Topological Flat Bands Research Articles

Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices

Inducing topological flat bands in bilayer graphene with electric and magnetic superlattices

Identification of graphite with perfect rhombohedral stacking by electronic Raman scattering

Rhombohedral graphite (RG) shows strong correlations in its topological flat band and is pivotal for exploring emergent, correlated electronic phenomena. One key advantage is the enhancement of electronic interactions with the increase in the number of rhombohedrally stacked graphene layers. Increasing thickness also leads to an exponential increase in the number of stacking configurations, necessitating a precise method to identify flawless rhombohedral stackings. Overcoming this challenge is difficult because the established technique for stacking sequence identification, based on phonon originated Raman processes (e.g. the 2D peak), fails in thick RG samples. We demonstrate that the strong layer dependence of the band structure can be harnessed to identify RG without stacking faults. For thicknesses ranging from 3 to 12 layers, we show that each perfect RG structure presents distinctive peak positions in electronic Raman scattering (ERS), directly fingerprinting the flawless stacking. This measurement can be carried out using a conventional confocal Raman spectrometer at room temperature, using visible excitation wavelengths. Consequently, this overcomes the identification challenge by providing a simple and fast optical measurement technique, thereby helping to establish RG as a platform for studying strong correlations in one of the simplest crystals possible.

Persistent flat band splitting and strong selective band renormalization in a kagome magnet thin film.

Magnetic kagome materials provide a fascinating playground for exploring the interplay of magnetism, correlation and topology. Many magnetic kagome systems have been reported including the binary FemXn (X = Sn, Ge; m:n = 3:1, 3:2, 1:1) family and the rare earth RMn6Sn6 (R = rare earth) family, where their kagome flat bands are calculated to be near the Fermi level in the paramagnetic phase. While partially filling a kagome flat band is predicted to give rise to a Stoner-type ferromagnetism, experimental visualization of the magnetic splitting across the ordering temperature has not been reported for any of these systems due to the high ordering temperatures, hence leaving the nature of magnetism in kagome magnets an open question. Here, we probe the electronic structure with angle-resolved photoemission spectroscopy in a kagome magnet thin film FeSn synthesized using molecular beam epitaxy. We identify the exchange-split kagome flat bands, whose splitting persists above the magnetic ordering temperature, indicative of a local moment picture. Such local moments in the presence of the topological flat band are consistent with the compact molecular orbitals predicted in theory. We further observe a large spin-orbital selective band renormalization in the Fe spin majority channel reminiscent of the orbital selective correlation effects in the iron-based superconductors. Our discovery of the coexistence of local moments with topological flat bands in a kagome system echoes similar findings in magic-angle twisted bilayer graphene, and provides a basis for theoretical effort towards modeling correlation effects in magnetic flat band systems.

Correlated topological flat bands in rhombohedral graphite

Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here, we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon in situ electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states.

Topological phase transitions and flat bands on a square-octagon lattice

We construct a square-octagon lattice model by considering the nearest-neighbor (NN) hoppings with staggered magnetic fluxes and the next-nearest-neighbor (NNN) hoppings, where zero-Chern-number topological insulator (ZCNTI) phases emerge. At 1/4 filling, by tuning the staggered fluxes and NNN hopping potential, this model supports the phase transition from a Chern insulator (CI) with Chern number C = 2 to a ZCNTI phase. At half filling, we observe that staggered magnetic fluxes can induce a higher-order topological insulator (HOTI) state. Interestingly, the ZCNTI appears at 3/4 filling when considering the NN and NNN hoppings in the absence of staggered fluxes, which has been rarely reported in previous work. Contrary to conventional HOTIs, this ZCNTI phase hosts both robust corner states and gapless edge states which can be identified based on the quantized dipole and quadrupole moments. Additionally, a topological flat band (TFB) with flatness ratio about 24 appears. We further investigate ν = 1/2 fractional Chern insulator (FCI) state when hard-core bosons fill into this TFB model.

Three-component fractional quantum Hall effect in topological flat bands

Three-component fractional quantum Hall effect in topological flat bands

Long-Lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: A Bosonic Kane-Mele Model Platform.

Moiré superlattices based on two-dimensional transition metal dichalcogenides (TMDs) have emerged as a highly versatile and fruitful platform for exploring correlated topological electronic phases. One of the most remarkable examples is the recently discovered fractional quantum anomalous Hall effect (FQAHE) under zero magnetic field. Here, we propose a minimal structure that hosts long-lived excitons-a ubiquitous bosonic excitation in TMD semiconductors-with narrow topological bosonic bands. The nontrivial exciton topology originates from hybridization of moiré interlayer excitons and is tunable by controlling twist angle and electric field. At small twist angle, the lowest exciton bands are isolated from higher energy bands and provide a solid-state realization of the bosonic Kane-Mele model with topological flatbands, which could potentially support the bosonic version of FQAHE.

Designer topological flat bands in one-dimensional armchair graphene antidot lattices

Designer topological flat bands in one-dimensional armchair graphene antidot lattices

Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators

The quantum metric of single-particle wave functions in topological flat bands plays a crucial role in determining the stability of fractional Chern insulating (FCI) states. Here, we unravel that the quantum metric causes the many-body Chern number of the FCI states to deviate sharply from the expected value associated with partial filling of the single-particle topological flat band. Furthermore, the variation of the quantum metric in momentum space induces band dispersion through interactions, affecting the stability of the FCI states. This causes a reentrant transition into the Fermi liquid from the FCI phase as the interaction strength increases. Published by the American Physical Society 2024

From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands.

Symmetry-breaking orders can not only compete with each other, but also be interwined, and the interwined topological and symmetry-breaking orders make the situation more intriguing. This work examines the archetypal correlated flat band model on a checkerboard lattice at filling ν = 2/3 and we find the unique interplay between smectic charge order and topological order gives rise to two novel quantum states. As the interaction strength increases, the system first transitions from a Fermi liquid into FQAH smectic (FQAHS) state, where FQAH topological order coexists cooperatively with smectic charge order with enlarged ground-state degeneracy and interestingly, the Hall conductivity is σxy = ν = 2/3, different from the band-folding or doping scenarios. Further increasing the interaction strength, the system undergoes another quantum phase transition and evolves into a polar smectic metal (PSM) state. This emergent PSM is an anisotropic non-Fermi liquid, whose interstripe tunneling is irrelevant while it is metallic inside each stripe. Different from the FQAHS and conventional smectic orders, this PSM spontaneously breaks the two-fold rotational symmetry, resulting in a nonzero electric dipole moment and ferroelectric order. In addition to the exotic ground states, large-scale numerical simulations are also used to study low-energy excitations and thermodynamic characteristics. We find the onset temperature of the incompressible FQAHS state, which also coincides with the onset of non-polar smectic order, is dictated by the magneto-roton modes. Above this onset temperature, the PSM state exists at intermediate-temperature regime. Although the T = 0 quantum phase transition between PSM and FQAHS is first order, the thermal FQAHS-PSM transition could be continuous. We expect the features of the exotic states and thermal phase transitions could be accessed in future experiments.

Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides.

Van der Waals heterostructures have recently emerged as an exciting platform for investigating the effects of strong electronic correlations, including various forms of magnetic or electrical orders. Here, we perform an unbiased exact diagonalization study of the effects of interactions on topological flat bands of twisted transition metal dichalcogenides (TMDs) at odd integer fillings. For hole-filling ν_{h}=1, we find that the Chern insulator phase, expected from interaction-induced spin-valley polarization of the bare bands, is quite fragile, and gives way to spontaneous multiferroic order-coexisting ferroelectricity and ferromagnetism, in the presence of long-range Coulomb repulsion. We provide a simple real-space picture to understand the phase diagram as a function of interaction range and strength. Our findings establish twisted TMDs as a novel and highly tunable platform for multiferroicity, and we outline a potential route towards electrical control of magnetism in the multiferroic phase.

Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings

Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings

Design of fragile topological flat bands in an optical microcavity array

Design of fragile topological flat bands in an optical microcavity array

Evolution of an Overlapped Bandgap and Topological Flat Bands in a Higher‐Order Valley Photonic Insulator Based on Dendritic Structure

AbstractRobust edge states and corner states in photonic topological insulators provide effective ways to manipulate the propagation of electromagnetic waves. Bandgaps of the previously reported photonic topological insulators are independent of each other. In this paper, a higher‐order valley photonic insulator composed of arrays of dendritic structure is designed. The band structure shows an overlapped bandgap is observed, and the overlapped bandgap divides the band structure into three bandgaps. The evolution of the overlapped bandgap is investigated by changing the geometric parameters and increasing the fractal to break the C3v symmetry drastically. Besides, it is notable that the band structure of the proposed valley photonic insulator is flat bands. It is demonstrated that undistorted transmission can be observed as a plane electromagnetic wave transmits through the proposed valley photonic insulator. The interface consisting of two valley photonic structures with distinct topological nontrivial phases is constructed. Edge states and corner states with strong energy localization are obtained in multi‐band frequencies. Remarkably, two triangular structures with different Wannier center configurations both have corner states in the same bandgap, which does not obey the valley selectivity. The phenomenon is caused by the weak valley locking property due to the overlapped bandgap. The proposed valley photonic insulators are expected to benefit applications in optical devices such as topological lasers.

Rashba-splitting-induced topological flat band detected by anomalous resistance oscillations beyond the quantum limit in ZrTe5

Topological flat bands — where the kinetic energy of electrons is quenched — provide a platform for investigating the topological properties of correlated systems. Here, we report the observation of a topological flat band formed by polar-distortion-assisted Rashba splitting in the three-dimensional Dirac material ZrTe5. The polar distortion and resulting Rashba splitting on the band are directly detected by torque magnetometry and the anomalous Hall effect, respectively. The local symmetry breaking further flattens the band, on which we observe resistance oscillations beyond the quantum limit. These oscillations follow the temperature dependence of the Lifshitz–Kosevich formula but are evenly distributed in B instead of 1/B at high magnetic fields. Furthermore, the cyclotron mass gets anomalously enhanced about 102 times at fields ~ 20 T. Our results provide an intrinsic platform without invoking moiré or order-stacking engineering, which opens the door for studying topologically correlated phenomena beyond two dimensions.

Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers

The observation of zero field fractional quantum Hall analogs in twisted transition metal dichalcogenides (TMDs) asks for a deeper understanding of what mechanisms lead to topological flat bands in two-dimensional heterostructures, and what makes TMDs an excellent platform for topologically ordered phases, surpassing twisted bilayer graphene. To this aim, we explore the chiral limits of massive Dirac theories applicable to C3-symmetric moiré materials, and show their relevance for both bilayer graphene and TMD homobilayers. In the latter, the Berry curvature of valence bands leads to relativistic corrections of the moiré potential that promote band flattening, and permit a limit with exactly flat bands with nonzero Chern number. The relativistic corrections enter as a layer-orbit coupling, analogous to spin-orbit coupling for relativistic Dirac fermions, which we show is non-negligible on the moiré scale. The Berry curvature of the TMD monolayers therefore plays an essential role in the flattening of moiré Chern bands in these heterostructures.

Engineering Flat Bands in Twisted-Bilayer Graphene away from the Magic Angle with Chiral Optical Cavities.

Twisted bilayer graphene (TBG) is a recently discovered two-dimensional superlattice structure which exhibits strongly correlated quantum many-body physics, including strange metallic behavior and unconventional superconductivity. Most of TBG exotic properties are connected to the emergence of a pair of isolated and topological flat electronic bands at the so-called magic angle, θ≈1.05°, which are nevertheless very fragile. In this work, we show that, by employing chiral optical cavities, the topological flat bands can be stabilized away from the magic angle in an interval of approximately 0.8°<θ<1.3°. As highlighted by a simplified theoretical model, time reversal symmetry breaking (TRSB), induced by the chiral nature of the cavity, plays a fundamental role in flattening the isolated bands and gapping out the rest of the spectrum. Additionally, TRSB suppresses the Berry curvature and induces a topological phase transition, with a gap closing at the Γ point, towards a band structure with two isolated flat bands with Chern number equal to 0. The efficiency of the cavity is discussed as a function of the twisting angle, the light-matter coupling and the optical cavity characteristic frequency. Our results demonstrate the possibility of engineering flat bands in TBG using optical devices, extending the onset of strongly correlated topological electronic phases in moiré superlattices to a wider range in the twisting angle.

Atomic layer molecular beam epitaxy of kagome magnet RMn6Sn6 (R = Er, Tb) thin films

Kagome lattices have garnered substantial interest because their band structure consists of topological flat bands and Dirac cones. The RMn6Sn6 (R = rare earth) compounds are particularly interesting because of the existence of the large intrinsic anomalous Hall effect (AHE), which originates from the gapped Dirac cones near the Fermi level. This makes RMn6Sn6 an outstanding candidate for realizing the high-temperature quantum AHE. The growth of RMn6Sn6 thin films is beneficial for both fundamental research and potential applications. However, most of the studies on RMn6Sn6 have focused on bulk crystals, and the synthesis of RMn6Sn6 thin films has not been reported so far. Here, we report the atomic layer molecular beam epitaxy growth, structural and magnetic characterizations, and transport properties of ErMn6Sn6 and TbMn6Sn6 thin films. It is especially noteworthy that TbMn6Sn6 thin films have out-of-plane magnetic anisotropy, which is important for realizing the quantum AHE. Our work paves the avenue toward the control of the AHE using devices patterned from RMn6Sn6 thin films.

Topological Flat Bands in Graphene Super-Moiré Lattices.

Moiré-pattern-based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly studied 2D materials, monolayer graphene has remained an exception. We demonstrate theoretically that a single layer of graphene, when placed between two bulk boron nitride crystal substrates with the appropriate twist angles, can support a robust topological ultraflat band emerging as the second hole band. This is one of the simplest platforms to design and exploit topological flat bands.

Layered kagome compound Na2Ni3S4 with topological flat band

We report structural and electronic properties of Na2Ni3S4, a quasi-two-dimensional compound composed of alternating layers of [Ni3S4]2− and Na+. The compound features a remarkable Ni-based kagome lattice with a square planar configuration of four surrounding S atoms for each Ni atom. Magnetization and electrical measurements reveal a weak paramagnetic insulator with a gap of about 0.5 eV. Our band structure calculation highlights a set of topological flat bands of the kagome lattice derived from the rotated d xz -orbital with C 3 + T symmetry in the presence of crystal-field splitting.