Flat Band Research Articles

Robustness of Flat Bands on the Perturbed Kagome and the Perturbed Super-Kagome Lattice

We study spectral properties of perturbed discrete Laplacians on two-dimensional Archimedean tilings. The perturbation manifests itself in the introduction of non-trivial edge weights. We focus on the two lattices on which the unperturbed Laplacian exhibits flat bands, namely the (3.6)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(3.6)^2$$\\end{document} Kagome lattice and the (3.122)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(3.12^2)$$\\end{document} “Super-Kagome” lattice. We characterize all possible choices for edge weights which lead to flat bands. Furthermore, we discuss spectral consequences such as the emergence of new band gaps. Among our main findings is that flat bands are robust under physically reasonable assumptions on the perturbation, and we completely describe the perturbation-spectrum phase diagram. The two flat bands in the Super-Kagome lattice are shown to even exhibit an “all-or-nothing” phenomenon in the sense that there is no perturbation, which can destroy only one flat band while preserving the other.

First-principles prediction of moiré ultra-flat bands in twisted bilayer nitrogene

Based on first-principles density functional theory, we investigated the electronic structures of twisted bilayer nitrogene at various twist angles. This electron localization by the influence of the moiré superlattice with very small θ leads to flat bands, especially one of valence bands at the Fermi level on atoms in the AA zone whereas for a larger θ no strong localization occurs owning to a large proportion of the AB zone. Also, there is a linear relationship between the band gaps and the torsion angles of the twisted bilayer nitrogene. A smaller twist angle corresponds to a larger band gap, whereas a larger twist angle corresponds to a smaller band gap. This localization should also reduce considerably the mobility of the electrons and thus modify transport properties.

Stacking Order Engineering of Two-Dimensional Materials and Device Applications.

Stacking orders in 2D van der Waals (vdW) materials dictate the relative sliding (lateral displacement) and twisting (rotation) between atomically thin layers. By altering the stacking order, many new ferroic, strongly correlated and topological orderings emerge with exotic electrical, optical and magnetic properties. Thanks to the weak vdW interlayer bonding, such highly flexible and energy-efficient stacking order engineering has transformed the design of quantum properties in 2D vdW materials, unleashing the potential for miniaturized high-performance device applications in electronics, spintronics, photonics, and surface chemistry. This Review provides a comprehensive overview of stacking order engineering in 2D vdW materials and their device applications, ranging from the typical fabrication and characterization methods to the novel physical properties and the emergent slidetronics and twistronics device prototyping. The main emphasis is on the critical role of stacking orders affecting the interlayer charge transfer, orbital coupling and flat band formation for the design of innovative materials with on-demand quantum properties and surface potentials. By demonstrating a correlation between the stacking configurations and device functionality, we highlight their implications for next-generation electronic, photonic and chemical energy conversion devices. We conclude with our perspective of this exciting field including challenges and opportunities for future stacking order engineering research.

Twistronics of Kekulé Graphene: Honeycomb and Kagome Flat Bands.

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.

Effect of Fermi surface topology change on the Kagome superconductor CeRu2 under pressure

The cubic Laves phase compound CeRu2 with a Kagome substructure of Ru has been investigated to understand myriad fascinating phenomena resulting from competition among its various physical and geometric features. Such phenomena include flat bands, van Hove singularities, Dirac cones, reentrant superconductivity, magnetism, the Fulde–Ferrell–Larkin–Ovchinnikov state, valence fluctuations, time-irreversible anisotropic s-state superconductivity, etc. Extensive studies have thus been carried out since 1958 when the highly unusual coexistence of superconductivity and ferromagnetism was proposed for the mixed compounds (Ce,Gd)Ru2. Activity has accelerated in recent years due to increasing interest in topological states in superconductors. However, there has been little investigation of the mutual influence of these fascinating states. Therefore, we systematically investigated the superconductivity and possible Fermi surface topological change in CeRu2via magnetic, resistivity, and structural measurements under pressure up to ∼168 GPa. An unusual phase diagram that suggests an intriguing interplay between the compound's superconducting order and Fermi surface topological order has been constructed. A resurgence in its superconducting transition temperature was observed above 28 GPa. Our experiments have identified a structural transition above 76 GPa and a few tantalizing phase transitions driven by high pressure. Our high-pressure results further suggest that superconductivity and Fermi surface topology in CeRu2 are strongly intertwined.

Enhanced Electrochemical Activity Volcanoes in Flat-Band Twisted Trilayer Graphene

Electrochemical reactions at electrode-electrolyte interfaces are often controlled by modifying the substrate and thereby tuning the adsorption energy to reach peaks of activity volcanoes. In this work, we attempt to enhance interfacial charge transfer kinetics through modifying the electronic density of states of an electrode which offers highly tunable flat bands such as the twisted graphene system, allowing greater overlap with the redox couple states. Correspondingly, we develop a twist-dependent electrochemical activity map, combining a tight-binding electronic structure model with modified Marcus-Hush-Chidsey kinetics in trilayer graphene. We identify a counterintuitive rate enhancement region spanning the magic angle curve and incommensurate twists of the system geometry. At room temperature, we find a broad activity peak with a ruthenium hexamine redox couple in regions corresponding to both magic angles and incommensurate angles, a result qualitatively distinct from the twisted bilayer case. Flat bands and incommensurability offer new avenues for reaction rate enhancements in electrochemical transformations.

Separating the Effects of Band Bending and Covalency in Hybrid Perovskite Oxide Electrocatalyst Bilayers for Water Electrolysis

Testing single crystalline epitaxial thin films as model systems for metal oxide electrocatalysts in the oxygen evolution reaction (OER) enables differentiating the OER descriptors such as crystal facet orientation, surface chemical composition, electronic structure and band bending at the interface to the electrolyte [1,2,3]. We designed single crystalline perovskite oxide bilayer structures to systematically tune the surface electronic structure and the band bending at the electrode/electrolyte interface to understand their role in the OER.The Co−O covalency in perovskite oxide cobaltites such as La1 − x SrxCoO3 is believed to impact the electrocatalytic activity during the OER. Additionally, space charge layers through band bending at the interface to the electrolyte may affect the electron transfer into the electrode, complicating the analysis and identification of true OER activity descriptors. Here, we separate the influence of covalency and band bending in hybrid epitaxial bilayer structures of highly OER-active La0.6Sr0.4CoO3 and undoped and less-active LaCoO3. Ultrathin LaCoO3 capping layers of 2−8 unit cells on La0.6Sr0.4CoO3 show intermediate OER activity between La0.6Sr0.4CoO3 and LaCoO3 evidently caused by the increased surface Co−O covalency compared to single LaCoO3 as detected by X-ray photoelectron spectroscopy. A Mott−Schottky analysis revealed low flat band potentials for different LaCoO3 capping layer thicknesses, indicating that no limiting extended space charge layer exists under OER conditions as all catalyst bilayer films exhibited hole accumulation at the surface [1].The combined X-ray photoelectron spectroscopy and Mott−Schottky analysis of atomically defined bilayer structures thus enables us to differentiate between the influence of the covalency and intrinsic space charge layers, which are indistinguishable in a single physical or electrochemical characterization. Our results emphasize the prominent role of transition metal oxygen covalency in perovskite electrocatalysts and introduce a bilayer approach to fine-tune the surface electronic structure [1].[1] L. Heymann, M. L. Weber, M. Wohlgemuth, M. Risch, R. Dittmann, C. Baeumer, F. Gunkel (2022) Separating the Effects of Band Bending and Covalency in Hybrid Perovskite Oxide Electrocatalyst Bilayers for Water Electrolysis, ACS Appl. Mater. Interfaces[2] M. Wohlgemuth, M. L. Weber, L. Heymann, C. Baeumer, F. Gunkel (2022) Activity-Stability Relationships in Oxide Electrocatalysts for Water Electrolysis, Front. Chem.[3] M. L. Weber, G. Lole, A. Kormanyos, A. Schwiers, L. Heymann, F. D. Speck, T. Meyer, R. Dittmann, S. Cherevko, C. Jooss, C. Baeumer, F. Gunkel, (2022) Atomistic Insights into Activation and Degradation of La0.6Sr0.4CoO3-δ Electrocatalysts under Oxygen Evolution Conditions Figure 1

Hole Extraction Beyond the Depletion Layer in Ge-Doped Hematite Photoanode

As extensively discussed in the literature, photoelectrochemistry water splitting has enormous potential for the generation of green hydrogen. However, to obtain an efficient and economically viable photoelectrochemistry cell, it is necessary to use efficient semiconductor materials from the photogenerated charge separation point of view. In n-type semiconductors, based on transition metal oxides, where the diffusion length (Lp) is small compared to the absorption depth (α-1), i.e., αLp<< 1, the charge separation process will occur in the depletion layer region. Since this layer is typically tens of nanometers in size, only a fraction of the material exposed to light will contribute to the water photo-oxidation process, thus drastically restricting the efficiency of these semiconductor oxides. Hematite (α-Fe2O3) is an n-type semiconductor oxide widely explored as a photoanode for water photo-oxidation and is known to be a material dominated by the charge separation process in the depletion layer, following the Gartner-Butler model. In this way, we will only have photocurrent in Vappl>Vfb (Vappl is the applied potential, and Vfb is the flat band potential). Here we will explore the possibility of extracting holes at potentials smaller than Vfb in Ge-doped hematite photoanodes through rigorous measurements of Vfb and absorbed photon-to-current conversion efficiency (APCE) as a function of Vappl. We determined Vfb based on the Gartner–Butler analysis in the presence of a sacrificial reagent (H2O2) under different wavelength excitation and observed a dependence of the Vfb with the wavelength. The APCE measurements as a function of Vappl-Vfb clearly show the existence of photocurrent at potentials below Vfb, strongly suggesting that we are extracting holes even before the formation of the depletion layer (before the band bending). We estimate that the holes arrive from a region approximately 3nm close to the electrolyte-semiconductor interface. This phenomenon was only observed for Ge-doped hematite and not for pristine hematite.

Spin and charge persistent currents in a Kane Mele α-T 3 quantum ring

We conduct a thorough study of different persistent currents in a spin-orbit coupled α-T 3 (pseudospin-1) fermionic quantum ring (QR) that smoothly interpolates between graphene (α = 0, pseudospin-1/2) and a dice lattice (α = 1, pseudospin-1) in presence of an external perpendicular magnetic field. In particular, we have considered effects of intrinsic (ISOC) and Rashba spin-orbit couplings (RSOC) that are both inherent to two dimensional quantum structures and yield interesting consequences. The energy levels of the system comprise of the conduction bands, valence bands, and flat bands which show non-monotonic dependencies on the radius, R of the QR, in the sense that, for small R, the energy levels vary as 1/R , while the variation is linear for large R. The dispersion spectra corresponding to zero magnetic field are benchmarked with those for finite fields to enumerate the role played by the spin–orbit coupling terms therein. Further, it is noted that the flat bands demonstrate dispersive behavior, and hence is able to contribute to the transport properties only for finite ISOC. Moreover, RSOC yields spin-split bands, thereby contributing to the spin-resolved currents. The charge and the spin-polarized persistent currents are hence computed in presence of these spin-orbit couplings. The persistent currents in both the charge and spin sectors oscillate as a function of the magnetic field with a period equal to the flux quantum, as they should be; although they now depend upon the spin–orbit coupling parameters. Interestingly, the ISOC distorts the current profiles, owing to the distribution of the flat band caused by it, whereas RSOC alone preserves the flat band and hence a perfect periodicity of the current characteristic is maintained. Further, we have explored the role played by the parameter α in our entire analysis to enable studies while interpolating from graphene to a dice lattice.

Low-threshold single-mode nanowire array flat-band photonic-crystal surface-emitting lasers with high-reflectivity bottom mirrors.

A Si-based nanowire array photonic-crystal surface-emitting laser based on a flat band is designed and simulated. By introducing an air gap between the nanowire and substrate, the bottom reflectivity is significantly enhanced, resulting in much lower threshold and smaller cutoff diameter. Through adjusting the lattice constant (the distance between neighboring nanowires) and nanowire diameter, a photonic crystal structure with a flat band is achieved, in which strong interaction between light and matter occurs in the flat band mode. For the device with a small size, single-mode lasing is obtained with a side-mode suppression ratio of 21 dB, high quality factor of 3940, low threshold gain of 624 cm-1, and small beam divergency angle of ∼7.5°. This work may pave the way for the development of high-performance Si-based surface-emitting nanolasers and high-density photonic integrated circuits.

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.

Visualizing the localized electrons of a kagome flat band

Visualizing the localized electrons of a kagome flat band

Trans-dimensionality of electron/hole channels in multilayer in-plane heterostructures comprising graphene and hBN superlattice

Abstract Using density functional theory, we investigated trilayer in-plane heterostructures consisting of graphene and hBN strips in terms of their interlayer stacking arrangements. The trilayer hBN/graphene superlattices possess flat dispersion bands at their band edges, the wave function distribution of which strongly depends on the interlayer stacking arrangement. The wave functions of the valence and conduction band edges of the trilayer heterostructure with AA’ stacking are distributed throughout the layers implying a two-dimensional carrier distribution. In contrast, we found one-dimensional carrier channels along the border between graphene and hBN for electrons and holes in the trilayer heterosheet with rhombohedral interlayer stacking. These unique carrier distributions are ascribed to the interlayer dipole moment arising from asymmetric arrangements of B and N atoms across the layers. Therefore, the trilayer in-plane heterostructures of graphene and hBN superlattice possess trans-dimensional carriers in terms of their interlayer stacking arrangement.

Real-space tight-binding model for twisted bilayer graphene based on mapped Wannier functions

Twisted multi-layer heterostructures have been considered a platform for studying highly correlated many-particle systems, hosting the emerging phenomena of correlation physics. Electronic structure calculations of such materials which mainly focused on Twisted Bilayer Graphene (TBG) in the framework of the independent-electron approximation, despite the complexity, accurately match the experimental results around the Fermi level. Here, we present a convenient real space π-bands tight-binding model to calculate the band structure of TBG based on the Wannier interlayer hopping parameters obtained from non-twisted bilayer graphene. Our approach is based on mapping hopping parameters onto the real space TBG interlayer couplings, using Radial Basis Function (RBF) interpolation method. This accurate mapping, naturally, transfers all the symmetries and orbital shape features of the bilayer graphene lattice to the TBG lattice and preserves coupling orientation dependencies in addition to distance dependencies. The importance of this fact is explained by showing the effect of the threefold rotation symmetry of AB′ interlayer coupling on the flat band of the TBG band structure. In addition, due to real space study, the model gives us a comprehensive and intuitive view of the role of each interlayer orbital coupling in the TBG band structure and the structural variation relative to twisting.

Electronic Structures of Kitaev Magnet Candidates RuCl3 and RuI3.

Layered honeycomb magnets with strong atomic spin-orbit coupling at transition metal sites have been intensively studied for the search of Kitaev magnetism and the resulting non-Abelian braiding statistics. α-RuCl3 has been the most promising candidate, and there have been several reports on the realization of sibling compounds α-RuBr3 and α-RuI3 with the same crystal structure. Here, we investigate correlated electronic structures of α-RuCl3 and α-RuI3 by employing first-principles dynamical mean-field theory. Our result provides a valuable insight into the discrepancy between experimental and theoretical reports on transport properties of α-RuI3, and suggests a potential realization of correlated flat bands with strong spin-orbit coupling and a quantum spin-Hall insulating phase in α-RuI3.

Giant Correlated Gap and Possible Room-Temperature Correlated States in Twisted Bilayer MoS_{2}.

Moiré superlattices have emerged as an exciting condensed-matter quantum simulator for exploring the exotic physics of strong electronic correlations. Notable progress has been witnessed, but such correlated states are achievable usually at low temperatures. Here, we report evidence of possible room-temperature correlated electronic states and layer-hybridized SU(4) model simulator in AB-stacked MoS_{2} homobilayer moiré superlattices. Correlated insulating states at moiré band filling factors v=1, 2, 3 are unambiguously established in twisted bilayer MoS_{2}. Remarkably, the correlated electronic state at v=1 shows a giant correlated gap of ∼126 meV and may persist up to a record-high critical temperature over 285K. The realization of a possible room-temperature correlated state with a large correlated gap in twisted bilayer MoS_{2} can be understood as the cooperation effects of the stacking-specific atomic reconstruction and the resonantly enhanced interlayer hybridization, which largely amplify the moiré superlattice effects on electronic correlations. Furthermore, extreme large nonlinear Hall responses up to room temperature are uncovered near correlated electronic states, demonstrating the quantum geometry of moiré flat conduction band.

Flat-band localization and interaction-induced delocalization of photons

Lattices with dispersionless, or flat, energy bands have attracted substantial interest in part due to the strong dependence of particle dynamics on interactions. Using superconducting circuits, we experimentally study the dynamics of one and two particles in a single plaquette of a lattice whose band structure consists entirely of flat bands. We first observe strictly localized dynamics of a single particle, the hallmark of all-bands-flat physics. Upon initializing two particles on the same site, we see an interaction-enabled delocalized walk across the plaquette. We further find localization in Fock space for two particles initialized on opposite sides of the plaquette. These results mark the first experimental observation of a quantum walk that becomes delocalized due to interactions and establishes a key building block in superconducting circuits for studying flat-band dynamics with strong interactions.

Weak electronic correlations observed in magnetic Weyl Semimetal Mn3Ge

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, we systematically studied the electronic band structure of Mn3Ge in the vicinity of the Fermi level. We observe several bands crossing the Fermi level, confirming the metallic nature of the studied system. We further observe several flat bands along various high symmetry directions, consistent with the DFT calculations. The calculated partial density of states suggests a dominant Mn 3d orbital contribution to the total valence band DOS. With the help of orbital-resolved band structure calculations, we qualitatively identify the orbital information of the experimentally obtained band dispersions. Out-of-plane electronic band dispersions are explored by measuring the ARPES data at various photon energies. Importantly, our study suggests relatively weaker electronic correlations in Mn3Ge compared to Mn3Sn.

Improvement in the efficiency of solar cells based on the ZnSnN2/Si structure

This study aims to investigate the different optical properties of the ZnSnN2 absorber layer such as absorption, reflection and transmission coefficients. The effects of the ZnSnN2 absorber layer thickness, temperature,and defect density on electrical parameters such as short circuit current density, open circuit voltage, fill factor and efficiency have also been studied in detail. These factors play an important role in the performance of the ZnO/CdS/ZnSnN2/Si/Mo structure. The highest efficiency of about 23.32 % is achieved without defects in the ZnSnN2 absorber layer, under the 1-sun AM1.5 solar spectrum, by applying the flat band condition and considering the strain values of 0.37 % (ZnSnN2/Cds) and 7.17 % (ZnSnN2/Si). In addition to high efficiency, the ZnSnN2 has a high absorption coefficient. This device will play a crucial role in optoelectronic applications. This structure is a promising candidate for low cost and high efficiency photovoltaic technology.

Kagome and honeycomb flat bands in moiré graphene

Kagome and honeycomb flat bands in moiré graphene