify the exact expression of quadratic mobility edges through analytical calculation, then verify the theoretical predictions by numerically calculating the inverse participation ratio. Further more, we study the relationship between the real–complex spectrum transition and the localization–delocalization transition, and demonstrate that mobility edges in this non-Hermitian model not only separate localized from extended states but also indicate the coexistence of complex and real spectrum.

Amplitude-dependent edge states and discrete breathers in non-linear modulated phononic lattices

We explore the role of non-linearities on the spectral properties of modulated one-dimensional phononic lattices. In the linear regime, a spatial modulation of stiffness is known to produce topological gaps characterized by non-zero Chern numbers, which host topological states localized at the edges of finite domains. A continuation of the linear modes as a function of amplitude is performed, revealing a series of localization and de-localization transitions that are confirmed through direct time domain simulations. The results show that edge states whose eigenvalue branch remains within the gap remains localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches and remains tangential to the bulk bands experience delocalization transitions. Additionally, we observe a series of amplitude-induced phase transitions as the bulk modes become discrete breathers localized in one or more regions of the domain. Remarkably, these transitions are independent on the size of the lattice. These results bring to light the co-existence of topological edge states and discrete breathers for non-linear modulated lattices, whose interplay may exploited for amplitude-induced topological and localization transitions.

Modulated structure and hopping transport mechanism involving a defect-induced localization–delocalization transition in a Ca–Ce(La)–Nb–W–O system

CaCeNbWO8-δ (CCNWO) oxide is a three-dimensional semiconductor with potential applications in electronic devices. It has been reported that the temperature dependence of the resistivity of CCNWO deviates from that predicted by the Arrhenius equation over a wide temperature range. However, its complex hopping transport mechanism has remained unclear due to unknown defect structures. A combination of transmission electron microscopy and the density functional theory showed that CaCeNbWO8-δ and CaCe0.5La0.5NbWO8-δ have a modulated defect structure, and the carriers mainly undergo a Nb4d→W5d transition. At low temperatures, anisotropic defects promote the diversification of transport properties, variable-range hopping, and nearest neighbor hopping. With increasing temperature, isotropic defects promote simplification of the transport property. Compared with CCNWO, CaCe0.5La0.5NbWO8-δ, with a more stable structure, has stronger electron–electron interactions and shifts the localization–delocalization transition point to a higher temperature. The proposed hopping transport mechanism involving a defect-induced localization–delocalization transition allows semiconductor design and device integration schemes, thus impacting a variety of applications.

Delocalization transition in low energy excitation modes of vector spin glasses

We study the energy minima of the fully-connected mm-components vector spin glass model at zero temperature in an external magnetic field for m\ge 3m≥3. The model has a zero temperature transition from a paramagnetic phase at high field to a spin glass phase at low field. We study the eigenvalues and eigenvectors of the Hessian in the minima of the Hamiltonian. The spectrum is gapless both in the paramagnetic and in the spin glass phase, with a pseudo-gap behaving as \lambda^{m-1}λm−1 in the paramagnetic phase and as \sqrt{\lambda}λ at criticality and in the spin glass phase. Despite the long-range nature of the model, the eigenstates close to the edge of the spectrum display quasi-localization properties. We show that the paramagnetic to spin glass transition corresponds to delocalization of the edge eigenvectors. We solve the model by the cavity method in the thermodynamic limit. We also perform numerical minimization of the Hamiltonian for N\le 2048N≤2048 and compute the spectral properties, that show very strong corrections to the asymptotic scaling approaching the critical point.

Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model

Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.

Scaling theory of few-particle delocalization

We develop a scaling theory of interaction-induced delocalization of few-particle states in disordered quantum systems. In the absence of interactions, all single-particle states are localized in $d<3$, while in $d \geq 3$ there is a critical disorder below which states are delocalized. We hypothesize that such a delocalization transition occurs for $n$-particle bound states in $d$ dimensions when $d+n\geq 4$. Exact calculations of disorder-averaged $n$-particle Greens functions support our hypothesis. In particular, we show that $3$-particle states in $d=1$ with nearest-neighbor repulsion will delocalize with $W_c \approx 1.4t$ and with localization length critical exponent $\nu = 1.5 \pm 0.3$. The delocalization transition can be understood by means of a mapping onto a non-interacting problem with symplectic symmetry. We discuss the importance of this result for many-body delocalization, and how few-body delocalization can be probed in cold atom experiments.

Detecting delocalization-localization transitions from full density distributions

Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is a key open question in the field of nonequilibrium physics. We exploit that localization of particles as realized in Anderson and standard many-body localization (MBL) implies Fock-space localization in single-particle basis sets characterized by a real-space index. Using a recently introduced quantitative measure for Fock-space localization computed from the density distributions, the occupation distance, we systematically study its scaling behavior across delocalozation transitions and identify critical points from scaling collapses of numerical data. Excellent agreement with literature results is found for the critical disorder strengths of noninteracting fermions, such as the one-dimensional Aubry-Andr\'e and the three-dimensional Anderson model. We observe a distinctively different scaling behavior in the case of interacting fermions with random disorder consistent with a Kosterlitz-Thouless transition. Finally, we use our measure to extract the transition point as a function of filling for interacting fermions.

Metallization of colloidal crystals

Colloidal crystals formed by size-asymmetric binary particles coassemble into a wide variety of colloidal compounds with lattices akin to ionic crystals. Recently, a transition from a compound phase with a sublattice of small particles to a metal-like phase in which the small particles are delocalized has been predicted computationally and observed experimentally. In this colloidal metallic phase, the small particles roam the crystal maintaining the integrity of the lattice of large particles, as electrons do in metals. A similar transition also occurs in superionic crystals, termed sublattice melting. Here, we use energetic principles and a generalized molecular dynamics model of a binary system of functionalized nanoparticles to analyze the transition to sublattice delocalization in different coassembled crystal phases as a function of temperature ($T$), number of grafted chains on the small particles, and number ratio between the small and large particles ${n}_{s}:{n}_{l}$. We find that ${n}_{s}:{n}_{l}$ is the primary determinant of crystal type due to energetic interactions and interstitial site filling, while the number of grafted chains per small particle determines the stability of these crystals. We observe first-order sublattice delocalization transitions as $T$ increases, in which the host lattice transforms from low- to high-symmetry crystal structures, including A20 $\ensuremath{\rightarrow}$ bct $\ensuremath{\rightarrow}$ bcc, ${\mathrm{A}}_{\mathrm{d}}$ $\ensuremath{\rightarrow}$ bct $\ensuremath{\rightarrow}$ bcc, and bcc $\ensuremath{\rightarrow}$ bcc/fcc $\ensuremath{\rightarrow}$ fcc transitions and lattices. Analogous sublattice transitions driven primarily by lattice vibrations have been seen in some atomic materials exhibiting an insulator-metal transition also referred to as metallization. We also find minima in the lattice vibrations and diffusion coefficient of small particles as a function of ${n}_{s}:{n}_{l}$, indicating enhanced stability of certain crystal structures for ${n}_{s}:{n}_{l}$ values that form compounds.

Strain induced localization to delocalization transition on a Lieb photonic ribbon lattice

Ribbon lattices are kind of transition systems in between one and two dimensions, and their study is crucial to understand the origin of different emerging properties. In this work, we study a Lieb ribbon lattice and the localization–delocalization transition occurring due to a reduction of lattice distances (compression) and the corresponding flat band deformation. We observe how above a critical compression ratio the energy spreads out and propagates freely across the lattice, therefore transforming the system from being a kind of insulator into a conductor. We implement an experiment on a photonic platform and show an excellent agreement with the predicted phenomenology. Our findings suggest and prove experimentally the use of compression or mechanical deformation of lattices to switch the transport properties of a given system.

Adiabatic Pumping in a Generalized Aubry–André Model Family with Mobility Edges

AbstractThe adiabatic pumping between left and right end modes in a generalized Aubry–André model family with mobility edges by resorting to two end–bulk–end channels is investigated. It is shown that the system can be in an intermediate regime mixed with localized and extended phases as the mobility edge is introduced. One of the channels can remain intact even when the parameter determining the localization–delocalization transition exceeds the threshold of the paradigmatic Aubry–André model, leading to that the parametric condition for successful pumping is relaxed. Moreover, it is found that widening the region of the hybrid phase can further enhance the effect of the mobility edge. The pumping result is also quantified based on the fidelity and check the corresponding pumping process to validate these observations. Furthermore, another channel to realize a flexible adiabatic pumping among four types of generalized end modes is engineered. This work enables the potential application of mobility edges in strong–quasidisorder–immune quantum state transfer.

Delocalization of a non-Hermitian quantum walk on random media in one dimension

We first review the localization–delocalization transition of a non-Hermitian random tight-binding Anderson model, called the Hatano–Nelson model. We then report a new result for a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium; we numerically find a delocalization transition similar to one of the Hatano–Nelson model. As a common feature to both models, at the transition point, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (for the latter quantum-walk model, the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. One of the unique properties of the present non-Hermitian quantum walk is that the localization length of all eigenvectors is the same, and thereby all eigenstates simultaneously undergo the delocalization transition and all energy eigenvalues become complex at the same time when we turn up a non-Hermitian parameter.

Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-André-Fibonacci chain

In this paper, the interplay of the non-Herimiticity and the cascade of delocalization transition in the quasi-periodic chain is studied. The study is applied in a non-Hermitian interpolating Aubry-Andr{\'e}-Fibonacci (IAAF) model, which combines the non-Hermitian Aubry-Andr{\'e} (AA) model and the non-Hermitian Fibonacci model through a varying parameter, and the non-Hermiticity in this model is introduced by the non-reciprocal hopping. In the non-Hermitian AA limit, the system undergoes a delocalization transition by tuning the potential strength. At the critical point, the spatial distribution of the critical state shows a self-similar structure with the relative distance between the peaks being the Fibonacci sequence, and the finite-size scaling of the inverse participation ratios $({\rm IPRs})$ of the critical ground state with lattice size $L$ shows that ${\rm IPR}_g\propto L^{-0.1189}$. In the non-Hermitian Fibonacci limit, we find that the system is always in the extended phase. Along the continuous deformation from the non-Hermitian AA model into the non-Hermitian Fibonacci model in the IAAF model, the cascade of the delocalization transition is found, but only a few plateaux appear. Moreover, the self-similar structure of spatial distribution for the critical modes along the cascade transition is also found. In addition, we find that the delocalization transition and the real-complex transition for the excited states happen at almost the same parameter. Our results show that the non-Hermiticity provides an additional knob to control the cascade of the delocalization transition besides the on-site potential.