Flat-band Lattices Research Articles

Compact Topological Edge States in Flux-Dressed Graphenelike Photonic Lattices.

Flat band lattice systems promote the appearance of perfectly compact bulk states, whereas topology favors edge localization. In this work, we report the existence of compact topological edge states on flux-dressed photonic graphene ribbons. We found that robust localization is achieved through a synergy of Aharonov-Bohm caging and topological protection mechanisms. The topological nontriviality of the compact edge states is characterized through both theoretical derivations and experimental observations of an integer Zak phase obtained from the mean chiral displacement. Experiments are performed using direct laser writing of a graphene ribbon photonic lattice having 0 or π effective magnetic fluxes. Mode stability is demonstrated by the exceptional localization of the edge compact mode and its resilience to fabrication tolerances and input phase deviations. Our findings demonstrate the existence of perfectly compact topological edge states, as a concrete and promising example of synergy in between flat band physics and topology.

Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations

Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations

Critical regions in a one-dimensional flat band lattice with a quasi-periodic potential

In our previous work, the concept of critical region in a generalized Aubry–André model (Ganeshan–Pixley–Das Sarma’s model) has been established. In this work, we find that the critical region can be realized in a one-dimensional flat band lattice with a quasi-periodic potential. It is found that the above flat band lattice model can be reduced to an effective Ganeshan–Pixley–Das Sarma’s model. Depending on various parameter ranges, the effective quasi-periodic potential may be bounded or unbounded. In these two cases, the Lyapunov exponent, mobility edge, and critical indices of localized length are obtained exactly. In this flat band model, the localized-extended, localized-critical and critical-extended transitions can coexist. Furthermore, we find that near the transitions between the bound and unbounded cases, the derivative of Lyapunov exponent of localized states with respect to energy is discontinuous. At the end, the localized states in bounded and unbounded cases can be distinguished from each other by Avila’s acceleration.

Non-perturbative dynamics of flat-band systems with correlated disorder

Abstract We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder. To achieve this, we introduce a method to generate random on-site energies with prescribed correlations. We verify this method with a one-dimensional (1D) cross-stitch model, and find good agreement with analytical results obtained from the disorderdressed evolution equations. This allows us to reproduce previous findings, that disorder can mobilize 1D flat-band states which would otherwise remain localized. As explained by the corresponding disorder-dressed evolution equations, such mobilization requires an asymmetric disorder-induced coupling to dispersive bands, a condition that is generically not fulfilled when the flat-band is resonant with the dispersive bands at a Dirac point-like crossing. We exemplify this with the 1D Lieb lattice. While analytical expressions are not available for the two-dimensional (2D) system due to its complexity, we extend the numerical method to the 2D α-T 3 model, and find that the initial flat-band wave packet preserves its localization when α = 0, regardless of disorder and intersections. However, when α ≠ 0, the wave packet shifts in real space. We interpret this as a Berry phase controlled, disorder-induced wave-packet mobilization. In addition, we present density functional theory calculations of candidate materials, specifically Hg1-xCdxTe. The flat-band emerges near the Γ point (k =0) in the Brillouin zone.

Lasing in Non-Hermitian Flat Bands: Quantum Geometry, Coherence, and the Fate of Kardar-Parisi-Zhang Physics.

We show that lasing in flat-band lattices can be stabilized by means of the geometrical properties of the Bloch states, in settings where the single-particle dispersion is flat in both its real and imaginary parts. We illustrate a general projection method and compute the collective excitations, which display a diffusive behavior ruled by quantum geometry through a peculiar coefficient involving gain, losses and interactions, and entailing resilience against modulational instabilities. Then, we derive an equation of motion for the phase dynamics and identify a Kardar-Parisi-Zhang term of geometric origin. This term is shown to exactly cancel whenever the real and imaginary parts of the laser nonlinearity are proportional to each other, or when the uniform-pairing condition is satisfied. We confirm our results through numerical studies of the π-flux diamond chain. This Letter highlights the key role of Bloch geometric effects in nonlinear dissipative systems and KPZ physics, with direct implications for the design of laser arrays with enhanced coherence.

Crystal net catalog of model flat band materials

Flat band systems are currently under intense investigation in quantum materials, optical lattices, and metamaterials. These efforts are motivated by potential realization of strongly correlated phenomena enabled by frustration-induced flat band dispersions; identification of candidate platforms plays an important role in these efforts. Here, we develop a high-throughput materials search for bulk crystalline flat bands by automated construction of uniform-hopping near-neighbor tight-binding models. We show that this approach captures many of the essential features relevant to identifying flat band lattice motifs in candidate materials in a computationally inexpensive manner, and is of use to identify systems for further detailed investigation as well as theoretical and metamaterials studies of model systems. We apply this algorithm to 139,367 materials in the Materials Project database and identify 63,076 materials that host at least one flat band elemental sublattice. We further categorize these candidate systems into at least 31,635 unique flat band crystal nets and identify candidates of interest from both lattice and band structure perspectives. This work expands the number of known flat band lattices that exist in physically realizable crystal structures and classifies the majority of these systems by the underlying lattice, providing additional insights for familiar (e.g., kagome, pyrochlore, Lieb, and dice) as well as previously unknown motifs.

Non-Fermi liquid behaviour in a correlated flat-band pyrochlore lattice

Non-Fermi liquid behaviour in a correlated flat-band pyrochlore lattice

Compact gap solitons and compact edge states of exciton–polariton condensates with spin–orbit coupling in a one-dimensional flatband lattice

We propose that the compact gap solitons and compact edge states can be excited in a flatband of the incoherently-pumped exciton–polariton condensate under a one-dimensional periodic potential lattice. The combined effects of spin–orbit coupling and periodic potential depth on the flatband structures are investigated. Then how the compact gap solitons and edge states are localized and extended inside only a fraction of a single lattice site will be studied with varying pump strengths, pump spot-sizes as well as energy detuning.

Size effects on atomic collapse in the dice lattice.

We study the role of size effects on atomic collapse of charged impurity in the flat band system. The tight-binding simulations are made for the dice lattice with circular quantum dot shapes. It is shown that the mixing of in-gap edge states with bound states in impurity potential leads to increasing the critical charge value. This effect, together with enhancement of gap due to spatial quantization, makes it more difficult to observe the dive-into-continuum phenomenon in small quantum dots. At the same time, we show that if in-gap states are filled, the resonant tunneling to bound state in the impurity potential might occur at much smaller charge, which demonstrates non-monotonous dependence with the size of sample lattice. In addition, we study the possibility of creating supercritical localized potential well on different sublattices, and show that it is possible only on rim sites, but not on hub site. The predicted effects are expected to naturally occur in artificial flat band lattices.

Surge of power transmission in flat and nearly flat band lattices.

Flat band systems can yield interesting phenomena, such as dispersion suppression of waves with frequency at the band. While linear transport vanishes, the corresponding nonlinear case is still an open question. Here, we study power transmission along nonlinear sawtooth lattices due to waves with the flat band frequency injected at one end. While there is no power transfer for small intensity, there is a threshold amplitude above which a surge of power transmission occurs, i.e., supratransmission, for defocusing nonlinearity. This is due to a nonlinear evanescent wave with the flat band frequency that becomes unstable. We show that dispersion suppression and supratransmission also exist even when the band is nearly flat.

RKKY interaction in one-dimensional flat-band lattices

RKKY interaction in one-dimensional flat-band lattices

Suppression of Nonequilibrium Quasiparticle Transport in Flat-Band Superconductors.

We study nonequilibrium transport through a superconducting flat-band lattice in a two-terminal setup with the Schwinger-Keldysh method. We find that quasiparticle transport is suppressed and coherent pair transport dominates. For superconducting leads, the ac supercurrent overcomes the dc current, which relies on multiple Andreev reflections. With normal-normal and normal-superconducting leads, the Andreev reflection and normal currents vanish. Flat-band superconductivity is, thus, promising not only for high critical temperatures, but also for suppressing unwanted quasiparticle processes.

Topological Flatband Loop States in Fractal‐Like Photonic Lattices

AbstractNoncontractible loop states (NLSs) are a recently realized topological entity in flatband lattices, arising typically from the band touching at a point where a flat band intersects one or more dispersive bands. There exists also band touching across a plane, where one flat band overlaps another all over the Brillouin zone without crossing a dispersive band. Such isolated plane‐touching flat bands remain largely unexplored. For example, what are the topological features associated with such flatband degeneracy? Here, nontrivial NLSs and robust boundary modes in a system with such degeneracy are demonstrated. Based on a tailored photonic lattice constructed from the well‐known fractal Sierpinski gasket, the wavefunction singularities and the conditions for the existence of the NLSs are theoretically analyzed. It is shown that the NLSs can exist in both singular and nonsingular flat bands, as a direct reflection of the real‐space topology. Experimentally, directly such flatband NLSs in a laser‐written Corbino‐shaped fractal‐like lattice are observed. This work not only leads to a deep understanding of the mechanism behind the nontrivial flatband states, but also opens up new avenues to explore fundamental phenomena arising from the interplay of flatband degeneracy, fractal structures, and band topology.

Excitation spectra of strongly interacting bosons in the flat-band Lieb lattice

The strongly correlated bosons in flat band systems are an excellent platform to study a wide range of quantum phenomena. Such systems can be realized in optical lattices filled with ultracold atomic gases. In this paper we study the Bose-Hubbard model in the Lieb lattice by means of the time-dependent Gutzwiller mean-field approach. We find that in the Mott insulator phase the excitation modes are gapped and display purely particle or purely hole character, while in the superfluid phase the excitation spectrum is gapless. The geometry of the Lieb lattice leads to a non-uniform order parameter and non-uniform oscillation energy in the ground state. This results in additional anti-crossings between dispersive bands in the excitation spectra, while the flat bands remain insensitive to this effect. We analyze the oscillations of the order parameter on the sublattices as well as the particle-hole character of the excitations. For certain model parameters we find simultaneous pure phase and pure amplitude oscillations within the same mode, separated between the sublattices. Also, we propose a simple method to differentiate between the hole- and particle superfluid regions in the Lieb lattice by in-situ measurement of the atom population on the sublattices.

Demonstration of Robust Boundary Modes in Photonic Decorated Honeycomb Lattices

AbstractThe decorated honeycomb lattices (DHLs) represent a typical model that evinces nontrivial chiral spin liquid and rich topological insulating phases in condensed matter physics, yet in natural materials such lattice structures are not commonly found. Here, a photonic DHL that exhibits two singular flat bands is experimentally demonstrated, thereby observing two distinct robust boundary modes (RBMs) associated with each flat band. These RBMs rely on specially tailored open boundaries in the flatband lattice with wavefunction singularities due to band‐touching, manifesting topological noncontractible loop states that cannot be simply constructed from superposition of conventional flatband states. The robustness of such boundary modes to perturbations is also examined, corroborated by numerical simulations and theoretical analysis. This work illustrates a photonic platform exhibiting Dirac cones, singular band‐touching and multiple flat bands that may be employed to study exotic flatband phenomena and topological insulating phases in optics and beyond.

Localization in a non-Hermitian flat band lattice with nonlinearity

In this article, we aim to report the competing role of non-Hermiticity and nonlinearity introduced in the flat band lattice. For this, we initially examine the dynamics of a non-Hermitian single chain diamond network and show a pure imaginary flat band between the complex dispersive bands. The presence of a pure imaginary flat band leads to light propagation either with amplification or attenuation in a confined manner. With this information, we shift to exploiting the non-Hermitian dual chain diamond lattice which shows PT-symmetric nature in a particular situation. In the linear case, the model has two flat bands in its spectrum, whereas its nature depends on the system parameters. This gives rise to the distinct nature of localized light propagation in the system with controllable intensity. Interestingly, in the case of a pure real flat band with broad-site excitation, large-site stable oscillations appear in the system and exist for a long propagation distance. Finally, we study the dual chain lattice with on-site cubic nonlinearity which shows transient localized propagation for initially localized excitation and stationary kovaton like localization for broad-site excitation. Our results reveal the possibility of controlling transport dynamics in non-Hermitian systems with nonlinearity. Our system also acts as a candidate for optical applications, as in the long-distance diffraction-less transmission of information.

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.

Higher-order exceptional point and Landau–Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices

We propose a scheme to realize parity-time (PT) symmetric photonic Lieb lattices of ribbon shape and complex couplings, thereby demonstrating the higher-order exceptional point (EP) and Landau–Zener Bloch (LZB) oscillations in the presence of a refractive index gradient. Quite different from non-Hermitian flatband lattices with on-site gain/loss, which undergo thresholdless PT symmetry breaking, the spectrum for such quasi-one-dimensional Lieb lattices has completely real values when the index gradient is applied perpendicular to the ribbon, and a triply degenerated higher-order EP (EP3) with coalesced eigenvalues and eigenvectors emerges only when the amplitude of the gain/loss ratio reaches a certain threshold value. When the index gradient is applied parallel to the ribbon, the LZB oscillations exhibit intriguing characteristics, including asymmetric energy transition and pseudo-Hermitian propagation, as the flatband is excited. Meanwhile, a secondary emission occurs each time when the oscillatory motion passes through the EP3, leading to distinct energy distribution in the flatband when a dispersive band is excited. Such novel phenomena may appear in other non-Hermitian flatband systems. Our work may also bring insight and suggest a photonic platform to study the symmetry and topological characterization of higher-order EP that may find unique applications in, for example, enhancing sensitivity.

Excitations of a Bose-Einstein condensate and the quantum geometry of a flat band

The quantum geometry of Bloch states fundamentally affects a wide range of physical phenomena. The quantum Hall effect, for example, is governed by the Chern number, and flat-band superconductivity by the distance between the Bloch states: the quantum metric. While understanding quantum geometry phenomena in the context of fermions is well established, less is known about the role of quantum geometry in bosonic systems where particles can undergo Bose-Einstein condensation (BEC). In conventional single-band or continuum systems, excitations of a weakly interacting BEC are determined by the condensate density and the interparticle interaction energy. In contrast to this, we discover here fundamental connections between the properties of a weakly interacting BEC and the underlying quantum geometry of a multiband lattice system. We show that, in the flat-band limit, the defining physical quantities of BEC, namely, the speed of sound and the quantum depletion, are dictated solely by the quantum geometry. We find that the speed of sound becomes proportional to the quantum metric of the condensed state. Furthermore, the quantum distance between the Bloch functions forces the quantum depletion and the quantum fluctuations of the density-density correlation to obtain finite values for infinitesimally small interactions. This is in striking contrast to dispersive bands where these quantities vanish with the interaction strength. Additionally, we show how in the flat-band limit the supercurrent is carried by the quantum fluctuations and is determined by the Berry connections of the Bloch states. Our results reveal how nontrivial quantum geometry allows reaching strong quantum correlation regime of condensed bosons even with weak interactions. This is highly relevant, for example, for polariton and photon BECs where interparticle interactions are inherently small. Our predictions can be experimentally tested with flat-band lattices already implemented in ultracold gases and various photonic platforms.

Quantum Geometry and Flat Band Bose-Einstein Condensation.

We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using the multiband Bogoliubov theory and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.