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Searching for the dispersionless flat band (FB) in quantum materials, especially in topological systems, becomes an interesting topic. The kagome lattice is an ideal platform for such exploration because the FB can be naturally induced by the underlying destructive interference. Nevertheless, the magnetic kagome system that hosts the FB close to the Fermi level (E F) is exceptionally rare. Here, we study the electronic structure of a kagome magnet LuMn6Sn6 by combining angle-resolved photoemission spectroscopy and density functional theory calculations. The observed Fermi-surface topology and overall band dispersions are similar to previous studies of the X Mn6Sn6 (X = Dy, Tb, Gd, Y) family of compounds. We clearly observe two kagome-derived FBs extending through the entire Brillouin zone, and one of them is located just below E F. The photon-energy-dependent measurements reveal that these FBs are nearly dispersionless along the kz direction as well, supporting the quasi-two-dimensional character of such FBs. Our results complement the X Mn6Sn6 family and demonstrate the robustness of the FB features across this family. [ABSTRACT FROM AUTHOR]

Dispersionless flat bands (FBs) in momentum space, given rise to electron destructive interference in frustrated lattices, offer opportunities to enhance electronic correlations and host exotic many‐body phenomena, such as Wigner crystal, fractional quantum hall state, and superconductivity. Despite successes in theory, great challenges remain in experimentally realizing FBs in frustrated lattices due to thermodynamically structural instability. Here, the observation of electronic FB in a potassium distorted colouring triangle (DCT) lattice is reported, which is supported on a blue phosphorene‐gold network. It is verified that the interaction between potassium and the underlayer dominates and stabilizes the frustrated structures. Two‐dimensional electron gas is modulated by the DCT lattice, and in turn results in a FB dispersion due to destructive quantum interferences. The FB exhibits suppressed bandwidth with high density of states, which is directly observed by scanning tunneling microscopy and confirmed by the first‐principles calculation. This work demonstrates that DCT lattice is a promising platform to study FB physics and explore exotic phenomena of correlation and topological matters. [ABSTRACT FROM AUTHOR]

The heavy fermion (HF) state of d-electron systems is of great current interest since it exhibits various exotic phases and phenomena that are reminiscent of the Kondo effect in f -electron HF systems. Here, we present a combined infrared spectroscopy and first-principles band structure calculation study of the 3d-electron HF compound YFe2Ge2. The infrared response exhibits several charge-dynamical hallmarks of HF and a corresponding scaling behavior that resemble those of the f -electron HF systems. In particular, the low-temperature spectra reveal a dramatic narrowing of the Drude response along with the appearance of a hybridization gap (Δ ~50 meV) and a strongly enhanced quasiparticle effective mass. Moreover, the temperature dependence of the infrared response indicates a crossover around T* ~100K from a coherent state at low temperature to a quasi-incoherent one at high temperature. Despite of these striking similarities, our band structure calculations suggest that the mechanism underlying the HF behavior in YFe2Ge2 is distinct from the Kondo scenario of the f -electron HF compounds and even from that of the d-electron iron-arsenide superconductor KFe2As2. For the latter, the HF state is driven by orbital-selective correlations due to a strong Hund's coupling. Instead, for YFe2Ge2 the HF behavior originates from the band flatness near the Fermi level induced by the combined effects of kinetic frustration from a destructive interference between the direct Fe-Fe and indirect Fe-Ge-Fe hoppings, band hybridization involving Fe 3d and Y 4d electrons, and electron correlations. This highlights that rather different mechanisms can be at the heart of the HF state in d-electron systems. [ABSTRACT FROM AUTHOR]

The heavy fermion (HF) state of d-electron systems is of great current interest since it exhibits various exotic phases and phenomena that are reminiscent of the Kondo effect in f -electron HF systems. Here, we present a combined infrared spectroscopy and first-principles band structure calculation study of the 3d-electron HF compound YFe2Ge2. The infrared response exhibits several charge-dynamical hallmarks of HF and a corresponding scaling behavior that resemble those of the f -electron HF systems. In particular, the low-temperature spectra reveal a dramatic narrowing of the Drude response along with the appearance of a hybridization gap (Δ ~50 meV) and a strongly enhanced quasiparticle effective mass. Moreover, the temperature dependence of the infrared response indicates a crossover around T* ~100K from a coherent state at low temperature to a quasi-incoherent one at high temperature. Despite of these striking similarities, our band structure calculations suggest that the mechanism underlying the HF behavior in YFe2Ge2 is distinct from the Kondo scenario of the f -electron HF compounds and even from that of the d-electron iron-arsenide superconductor KFe2As2. For the latter, the HF state is driven by orbital-selective correlations due to a strong Hund's coupling. Instead, for YFe2Ge2 the HF behavior originates from the band flatness near the Fermi level induced by the combined effects of kinetic frustration from a destructive interference between the direct Fe-Fe and indirect Fe-Ge-Fe hoppings, band hybridization involving Fe 3d and Y 4d electrons, and electron correlations. This highlights that rather different mechanisms can be at the heart of the HF state in d-electron systems. [ABSTRACT FROM AUTHOR]

Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flat-band solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems. [ABSTRACT FROM AUTHOR]

Flat bands – single-particle energy bands – in tight-binding lattices, aka networks, have attracted attention due to the presence of macroscopic degeneracies and their sensitivity to perturbations. They support compact localized eigenstates protected by destructive interference. This makes them natural candidates for emerging exotic phases and unconventional orders. In this review we consider the recently proposed systematic ways to construct flat band networks based on symmetries or fine-tuning. We then discuss how the construction methods can be further extended, adapted or exploited in presence of perturbations, both single-particle and many-body. This strategy has lead to the discovery of non-perturbative metal-insulator transitions, fractal phases, nonlinear and quantum caging and many-body nonergodic quantum models. We discuss what implications these results may have for the design of fine-tuned nanophotonic systems including photonic crystals, nanocavities, and metasurfaces. [ABSTRACT FROM AUTHOR]

Flat, nondispersive bands and topological phase transition in multiple Su–Schrieffer–Heeger (SSH) chains, cross-linked via periodically arranged nodal points are explored within a tight binding framework. We give an analytic prescription, based on a real space decimation scheme, which extracts the energy eigenvalues corresponding to the flat bands along with their degeneracy. The topological phase transition is confirmed through the existence of quantized Zak phase for all the Bloch bands, and the edge states that are protected by chiral symmetry, consistent with the bulk-boundary correspondence. In addition to the edge states, the entangled systems are shown to give rise to clusters of localized eigenstates in the bulk of the system, in contrast to a purely one-dimensional SSH system. [ABSTRACT FROM AUTHOR]

We study the broadening of initially localized wave packets in a quasi one-dimensional diamond ladder with interacting, spinless fermions. The lattice possesses a flat band causing localization. We place special focus on the transition away from the flat band many-body localized case by adding very weak dispersion. By doing so, we allow propagation of the wave packet on significantly different timescales which causes anomalous diffusion. Due to the temporal separation of dynamic processes, an interaction-induced, prethermal equilibrium becomes apparent. A physical picture of light and heavy modes for this prethermal behavior can be obtained within Born–Oppenheimer approximation via basis transformation of the original Hamiltonian. This reveals a detachment between light, symmetric and heavy, anti-symmetric particle species. We show that the prethermal state is characterized by heavy particles binding together mediated by the light particles. [ABSTRACT FROM AUTHOR]

A unique feature of non-Hermitian systems is the extreme sensitivity of the eigenspectrum to boundary conditions with the emergence of the non-Hermitian skin effect (NHSE). A NHSE originates from the point-gap topology of complex eigenspectrum, where an extensive number of eigen-states are anomalously localized at the boundary driven by nonreciprocal dissipation. Two different approaches to create localization are disorder and flat-band spectrum, and their interplay can lead to the anomalous inverse Anderson localization, where the Bernoulli anti-symmetric disorder induces mobility in a full-flat band system in the presence of Aharonov–Bohm (AB) Cage. In this work, we study the localization–delocalization transitions due to the interplay of the point-gap topology, flat band and correlated disorder in the one-dimensional rhombic lattice, where both its Hermitian and non-Hermitian structures show AB cage in the presence of magnetic flux. Although it remains the coexistence of localization and delocalization for the Hermitian rhombic lattice in the presence of the random anti-symmetric disorder, it surprisingly becomes complete delocalization, accompanied by the emergence of NHSE. To further study the effects from the Bernoulli anti-symmetric disorder, we found the similar NHSE due to the interplay of the point-gap topology, correlated disorder and flat bands. Our anomalous localization–delocalization property can be experimentally tested in the classical physical platform, such as electrical circuit. [ABSTRACT FROM AUTHOR]

ABC-stacked trilayer graphene on boron nitride (ABC-TLG/hBN) moiré superlattices provides a tunable platform for exploring Wigner crystal states in which the electron correlation can be controlled by electric and magnetic fields. Here we report the observation of magnetic field-stabilized Wigner crystal states in a ABC-TLG/hBN. We show that correlated insulating states emerge at multiple fractional and integer fillings corresponding to ν = 1/3, 2/3, 1, 4/3, 5/3, and 2 electrons per moiré lattice site under a magnetic field. These correlated insulating states can be attributed to generalized Mott states for the integer fillings and generalized Wigner crystal states for the fractional fillings. The generalized Wigner crystal states are stabilized by a vertical magnetic field and are strongest at one magnetic flux quantum per three moiré superlattices. The ν = 2 insulating state persists up to 30 T, which can be described by a Mott-Hofstadter transition at a high magnetic field.

Abstract Dispersionless flat bands (FBs) in momentum space, given rise to electron destructive interference in frustrated lattices, offer opportunities to enhance electronic correlations and host exotic many‐body phenomena, such as Wigner crystal, fractional quantum hall state, and superconductivity. Despite successes in theory, great challenges remain in experimentally realizing FBs in frustrated lattices due to thermodynamically structural instability. Here, the observation of electronic FB in a potassium distorted colouring triangle (DCT) lattice is reported, which is supported on a blue phosphorene‐gold network. It is verified that the interaction between potassium and the underlayer dominates and stabilizes the frustrated structures. Two‐dimensional electron gas is modulated by the DCT lattice, and in turn results in a FB dispersion due to destructive quantum interferences. The FB exhibits suppressed bandwidth with high density of states, which is directly observed by scanning tunneling microscopy and confirmed by the first‐principles calculation. This work demonstrates that DCT lattice is a promising platform to study FB physics and explore exotic phenomena of correlation and topological matters.

Abstract Materials featuring touching points, localized states, and flat bands are of great interest in condensed matter and artificial systems due to their implications in topology, quantum geometry, superconductivity, and interactions. In this theoretical study, the experimental realization of the dice lattice with adjustable parameters is proposed by arranging carbon monoxide molecules on a two‐dimensional (2D) electron system at a (111) copper surface. First, a theoretical framework is developed to obtain the spectral properties within a nearly free electron approximation and then compare them with tight‐binding calculations. This investigation reveals that the high mobility of Shockley state electrons enables an accurate theoretical description of the artificial lattice using a next‐nearest‐neighbor tight‐binding model, resulting in the emergence of a touching point, a quasi‐flat band, and localized lattice site behavior in the local density of states. Additionally, theoretical results for a long‐wavelength low‐energy model that accounts for next‐nearest‐neighbor hopping terms are presented. Furthermore, the model's behavior under an external magnetic field is theoretically examined by employing Peierl's substitution, a commonly used technique in theoretical physics to incorporate magnetic fields into lattice models. The theoretical findings suggest that, owing to the exceptional electron mobility, the highly degenerate eigenenergy associated with the Aharonov‐Bohm caging mechanism may not manifest in the proposed experiment.

Benefited from the lower dimensionality compared to their 3D counterpart, 2D flat‐band systems provide cleaner lattice models, easier experimental verification, and higher tunability, which make the 2D van der Waals (vdW) system an ideal playground for exploring flat‐band physics as well as their potential applications. Given the vast amount of research in the field of flat bands, a simple and efficient approach to search for realistic vdW materials with flat bands is still missing. Here, a two‐tier framework to filter and diagnose high‐quality flat‐band vdW materials by combining high‐throughput first‐principles calculations and the proposed 2D flat‐band score criterion is presented. Based on systematic geometrical analysis, 861 potential monolayer vdW materials are initially obtained amounting to 187,093 structures as stored in the Inorganic Crystal Structure Database. By applying the 2D flat‐band score criterion, 229 flat‐band candidates are efficiently identified, among which a sub‐catalog of 74 materials with flat bands right next to the Fermi level is further provided to facilitate experimental verification. All these efforts to screen experimentally available flat‐band candidates will certainly motivate continuing exploration toward the realization of this class of special materials and their applications in material science. [ABSTRACT FROM AUTHOR]

Twist-induced lattice misalignment of bilayer graphene leads to moiré patterns that generate electronic flat bands with strongly correlated electronic states, but it still requires a sophisticated process to precisely control the twist angle. Here, we propose a different way to generate hexagonal moirés in bilayer graphene by uniaxially stretching the two layers along two distinct armchair directions, respectively. The heterostrain-induced moiré gives rise to flat bands near the Fermi level due to the deformation-induced equivalent misaligned angle between two graphene layers, featuring an electronic equivalence of twisted bilayer graphene. We demonstrate the flat bands at a heterostrain of 2.1%, equivalent to the first magic angle of 1.05°. Yet, a slight shift of Dirac point from K point due to the uniaxial strain splits the flat bands into two van Hove singularity peaks that are separated by 18 meV and located above and below the Fermi level, respectively. Our results suggest a potential way to control the electronic strong correlation in bilayer graphene of natural stacking. [ABSTRACT FROM AUTHOR]

Novel quantum materials have broad application prospects in spintronic devices and low‐power‐consumption devices. The kagome‐type lattice has special corner‐sharing triangle geometry, providing a rich platform to investigate the relationship of novel correlated topological states, geometry, and strong electron interactions. However, the orbital hybridization in the presence of flat band that originated from the electron localization due to the unique kagome lattice configuration is still unclear. Resonant‐angle‐resolved photoemission spectroscopy is utilized to study the valence band structures of a new vanadium‐based kagome material GdV6Sn6, combined with density functional theory calculation. Herein, a significant hybridization between V 3d and Sn 5p electrons, which paves the way to understand the formation of long‐range magnetic ordering of GdV6Sn6 and other kagome materials at low temperature, is unambiguously revealed in the results. [ABSTRACT FROM AUTHOR]

Flat band systems are commonly associated with compact localized states (CLSs) that arise from the macroscopic degeneracy of eigenstates at the flat band energy. However, in the case of singular flat bands, conventional localized flat band states are incomplete, leading to the existence of noncontractible loop states (NLSs) with nontrivial real-space topology. In this study, we experimentally and analytically demonstrate the existence of NLSs in a 2D photonic borophene lattice without a CLS counterpart, owing to a band that is flat only along high-symmetry lines and dispersive along others. Our findings challenge the conventional notion that NLSs are necessarily linked to robust boundary modes due to a bulk-boundary correspondence. Protected by the band flatness that originates from band touching, NLSs play a significant role in investigating the fundamental physics of flat band systems.

The flat electronic band has remarkable relevance in the strongly correlated phenomena mainly due to its reduced kinetic energy in comparison to the many-body potential energy. The formation of such bands in cubically structured nanowires is addressed in this article by means of a new independent channel method and a generalized convolution theorem developed for the Green's function including the first, second, and third neighbor interactions. A real-space renormalization method is further applied to address macroscopic-length aperiodic nanowires. We also determined the appearance condition of these flat bands, as well as their degeneracy and robustness in the face of perturbations, such as structural dislocations. Finally, the possible experimental detection of this flat band via the electronic specific heat is analyzed. [ABSTRACT FROM AUTHOR]

Flat band has attracted more and more interest in recent years, motivated by its discovery in twisted bilayer graphene (TBG). In this work, we report our study of the impurity effect on this flat band system, which is an important issue for real materials. Employing the Lanczos recursive method, we solve the local density of states (LDOS) around a potential impurity. We find for large impurity size, a series of bound states are formed inside the impurity, and the flat band peak in LDOS is suppressed near the impurity boundary and shifted by the impurity potential deep inside the impurity. As the impurity size becomes smaller, the effect on the flat band becomes weaker, as anticipated from the large scale of the underlying Wannier function. This property distinguishes with the usual flat band systems with small localized Wannier orbitals, and indicates the flat band in TBG is more stable against small-size impurities. [ABSTRACT FROM AUTHOR]

We investigate a quantum-state transfer protocol through a quasi-1D spin-1/2 channel defined on a hexagonal layer featuring hopping disorder. In the absence of disorder, the quantum channel displays two flat bands hosting compact localized states. That is signalled by the appearance of singularities in the density of states. We show that an arbitrary qubit state can be transmitted with high fidelity between the two ends even in the presence of noise as long as they are not in resonance with energy levels surrounding the flat band. This higher sensitivity against disorder is due to the residual single-cell compact localized states accompanied by a degeneracy lifting. [ABSTRACT FROM AUTHOR]

We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The dynamics of this Floquet-engineered flat-band system is entirely driven by correlations and described by exotic Hamiltonian and current operators. We employ exact diagonalization and compare our results with those of the conventional, undriven Bose–Hubbard system. We focus on the two main manifestations of superfluidity, the Hess-Fairbank effect and the metastability of supercurrents, with explicit inclusion of an impurity when relevant. Among the novel superfluid features, we highlight the presence of a cat-like ground state, with branches that have opposite crystal momentum but carry the same flux-dependent current, and the essential role of the interference between the collective components of the ground-state wave function. Calculation of the dynamic form factor reveals the presence of an acoustic mode that guarantees superfluidity in the thermodynamic limit. [ABSTRACT FROM AUTHOR]

Employing a combination of first-principles calculations and low-energy effective models, we present a comprehensive investigation on the electronic structure of Pb _10 (PO _4 ) _6 O _4 , which exhibits remarkable quasi-one-dimensional topological flat-band around the Fermi level. These flat bands predominantly originate from the $p_x/p_y$ orbitals of the oxygen molecules chain at the fully-occupied 4 e Wyckoff positions and thus can be well-captured by a minimal four-band tight-binding model. Furthermore, the abundant crystal symmetry inherent in Pb _10 (PO _4 ) _6 O _4 provides an ideal platform for the emergence of various quasi-fermions characterized by different dispersion, degeneracy, and dimensionality. These include a 0D four-fold degenerate Dirac fermion exhibiting quadratic dispersion, a 1D quadratic/linear nodal-line fermion along symmetric k -paths, a 1D hourglass nodal-line (HNL) fermion associated with the Dirac fermion, and a 2D symmetry-enforced nodal surface located on the k _z = π plane. Moreover, when considering the weak ferromagnetic order, Pb _10 (PO _4 ) _6 O _4 transforms into a rare semi-half-metal, which is characterized by the presence of Dirac fermion and HNL fermion at the Fermi level for a single spin channel exhibiting 100 $\%$ spin polarization. Our findings reveal the rarely coexistence of flat bands, diverse topological semimetal states and ferromagnetism in Pb _10 (PO _4 ) _6 O _4 , which may provide valuable insights for further exploring the intriguing interplay between superconductivity and exotic electronic states.

We study the broadening of initially localized wave packets in a quasi one-dimensional diamond ladder with interacting, spinless fermions. The lattice possesses a flat band causing localization. We place special focus on the transition away from the flat band many-body localized case by adding very weak dispersion. By doing so, we allow propagation of the wave packet on significantly different timescales which causes anomalous diffusion. Due to the temporal separation of dynamic processes, an interaction-induced, prethermal equilibrium becomes apparent. A physical picture of light and heavy modes for this prethermal behavior can be obtained within Born–Oppenheimer approximation via basis transformation of the original Hamiltonian. This reveals a detachment between light, symmetric and heavy, anti-symmetric particle species. We show that the prethermal state is characterized by heavy particles binding together mediated by the light particles.

We study the electronic structure of double-twisted few-layer graphite (DTFLG), which consists of three few-layer graphites (FLGs), i.e., an ABA-stacked graphene multilayer, stacked with two twist angles. We consider two categories of DTFLG, the alternately and chirally twisted cases, according to the rotation direction of the two twist angles. We show that, once the middle FLG of DTFLG is not thinner than the trilayer, both types of DTFLG can remarkably host two pairs of degenerate Moiré flat bands (MFBs) at EF, twice that of the magic angle twisted bilayer graphene (TBG). The doubled MFBs of DTFLG lead to a doubled density of states (DOS) at the Fermi level EF, which implies much stronger correlation effects than TBG. The degeneracy of MFBs can be lifted by a perpendicular electric field, and the isolated MFBs have a nonzero valley Chern number. We also reveal the peculiar wave function patterns of the MFBs in DTFLG. Our results establish a new family of Moiré systems that have a much higher DOS at EF and thus possibly much stronger correlation effects. [ABSTRACT FROM AUTHOR]

We report that the twisted few layer graphite (tFL-graphite) is a new family of moiré heterostructures (MHSs), which has richer and highly tunable moiré flat band structures entirely distinct from all the known MHSs. A tFL-graphite is composed of two few-layer graphite (Bernal stacked multilayer graphene), which are stacked on each other with a small twisted angle. The moiré band structure of the tFL-graphite strongly depends on the layer number of its composed two van der Waals layers. Near the magic angle, a tFL-graphite always has two nearly flat bands coexisting with a few pairs of narrowed dispersive (parabolic or linear) bands at the Fermi level, thus, enhances the DOS at EF. This coexistence property may also enhance the possible superconductivity as been demonstrated in other multiband superconductivity systems. Therefore, we expect strong multiband correlation effects in tFL-graphite. Meanwhile, a proper perpendicular electric field can induce several isolated nearly flat bands with nonzero valley Chern number in some simple tFL-graphites, indicating that tFL-graphite is also a novel topological flat band system. [ABSTRACT FROM AUTHOR]

We investigate the origin of the ubiquitous existence of flat bands in the network superstructures of atomic chains, where one-dimensional (1D) atomic chains array periodically. While there can be many ways to connect those chains, we consider two representative ways of linking them, the dot-type and triangle-type links. Then, we construct a variety of superstructures, such as the square, rectangular, and honeycomb network superstructures with dot-type links and the honeycomb superstructure with triangle-type links. These links provide the wavefunctions with an opportunity to have destructive interference, which stabilizes the compact localized state (CLS). In the network superstructures, there exist multiple flat bands proportional to the number of atoms of each chain, and the corresponding eigenenergies can be found from the stability condition of the compact localized state. Finally, we demonstrate that the finite bandwidth of the nearly flat bands of the network superstructures arising from the next-nearest-neighbor hopping processes can be suppressed by increasing the length of the chains consisting of the superstructures. [ABSTRACT FROM AUTHOR]

The controlled manipulation of doping levels in graphene is crucial for advancing next-generation low-power electronics. Owing to its peculiar band structure, graphene's electronic functionalities can be easily tuned by electron doping, resulting in the bandgap openings, orbital hybridization, and induced spin-polarization. Here, we unveil the substantial doping of the graphene layer and the emergence of a significant bandgap by sandwiching a monolayer graphene, supported on ferromagnetic cobalt, between two europium layers. Our angle- and spin-resolved photoemission spectroscopy experiments, accompanied by dedicated density functional theory calculations, demonstrate that single-spin electron pockets form as a result of the hybridization of the topmost europium majority bands with graphene, while hybridization gaps are induced in the graphene π∗ bands by the Eu minority bands. Spin-resolved measurements further emphasize a single-spin dispersionless contribution proximal to the Fermi level, possibly arising from the coupling of single-spin polarized graphene bands to optical phonons. This work provides crucial insights into the phase diagram of heavily doped graphene, with significant potential for the design and development of novel 2D systems. [Display omitted] [ABSTRACT FROM AUTHOR]

The Kagome lattice is rich in unique electronic and magnetic properties, such as flat band, superconductivity, charge density waves, and so on. In this paper, the magnetic properties, flat and Dirac bands of monolayer Mn 3 Sn 3 Se 2 with Kagome lattice are investigated based on first-principles calculations. A total of four magnetic configurations are considered, and the intrinsic ground state of Mn 3 Sn 3 Se 2 is identified as the ferromagnetic state. Strain has a significant effect on its magnetic ground state, which changes to an in-plane AFM state when the tensile strain exceeds 5 %. Monolayer Mn 3 Sn 3 Se 2 has an out-of-plane magnetic anisotropy of up to 0.777 meV, and the Curie temperature is 528 K. The band structure of the FM state is shown to be metallic, and spin polarized flat and Dirac bands appear near the Fermi level, which are degenerate. Monolayer Mn 3 Sn 3 Se 2 changes to half-metallic when a strain of 1%–2% is applied. Strain and correlation effects can significantly alter the flatness of flat band and the relative energy with Dirac bands. These results not only enrich the family of two-dimensional ferromagnets, but also provide a reference for studying the regulation of flat and Dirac bands. • The intrinsic Mn 3 Sn 3 Se 2 monolayer is room-temperature ferromagnetic metal. • The Curie temperature is 528 K and out-of-plane MAE is 0.777 meV. • A tensile strain of 1 %∼2 % makes it a half-metal. • There are flat band and Dirac point near the Fermi level, which are degenerate. • U-value and strain can regulate the degeneracy and the flatness of flat band. [ABSTRACT FROM AUTHOR]

The flat electronic band has remarkable relevance in the strongly correlated phenomena mainly due to its reduced kinetic energy in comparison to the many-body potential energy. The formation of such bands in cubically structured nanowires is addressed in this article by means of a new independent channel method and a generalized convolution theorem developed for the Green’s function including the first, second, and third neighbor interactions. A real-space renormalization method is further applied to address macroscopic-length aperiodic nanowires. We also determined the appearance condition of these flat bands, as well as their degeneracy and robustness in the face of perturbations, such as structural dislocations. Finally, the possible experimental detection of this flat band via the electronic specific heat is analyzed.

Quantum anomalous Hall effect (QAHE) and quantum spin Hall effect (QSHE) are two interesting physical manifestations of 2D materials that have an intrinsic nontrivial band topology. In principle, they are ground-state equilibrium properties characterized by Fermi level lying in a topological gap, below which all the occupied bands are summed to a non-zero topological invariant. Here, we propose theoretical concepts and models of ‘excited’ QAHE (EQAHE) and EQSHE generated by dissociation of an excitonic insulator (EI) state with complete population inversion (CPI), a unique many-body ground state enabled by two yin-yang flat bands (FBs) of opposite chirality hosted in a diatomic Kagome lattice. The two FBs have a trivial gap in between, i.e. the system is a trivial insulator in the single-particle ground-state, but nontrivial gaps above and below, so that upon photoexcitation the quasi-Fermi levels of both electrons and holes will lie in a nontrivial gap achieved by the CPI-EI state, as demonstrated by exact diagonalization calculations. Then dissociation of singlet and triplet EI state will lead to EQAHE and EQSHE, respectively. Realizations of yin-yang FBs in real materials are also discussed. [ABSTRACT FROM AUTHOR]

Carrier dynamics is crucial in semiconductors, and it determines their conductivity, response time, and overall functionality. In flat bands (FBs), carriers with high effective masses are predicted to host unconventional transport properties. The FBs usually overlap with other trivial energy bands, however, making it difficult to accurately distinguish their carrier dynamics. In this paper, we have investigated the flat-band carrier dynamics of excited electrons in Nb 3 Cl 8 , which hosts ideal nonoverlapping FBs near the Fermi level. The optical transition between Hubbard bands is abnormally weakened, exhibiting weak interband absorption and its related slow photoresponse with a time constant of ∼120 s, which are associated with flat-band Mottness-induced large electron effective mass and parity-forbidden transitions. Besides, the localized states created by chlorine vacancies also act as trapping centers for carriers with a time constant of ∼600 s, which are similar to those of the compact localized states of the FB, making the relaxation behavior even more extraordinary. The presence and impacts of atomic defects are confirmed experimentally and theoretically. This work has revealed the abnormal flat-band carrier dynamics of Nb 3 Cl 8 , which is essential for understanding the optical, electrical, and thermal transport properties of flat-band materials.

The heavy fermion (HF) state of [Formula: see text]-electron systems is of great current interest since it exhibits various exotic phases and phenomena that are reminiscent of the Kondo effect in [Formula: see text]-electron HF systems. Here, we present a combined infrared spectroscopy and first-principles band structure calculation study of the [Formula: see text]-electron HF compound YFe[Formula: see text]Ge[Formula: see text]. The infrared response exhibits several charge-dynamical hallmarks of HF and a corresponding scaling behavior that resemble those of the [Formula: see text]-electron HF systems. In particular, the low-temperature spectra reveal a dramatic narrowing of the Drude response along with the appearance of a hybridization gap ([Formula: see text] 50 meV) and a strongly enhanced quasiparticle effective mass. Moreover, the temperature dependence of the infrared response indicates a crossover around [Formula: see text] 100 K from a coherent state at low temperature to a quasi-incoherent one at high temperature. Despite of these striking similarities, our band structure calculations suggest that the mechanism underlying the HF behavior in YFe[Formula: see text]Ge[Formula: see text] is distinct from the Kondo scenario of the [Formula: see text]-electron HF compounds and even from that of the [Formula: see text]-electron iron-arsenide superconductor KFe[Formula: see text]As[Formula: see text]. For the latter, the HF state is driven by orbital-selective correlations due to a strong Hund's coupling. Instead, for YFe[Formula: see text]Ge[Formula: see text] the HF behavior originates from the band flatness near the Fermi level induced by the combined effects of kinetic frustration from a destructive interference between the direct Fe-Fe and indirect Fe-Ge-Fe hoppings, band hybridization involving Fe [Formula: see text] and Y [Formula: see text] electrons, and electron correlations. This highlights that rather different mechanisms can be at the heart of the HF state in [Formula: see text]-electron systems., Competing Interests: Competing interests statement:The authors declare no competing interest.

Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the d -wave pairing correlation for repulsive on-site Hubbard interaction and s -wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity. [ABSTRACT FROM AUTHOR]

This review considers the topological fermion condensation quantum phase transition (FCQPT) that explains the complex behavior of strongly correlated Fermi systems, such as frustrated insulators with quantum spin liquid and heavy fermion metals. The review contrasts theoretical consideration with recent experimental data collected on both heavy fermion metals (HF) and frustrated insulators. Such a method allows to understand experimental data. We also consider experimental data collected on quantum spin liquid in Lu 3 Cu 2 Sb 3 O 14 and quasi-one dimensional (1D) quantum spin liquid in both YbAlO 3 and Cu (C 4 H 4 N 2) (NO 3) 2 with the aim to establish a sound theoretical explanation for the observed scaling laws, Landau Fermi liquid (LFL) and non-Fermi-liquid (NFL) behavior exhibited by these frustrated insulators. The recent experimental data on the heavy-fermion metal α − YbAl 1 − x Fe x B 4 , with x = 0.014 , and on its sister compounds β − YbAlB 4 and YbCo 2 Ge 4 , carried out under the application of magnetic field as a control parameter are analyzed. We show that the thermodynamic and transport properties as well as the empirical scaling laws follow from the fermion condensation theory. We explain how both the similarity and the difference in the thermodynamic and transport properties of α − YbAl 1 − x Fe x B 4 and in its sister compounds β − YbAlB 4 and YbCo 2 Ge 4 emerge, as well as establish connection of these (HF) metals with insulators Lu 3 Cu 2 Sb 3 O 14 , Cu (C 4 H 4 N 2) (NO 3) 2 and YbAlO 3 . We demonstrate that the universal LFL and NFL behavior emerge because the HF compounds and the frustrated insulators are located near the topological FCQPT or are driven by the application of magnetic fields. [ABSTRACT FROM AUTHOR]

The stability of the dumbbell structure has been confirmed by previous theory and experiment. Based on first-principles calculations, we proposed hexagonal dumbbell graphene (HDB C 10) and rectangular dumbbell graphene (RDB C 10) monolayers containing periodically raised C (C R) atoms. They turn out to have high mobility semiconductor properties. By adsorbing H atoms on these C R atoms, their band structures can be widely tuned from semiconductor to semimetal. When considering adsorption of two/four H atoms on the unit cell of the dumbbell structure, the bandgap can be increased, and isolated flat band structures can be obtained by further adding or removing H atoms. Remarkably, two different Dirac band structures can be found in the HDB/RDB C 10 H 2 -I monolayers. The HDB C 10 H 2 -I shows a Dirac cone with isotropic Fermi velocities, while the RDB C 10 H 2 -I monolayer exhibits a quasi-one-dimensional Dirac nodal line with varying Fermi velocities along the XS path. Tight-binding (TB) models are constructed including nearest neighbor (NN) and next NN hopping in order to understand our DFT results. These TB models are related to the Su-Schrieffer-Heeger model, and are able to explain the tunable topological properties of the RDB C 10 H 2 -I monolayer. They not only are able to explain the different kinds of Fermi velocity, but also can predict the emergence of topological edge states, providing a good platform for research on Dirac fermions. The HDB/RDB C 10 monolayer exhibits more freedom of tunable band structures and more stable hydrogen storage capacity, making it superior to graphene. Finally, possible experimental synthesis paths of these DB monolayers are provided. [Display omitted] • Based on the experimental dumbbell structures, twelve stable hydrocarbon monolayers with a hexagonal/rectangular lattice have been predicted. • The carbon atoms in the dumbbell structures exhibit the more stable and diverse adsorption for hydrogen atoms than graphene. • The dumbbell graphene can realize the hydrogenation-controlled band engineering, including semiconductors, flat band structures, and Dirac band structures. • The proposed tight-binding models not only are able to explain the different kinds of Fermi velocities, but also can predict the emergence of topological edge states. [ABSTRACT FROM AUTHOR]

In this work, we investigate the bound-state problem in a one-dimensional spin-1 Dirac Hamiltonian with a flat band. It is found that the flat band has significant effects on the bound states. For example, for Dirac delta potential gδ (x), there exists one bound state for both the positive and negative potential strength g. Furthermore, when the potential is weak, the bound-state energy is proportional to the potential strength g. For square well potential, the flat band results in the existence of infinite bound states for arbitrarily weak potential. In addition, when the bound-state energy is very near the flat band, the energy displays a hydrogen atom-like spectrum, i.e. the bound-state energies are inversely proportional to the square of the natural number n (e.g., E n ∝ 1/ n 2, n = 1, 2, 3, …). Most of the above nontrivial behaviors can be attributed to the infinitely large density of states of the flat band and its ensuing 1/ z singularity of the Green function. The combination of a short-ranged potential and flat band provides a new possibility to get an infinite number of bound states and a hydrogen atom-like energy spectrum. In addition, our findings provide some useful insights and further our understanding of the many-body physics of the flat band. [ABSTRACT FROM AUTHOR]

The geometry of optical lattices can be engineered allowing the study ofatomic transport along paths arranged in patterns that are otherwise difficultto probe in the solid state. A question readily accessible to atomic systems isrelated to the speed of propagation of matter-waves as a function of thelattice geometry. To address this issue, we have investigated theoretically thequantum transport of non-interacting and weakly-interacting ultracold fermionicatoms in several 2D optical lattice geometries. We find that the triangularlattice has a higher propagation velocity compared to the square lattice,despite supporting longer paths. The body-centered square lattice has evenlonger paths, nonetheless the propagation velocity is yet faster. This apparentparadox arises from the mixing of the momentum states which leads to differentgroup velocities in quantum systems. Standard band theory provides anexplanation and allows for a systematic way to search and design systems withcontrollable matter-wave propagation. Moreover, the presence of a flat bandsuch as in a two-leg ladder geometry leads to a dynamical densitydiscontinuity, which contrasts the behavior of mobile and localized atoms inquantum transport. Our predictions are realizable with present experimentalcapability.

We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The dynamics of this Floquet-engineered flat-band system is entirely driven by correlations and described by exotic Hamiltonian and current operators. We employ exact diagonalization and compare our results with those of the conventional, undriven Bose–Hubbard system. We focus on the two main manifestations of superfluidity, the Hess-Fairbank effect and the metastability of supercurrents, with explicit inclusion of an impurity when relevant. Among the novel superfluid features, we highlight the presence of a cat-like ground state, with branches that have opposite crystal momentum but carry the same flux-dependent current, and the essential role of the interference between the collective components of the ground-state wave function. Calculation of the dynamic form factor reveals the presence of an acoustic mode that guarantees superfluidity in the thermodynamic limit.

The distinct over-tiltings of band crossings in topological semimetals generate the type-I and type-II classification of Dirac/Weyl and nodal-line fermions, accompanied by exotic electronic and magnetic transport properties. In this work, we propose a concept of hybrid nodal-chain semimetal (NCSM), which is identified by linked type-I and type-II nodal rings (NRs) and hosts inevitable flat band. Using first-principles calculations and structure search technique, a new ternary nitride MgCaN _2 is proposed as the first candidate to realize a novel 3D hybrid NCSM state. Remarkably, flat band is emergent along specific direction as a characteristic signature of such a hybrid nodal-chain, thus offering a platform to explore the interplay between topological states and flat bands. By analyzing the mirror Z _2 topological invariant and developing a low-energy effective ${\boldsymbol{k}}\cdot{\boldsymbol{p}}$ model, we unveil the physical origin of the hybrid nodal-chain structure with multiple-mirror protected mechanism. Moreover, when the linked NRs are projected onto the (010) and (001) surfaces, considerable drumhead-like topological surface states can be illustrated with unique connection patterns. These results expand our understanding of NCSMs from significant band tilting effects and provide a new candidate on realizing hybrid nodal-chain fermion for further theoretical and experimental investigations.

Summary: Opening the graphene zero bandgap and simultaneously keeping its linear electronic dispersion has been widely accepted as a very challenging scientific puzzle. Moreover, one of the biggest obstacles for all-perovskite tandem solar cells is the lack of perovskite semiconductors with a narrow bandgap (

Moiré superlattices with a robust twist proximity effect in the low-dimensional regime can facilitate nanoscale thermoelectric devices. In pristine systems, the low efficiency and lack of proficient control of thermoelectric properties impede desirable advancements in the field of energy conversion. In the present study, we demonstrate remarkable macroscopic thermoelectric response as a consequence of microscopic band structure modulation via the twist proximity in an engineered CrI 3 /1T-MoS 2 moiré superlattice. The local twist effect, which leads to the microscopic phenomena of electron localization, results in a comprehensive electronic structure modulation. Consequently, these local effects convolute the macroscopic thermoelectric effect. Additionally, flat bands and angle-dependent metallic to semiconducting transitions are observed at 10.89, 23.41, and 30° twist angles. We correlate the observed phenomenon with the augmented spin-charge transport and interconversion via the twist proximity effect in its semiconducting phase. The estimated ultralow electronic and lattice thermal conductivities further corroborate with the observed large figure of merit and Seebeck coefficient. The maximum values of the Seebeck coefficient and figure of merit are estimated to be ∼413 μV/K and ∼4.3 at 200 K for 30° under the constant time relaxation approach. The twist-endowed outstanding thermoelectric effect in moiré superlattices with band modulation unveils a distinctive approach to establish efficient thermoelectric devices.

We investigate the origin of the ubiquitous existence of flat bands in the network superstructures of atomic chains, where one-dimensional (1D) atomic chains array periodically. While there can be many ways to connect those chains, we consider two representative ways of linking them, the dot-type and triangle-type links. Then, we construct a variety of superstructures, such as the square, rectangular, and honeycomb network superstructures with dot-type links and the honeycomb superstructure with triangle-type links. These links provide the wavefunctions with an opportunity to have destructive interference, which stabilizes the compact localized state (CLS). In the network superstructures, there exist multiple flat bands proportional to the number of atoms of each chain, and the corresponding eigenenergies can be found from the stability condition of the compact localized state. Finally, we demonstrate that the finite bandwidth of the nearly flat bands of the network superstructures arising from the next-nearest-neighbor hopping processes can be suppressed by increasing the length of the chains consisting of the superstructures.

Two-dimensional van der Waals materials have become an established platform to engineer flat bands which can lead to strongly-correlated emergent phenomena. In particular, the family of Ta dichalcogenides in the 1T phase presents a star-of-David charge density wave that creates a flat band at the Fermi level. For TaS 2 and TaSe 2 this flat band is at half filling leading to a magnetic insulating phase. In this work, we theoretically demonstrate that ligand substitution in the TaSe2-xTe x system produces a transition from the magnetic insulator to a non-magnetic metal in which the flat band gets doped away from half-filling. Forx∈[0.846,1.231]the spin-polarized flat band is self-doped and the system becomes a magnetic metal. In this regime, we show that attractive interactions promote three different spin-triplet superconducting phases as a function of x , corresponding to a nodal f-wave and two topologically-different chiral p-wave superconducting phases. Our results establish monolayer TaSe2-xTe x as a promising platform for correlated flat band physics leading to unconventional superconducting states., (Creative Commons Attribution license.)

Kagome materials have recently garnered substantial attention due to the intrinsic flat band feature and the stimulated magnetic and spin-related many-body physics. In contrast to their bulk counterparts, two-dimensional (2D) kagome materials feature more distinct kagome bands, beneficial for exploring novel quantum phenomena. Herein, we report the direct synthesis of an ultrathin kagome-structured Co-telluride (Co 9 Te 16 ) via a molecular beam epitaxy (MBE) route and clarify its formation mechanism from the Co-intercalation in the 1T-CoTe 2 layers. More significantly, we unveil the flat band states in the ultrathin Co 9 Te 16 and identify the real-space localization of the flat band states by in situ scanning tunneling microscopy/spectroscopy (STM/STS) combined with first-principles calculations. A ferrimagnetic order is also predicted in kagome-Co 9 Te 16 . This work should provide a novel route for the direct synthesis of ultrathin kagome materials via a metal self-intercalation route, which should shed light on the exploration of the intriguing flat band physics in the related systems.

The ground-state superfluid behavior of ultracold atomic Fermi gases with a short-range attractive interaction in a quasi-two-dimensional Lieb lattice is studied using BCS mean-field theory, within the context of BCS-BEC crossover. We find that the flat band leads to nontrivial exotic effects. As the Fermi level enters the flat band, both the pairing gap and the in-plane superfluid density exhibit an unusual power law as a function of interaction, with strongly enhanced quantum geometric effects, in addition to a dramatic increase of compressibility as the interaction approaches the BCS limit. As the Fermi level crosses the van Hove singularities, the character of pairing changes from particle-like to hole-like or vice versa. We present the computed phase diagram, in which a pair density wave state emerges at high densities with relatively strong interaction strength. • Flat band causes unusual power law of pairing gap versus interaction strength. • Unusual power law of in-plane superfluid density versus interaction. • And dramatic increase of the compressibility in the noninteracting limit. • Hole-like pairing emerges when chemical potential crosses van Hove singularities. • Pair density wave ground state emerges for strong pairing at high density. [ABSTRACT FROM AUTHOR]

We review recent progresses in the study of flat band systems, especially focusing on the fundamental physics related to the singularity of the flat band’s Bloch wave functions. We first explain that the flat bands can be classified into two classes: singular and non-singular flat bands, based on the presence or absence of the singularity in the flat band’s Bloch wave functions. The singularity is generated by the band crossing of the flat band with another dispersive band. In the singular flat band, one can find a special kind of eigenmodes, called the non-contractible loop states and the robust boundary modes, which exhibit nontrivial real-space topology. Then, we review the experimental realization of these topological eigenmodes of the flat band in the photonic lattices. While the singularity of the flat band is topologically trivial, we show that the maximum quantum distance around the singularity is a bulk invariant representing the strength of the singularity which protects the robust boundary modes. Finally, we discuss how the maximum quantum distance or the strength of the singularity manifests itself in the anomalous Landau level spreading of the singular flat band when it has a quadratic band-crossing with another band.