Progress on artificial flat band systems: classifying, perturbing, applying

Copper-doped lead apatite, called LK-99, was initially claimed to be a room temperature superconductor driven by flat electron bands, but was later found to be a wide gap insulator. Despite the lack of room temperature superconductivity, there is growing evidence that LK-99 and related compounds host various strong electron correlation phenomena arising from their flat electron bands. Depending on the copper doping site and crystal structure, LK-99 can exhibit two distinct flat bands crossing the Fermi level in the non-interacting limit: either a single or two entangled flat bands. We explore potential correlated metallic and insulating phases in the flat bands of LK-99 compounds by constructing their correlation phase diagrams, and find both non-Fermi liquid and Mott insulating states. We demonstrate that LK-99 is a charge-transfer Mott insulator driven by strong electron correlations, regardless of the flat band type. We also find that the non-Fermi liquid state in the multi-flat band system exhibits strange metal behaviour, while the corresponding state in the single flat band system exhibits pseudogap behaviour. Our findings align with available experimental observations and provide crucial insights into the correlation phenomenology of LK-99 and related compounds that could arise independently of superconductivity. Overall, our research highlights that LK-99 and related compounds offer a compelling platform for investigating correlation physics in flat band systems.

Aharonov-Bohm (AB) caging, a special flat-band localization mechanism, has spurred great interest in different areas of physics. AB caging can be harnessed to explore the rich and exotic physics of quantum transport in flatband systems, where geometric frustration, disorder, and correlations act in a synergetic and distinct way than that in ordinary dispersive band systems. In contrast to the ordinary Anderson localization, where disorder induces localization and prevents transport, in flat band systems disorder can induce mobility, a phenomenon dubbed inverse Anderson transition. Here, we report on the experimental realization of the AB cage using a synthetic lattice in the momentum space of ultracold atoms with tailored gauge fields, and demonstrate the geometric localization due to the flat band and the inverse Anderson transition when correlated binary disorder is added to the system. Our experimental platform in a many-body environment provides a fascinating quantum simulator where the interplay between engineered gauge fields, localization, and topological properties of flat band systems can be finely explored.

Certain lattices with specific geometries have one or more spectral bands that are strictly flat, i.e. the electron energy is independent of the momentum. This can occur robustly irrespective of the specific couplings between the lattices sites due to the lattice symmetry, or it can result from fine-tuned couplings between the lattice sites. While the theoretical picture behind flat electronic bands is well-developed, experimental realization of these lattices has proven challenging. Utilizing scanning tunnelling microscopy (STM) and spectroscopy (STS), we manipulate individual vacancies in a chlorine monolayer on Cu(100) to construct various atomically precise 1D lattices with engineered flat bands. We realize experimentally both gapped and gapless flat band systems with single or multiple flat bands. We also demonstrate tuneability of the energy of the flat bands and how they can be switched "on" and "off" by breaking and restoring the symmetry of the lattice geometry. The experimental findings are corroborated by tight-binding calculations. Our results constitute the first experimental realizations of engineered flat bands in a 1D solid-state system and pave the way towards the construction of e.g. topological flat band systems and experimental tests of flat-band-assisted superconductivity in a fully controlled system.

Photonic lattices have emerged as an ideal testbed for localizing light in space. Among others, the most promising approach is based on flat band systems and their related nondiffracting compact localized states. So far, only compact localized states arising from a single flat band have been found. Such states typically appear static, thus not allowing adaptive or evolutionary features of light localization. Here, we report on the first experimental realization of an oscillating compact localized state arising from multiple flat bands. We observe an oscillatory intensity beating during propagation in a two-dimensional photonic decorated Lieb lattice. The photonic system is realized by direct femtosecond laser writing and hosts most importantly multiple flat bands at different eigenenergies in its band structure. Our results open new avenues for evolution dynamics in the up to now static phenomenon of light localization in periodic waveguide structures and extend the current understanding of light localization in flat band systems.

It has long been speculated that electronic flat band systems can be a fertile ground for hosting novel emergent phenomena including unconventional magnetism and superconductivity. Although flat bands are known to exist in a few systems such as heavy fermion materials and twisted bilayer graphene, their microscopic roles and underlying mechanisms in generating emergent behavior remain elusive. Here we use scanning tunneling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is identified to arise from the kinetically frustrated kagome flat band. Increasing magnetic field up to +-8T, this state exhibits an anomalous magnetization-polarized Zeeman shift, dominated by an orbital moment in opposite to the field direction. Such negative magnetism can be understood as spin-orbit coupling induced quantum phase effects tied to non-trivial flat band systems. We image the flat band peak, resolve the associated negative magnetism, and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics can be dominated by the spin-orbit coupled flat band. Our methodology of probing band-resolved ordering phenomena such as spin-orbit magnetism can also be applied in future experiments to elucidate other exotic phenomena including flat band superconductivity and anomalous quantum transport.

Bloch oscillations in moiré flat band systems

We show that a quantum scar state, an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum, can be constructed in flat band systems. The key idea of our construction is to make use of orthogonal compact localized states. We concretely discuss our construction scheme, taking a saw-tooth flat lattice system as an example, and numerically demonstrate the presence of a quantum scar state. Examples of higher-dimensional systems are also addressed. Our construction method of quantum scar has broad applications to various flat band systems.

Kekulé-O order in graphene, which has recently been realized experimentally, induces Dirac electron masses on the order of m∼100 meV. We show that twisted bilayer graphene in which one or both layershave Kekulé-O order exhibits nontrivial flat electronic bands on honeycomb and kagome lattices. When only one layer has Kekulé-O order, there is a parameter regime for which the lowest four bands at charge neutrality form an isolated two-orbital honeycomb lattice model with two flat bands. The bandwidths are minimal at a magic twist angle θ≈0.7° and Dirac mass m≈100 meV. When both layers have Kekulé-O order, there is a large parameter regime around θ≈1° and m≳100 meV in which the lowest three valence and conduction bands at charge neutrality each realize isolated kagome lattice models with one flat band, while the next three valence and conduction bands are flat bands on triangular lattices. These flat band systems may provide a new platform for strongly correlated phases ofmatter.

The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes.

Electronic flat bands represent a paradigmatic platform to realize strongly correlated matter due to their associated divergent density of states. In common instances, including electron-electron interactions leads to magnetic instabilities for repulsive interactions and superconductivity for attractive interactions. Nevertheless, interactions of Kondo nature in flat band systems have remained relatively unexplored. Here we address the emergence of interacting states mediated by Kondo lattice coupled to a flat band system. Combining dynamical mean-field theory and tensor networks methods to solve flat band Kondo lattice models in one and two dimensions, we show the emergence of a robust underscreened regime leading to a magnetically ordered state in the flat band. Our results put forward flat band Kondo lattice models as a platform to explore the genuine interplay between flat band physics and many-body Kondo screening.

We investigated the one-dimensional diamond ladder in the momentum lattice platform. By inducing multiple two- and four-photon Bragg scatterings among specific momentum states, we achieved a flat band system based on the diamond model, precisely controlling the coupling strength and phase between individual lattice sites. Utilizing two lattice sites couplings, we generated a compact localized state associated with the flat band, which remained localized throughout the entire time evolution. We successfully realized the continuous shift of flat bands by adjusting the corresponding nearest neighbor hopping strength, enabling us to observe the complete localization process. This opens avenues for further exploration of more complex properties within flat-band systems, including investigating the robustness of flat-band localized states in disordered flat-band systems and exploring many-body localization in interacting flat-band systems.

Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned coupling. These flat bands display remarkable strongly interacting phases of matter. Originally considered as a theoretical convenience useful for obtaining exact analytical solutions of ferromagnetism, flat bands have now been observed in a variety of settings, ranging from electronic systems to ultracold atomic gases and photonic devices. Here we review the design and implementation of flat bands and chart future directions of this exciting field.

SummaryThe interplay between dissipation and localization in quantum systems has garnered significant attention due to its potential to manipulate transport properties and induce phase transitions. In this work, we explore the dissipation-induced extended-localized transition in a flat-band model, where the system’s asymptotic state can be controlled by tailored dissipative operators. By analyzing the steady-state density matrix and dissipative dynamics, we demonstrate that dissipation is able to drive the system to states dominated by either extended or localized modes, irrespective of the initial conditions. The control mechanism relies on the phase properties of the dissipative operators, which selectively favor specific Hamiltonian eigenstates. Our findings reveal that dissipation can be harnessed to induce transitions between extended and localized phases, offering a novel approach to manipulate quantum transport in flat-band systems. This work not only deepens our understanding of dissipation-induced phenomena in flat-band systems but also provides a new avenue for controlling quantum states in open systems.

Decoding flat bands from compact localized states

The increased ability to engineer two-dimensional (2D) systems, either using materials, photonic lattices, or cold atoms, has led to the search for 2D structures with interesting properties. One such property is the presence of flat bands. Typically, the presence of these requires long-ranged hoppings, fine-tuning of nearest neighbor hoppings, or breaking time-reversal symmetry by using a staggered flux distribution in the unit cell. We provide a prescription based on carrying out projections from a parent system to generate different flat band systems. We identify the conditions for maintaining the flatness and identify a path-exchange symmetry in such systems that cause the flat band to be degenerate with the other dispersive ones. Breaking this symmetry leads to lifting the degeneracy while still preserving the flatness of the band. This technique does not require changing the topology nor breaking time-reversal symmetry as was suggested earlier in the literature. The prescription also eliminates the need for any fine-tuning. Moreover, it is shown that the subsequent projected systems inherit the precise fine-tuning conditions that were discussed in the literature for similar systems, in order to have and isolate a flat band. As examples, we demonstrate the use of our prescription to arrive at the flat band conditions for popular systems like the Kagomé, the Lieb, and the Dice lattices. Finally, we are also able to show that a flat band exists in a recently proposed chiral spin-liquid state of the Kagomé lattice only if it is associated with a gauge field that produces a flux modulation of the Chern-Simons type.