Bilayer twisting as a mean to isolate connected flat bands in a kagome lattice through Wigner crystallization

The physics of flat band is novel and rich but difficult to access. In this regard, recently twisting of bilayer van der Waals(vd W)-bounded two-dimensional(2 D) materials has attracted much attention, because the reduction of Brillouin zone will eventually lead to a diminishing kinetic energy. Alternatively, one may start with a 2 D kagome lattice, which already possesses flat bands at the Fermi level, but unfortunately these bands connect quadratically to other(dispersive)bands, leading to undesirable effects. Here, we propose, by first-principles calculation and tight-binding modeling, that the same bilayer twisting approach can be used to isolate the kagome flat bands. As the starting kinetic energy is already vanishingly small, the interlayer vd W potential is always sufficiently large irrespective of the twisting angle. As such the electronic states in the(connected) flat bands become unstable against a spontaneous Wigner crystallization, which is expected to have interesting interplays with other flat-band phenomena such as novel superconductivity and anomalous quantum Hall effect.     

Anomalous Minimum and Scaling Behavior of Localization Length Near an Isolated Flat Band

Using one‐dimensional tight‐binding lattices and an analytical expression based on the Green's matrix, we show that anomalous minimum of the localization length near an isolated flat band, previously found for evanescent waves in a defect‐free photonic crystal waveguide, is a generic feature and exists in the Anderson regime as well, i.e., in the presence of disorder. Our finding reveals a scaling behavior of the localization length in terms of the disorder strength, as well as a summation rule of the inverse localization length in terms of the density of states in different bands. Most interestingly, the latter indicates the possibility of having two localization minima inside a band gap, if this band gap is formed by two flat bands such as in a double‐sided Lieb lattice.     

Floquet topological phase transitions and chiral edge states in a kagome lattice

The Floquet topological phases and chiral edge states in a kagome lattice under a circularly-polarized driving field are studied. In the off-resonant case, the system exhibits the similar character as the kagome lattice model with staggered magnetic fluxes, but the total band width is damped in oscillation. In the on-resonant case, the degeneracy splitting at the Γ point does not always result in a gap. The positions of the other two gaps are influenced by the flat band. With the field intensity increased, these two gaps undergo closing-then-reopening processes, accompanied with the changing of the winding numbers.     

Itinerant Topological Magnons in SU (2) Symmetric Topological Hubbard Models with Nearly Flat Electronic Bands

We show that a suitable combination of flat-band ferromagnetism,geometry and nontrivial electronic band topology can give rise to itinerant topological magnons.An SU(2) symmetric topological Hubbard model with nearly flat electronic bands,on a Kagome lattice,is considered as the prototype.This model exhibits ferromagnetic order when the lowest electronic band is half-filled.Using the numerical exact diagonalization method with a projection onto this nearly flat band,we can obtain the magnonic spectra.In the flat-band limit,the spectra exhibit distinct dispersions with Dirac points,similar to those of free electrons with isotropic hoppings,or a local spin magnet with pure ferromagnetic Heisenberg exchanges on the same geometry.Significantly,the non-flatness of the electronic band may induce a topological gap at the Dirac points,leading to a magnonic band with a nonzero Chern number.More intriguingly,this magnonic Chern number changes its sign when the topological index of the electronic band is reversed,suggesting that the nontrivial topology of the magnonic band is related to its underlying electronic band.Our work suggests interesting directions for the further exploration of,and searches for,itinerant topological magnons.     

Band structure of two-dimensional square lattice photonic crystals of circular dispersive metamaterial rods

By virtue of the efficiency of the Dirichlet-to-Neumann map method, the details of the band structure of a two-dimensional square lattice photonic crystal composed of dispersive metamaterial circular rods in air background has been studied. We show that there are two flat bands at the band structure of the system for both H-polarization and E-polarization. These flat bands are created around the magnetic resonance frequency, surface plasmon frequency and magnetic surface plasmon frequency. We realized that the modes with frequencies lying above the resonance frequency behave like resonant cavity modes created in a single metallic cylindrical waveguide. While, due to the relatively large and imaginary refractive index of the metamaterial rods at the frequencies lying below the resonance frequency, the modes are localized modes with negligible penetration into the rods. Moreover, the modes are localized at the interface of the cylindrical metamaterial rods and the air background for the frequencies around the surface plasmon frequency and the magnetic surface plasmon frequency.     

The quantum anomalous Hall effect on a star lattice with spin-orbit coupling and an exchange field

We study a star lattice with Rashba spin-orbit coupling and an exchange field and find that there is a quantum anomalous Hall effect in this system, and that there are five energy gaps at Dirac points and quadratic band crossing points. We calculate the Berry curvature distribution and obtain the Hall conductivity (Chern number ν) quantized as integers, and find that ν?=-?1,2,1,1,2 when the Fermi level lies in these five gaps. Our model can be viewed as a general quantum anomalous Hall system and, in limit cases, can give what the honeycomb lattice and kagome lattice give. We also find that there is a nearly flat band with ν?=?1 which may provide an opportunity for realizing the fractional quantum anomalous Hall effect. Finally, the chiral edge states on a zigzag star lattice are given numerically, to confirm the topological property of this system.     

Moiré flat bands of twisted few-layer graphite

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 E_F . 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.     

Detailed study of the flat bands appeared in two-dimensional magnetic photonic crystals with square symmetry

By virtue of the efficiency of the Dirichlet-to-Neumann map method, the details of the band structure of a two-dimensional magnetic photonic crystal having a square array of parallel circular ferrite rods in air background influenced by an external static magnetic field applied in the rod direction has been investigated. We show that there are two sets of flat bands at the band structure of the system for TM-polarization. These flat bands are created around the magnetic surface plasmon frequency and frequency in which the magnetic permeability has singular value. For the frequency around the magnetic surface plasmon, the modes are highly localized at the interface of the cylindrical ferrite rods and air background and also by approaching the modes to the magnetic surface plasmon frequency the localization length decreases and the number of field's nodes increases considerably. Moreover, we realized that the modes with frequencies lying immediately below the singular value act similar to as resonance cavity modes created in a single metallic cylindrical waveguide.     

Orbital ordering and frustration of p-band Mott insulators

We investigate the general structure of orbital exchange physics in Mott-insulating states of p-orbital systems in optical lattices. Orbital orders occur in both the triangular and kagome lattices. In contrast, orbital exchange in the honeycomb lattice is frustrated as described by a novel quantum 120 degrees model. Its classical ground states are mapped into configurations of the fully packed loop model with an extra U(1) rotation degree of freedom. Quantum orbital fluctuations select a six-site plaquette ground state ordering pattern in the semiclassical limit from the "order from disorder" mechanism. This effect arises from the appearance of a zero energy flat band of orbital excitations.     

Flat band localization due to self-localized orbital

We discover a new wave localization mechanism in a periodic wave system, which can produce a novel type of flat band and is distinct from the known localization mechanisms, i.e., Anderson localization and flat band lattices. The first example we give is a designed electron waveguide (EWG) on 2DEG with special periodic confinement potential. Numerical calculations show that, with proper confinement geometry, electrons can be completely localized in an open waveguide. We interpret this flat band localization (FBL) phenomenon by introducing the concept of self-localized orbitals. Essentially, each unit cell of the waveguide is equivalent to an artificial atom, where the self-localized orbital is a special eigenstate with unique spatial distribution. These self-localized orbitals form the flat bands in the waveguide. Such self-localized orbital induced FBL is a general phenomenon of wave motion, which can arise in any wave systems with carefully engineered boundary conditions. We then design a metallic waveguide (MWG) array to illustrate that similar FBL can be readily realized and observed with electromagnetic waves.     

Superfluid states in α–T_3 lattice

The superfluid states of attractive Hubbard model in α–T_3 lattice are investigated. It is found that one usual needs three non-zero superfluid order parameters to describe the superfluid states due to three sublattices. When two hopping amplitudes are equal, the system has particle–hole symmetry. The flat band plays an important role in superfluid pairing near half filling. For example, when the filling factor falls into the flat band, the large density of states in the flat band favors superfluid pairing and the superfluid order parameters reach relatively large values. When the filling factor is in the gap between the flat band and upper band, the superfluid order parameters take small values due to the vanishing of density of states. The superfluid order parameters show nonmonotonic behaviors with the increase of filling factor. At last, we also investigate the edge states with open boundary conditions. It is shown that there exist some interesting edge states in the middle of quasi-particle bands.     

Stability of ferromagnetism in the Hubbard model on the kagome lattice

The Hubbard model on the kagome lattice has highly degenerate ground states (the flat lowest band) in the corresponding single-electron problem and exhibits the so-called flat-band ferromagnetism in the many-electron ground states as was found by Mielke [J. Phys. A 24, L73 (1991)]]. Here we study the model obtained by adding extra hopping terms to the above model. The lowest single-electron band becomes dispersive, and there is no band gap between the lowest band and the other band. We prove that, at half filling of the lowest band, the ground states of this perturbed model remain saturated ferromagnetic if the lowest band is nearly flat.     

Topological quantum phase transitions and topological flat bands on the kagomé lattice

We investigate the topological properties of the tight-binding electrons on the two-dimensional kagomé lattice with two kinds of short-range hopping integral and two kinds of staggered magnetic flux. Considering the nearest-neighbor hopping (t(1)) with the staggered flux parameter φ(1) and the next nearest-neighbor hopping (t(2)) with the staggered flux parameter φ(2), we demonstrate a series of topological quantum phase transitions and find some topological bands with high Chern numbers, when tuning one parameter (t(2) or φ(2)) while the others are fixed. We have also found that, in some parameter regions, the system exhibits interesting topological flat bands with Chern number C =± 1 and a large gap above them, and the flatness ratio can reach a high value of about 170.     

Flat bands and Wigner crystallization in the honeycomb optical lattice

We study the ground states of cold atoms in the tight-binding bands built from p orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at n=1/6 with a sqrt[3] x sqrt[3] structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at n=1/2. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.     

Non-abelian quantum Hall effect in topological flat bands

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.     

Pair Formation of Hard Core Bosons in Flat Band Systems

Hard core bosons in a large class of one or two dimensional flat band systems have an upper critical density, below which the ground states can be described completely. At the critical density, the ground states are Wigner crystals. If one adds a particle to the system at the critical density, the ground state and the low lying multi particle states of the system can be described as a Wigner crystal with an additional pair of particles. The energy band for the pair is separated from the rest of the multi-particle spectrum. The proofs use a Gerschgorin type of argument for block diagonally dominant matrices. In certain one-dimensional or tree-like structures one can show that the pair is localised, for example in the chequerboard chain. For this one-dimensional system with periodic boundary condition the energy band for the pair is flat, the pair is localised.     

Topology of a parity-time symmetric non-Hermitian rhombic lattice

We investigate the topological properties of a trimerized parity–time(PT)symmetric non-Hermitian rhombic lattice.Although the system is PT-symmetric,the topology is not inherited from the Hermitian lattice;in contrast,the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices.The bulk–boundary correspondence is valid and the Bloch bulk captures the band topology.Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach.In addition,the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice.Our findings reveal the topological properties of the??PT-symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases.     

Solitons in One‐Dimensional Lattices with a Flat Band

We investigate the spectral properties of a quasi‐one‐dimensional lattice in two possible dimerisation configurations. Both configurations are characterised by the same lattice topology and the identical spectra containing a flat band at zero energy. We find that, one of the dimerised configuration has similar symmetry to a one‐dimensional chain proposed by Su‐Schrieffer‐Heeger for studying solitons in conjugated polymers. Whereas, the other dimerised configuration only shows non‐trivial topological properties in the presence of chiral‐symmetry breaking adiabatic pumping.     

Strain induced topological transitions in twisted double bilayer graphene

We theoretically study the band structures and the valley Chern numbers of the AB–AB and AB–BA stacked twisted double bilayer graphene under heterostrain effect. In the absence of heterostrain, due to the constrains by the spatial symmetries, the central two flat bands of the AB–AB are topological trivial bands, while in the AB–BA they have a finite Chern number. The heterostrain breaks all the point group symmetries and the constrains are lifted, hence the topological properties of the two arrangements can be tuned by different strain magnitudes ϵ and directions ϕ. The heterostrain has dissimilar impacts on the Chern numbers of the AB–AB and AB–BA, owing to their different band gaps, and these gaps can be modified by a vertical electric field. Our results show that the topological transitions for both arrangements occur in the ϵ range of 0.1%–0.4%, which can be realized in the graphene-based sample.     

Orbital order in Mott insulators of spinless p-band fermions

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.