Number Of Flat Bands Research Articles

Topological Exact Flat Bands in Two-Dimensional Materials under Periodic Strain.

We study flat bands and their topology in 2D materials with quadratic band crossing points under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for quadratic band crossing points serves as a director potential with angular momentum ℓ=2. We prove that when the strengths of the strain fields hit certain "magic" values, exact flat bands with C=±1 emerge at charge neutrality point in the chiral limit, in strong analogy to magic angle twisted-bilayer graphene. These flat bands have ideal quantum geometry for the realization of fractional Chern insulators, and they are always fragile topological. The number of flat bands can be doubled for certain point group, and the interacting Hamiltonian is exactly solvable at integer fillings. We further demonstrate the stability of these flat bands against deviations from the chiral limit, and discuss possible realization in 2D materials.

Many-body Aharonov-Bohm caging in a lattice of rings

We study a system of a few ultracold bosons loaded into the states with orbital angular momentum $l=1$ of a one-dimensional staggered lattice of rings. Local eigenstates with winding numbers $+l$ and $-l$ form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle $\phi$ of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective $\pi$-flux through the plaquettes. We find non-trivial topological band structures and many-body Aharonov-Bohm caging in the $N$-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle $\phi$ is introduced at an arbitrary lattice periodicity $\Gamma$. For $\Gamma>2$, the $\pi$-flux becomes non-uniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.

Magnon magic angles and tunable Hall conductivity in 2D twisted ferromagnetic bilayers

Twistronics is currently one of the most active research fields in condensed matter physics, following the discovery of correlated insulating and superconducting phases in twisted bilayer graphene (tBLG). Here, we present a magnonic analogue of tBLG. We study magnons in twisted ferromagnetic bilayers (tFBL) with collinear magnetic order, including exchange and weak Dzyaloshinskii-Moriya interactions (DMI). For negligible DMI, tFBL presents discrete magnon magic angles and flat moiré minibands analogous to tBLG. The DMI, however, changes the picture and renders the system much more exotic. The DMI in tFBL induces a rich topological magnon band structure for any twist angle. The twist angle turns to a control knob for the magnon valley Hall and Nernst conductivities. Gapped flat bands appear in a continuum of magic angles in tFBL with DMI. In the lower limit of the continuum, the band structure reconstructs to form several topological flat bands. The luxury of twist-angle control over band gaps, topological properties, number of flat bands, and valley Hall and Nernst conductivities renders tFBL a novel device from fundamental and applied perspectives.

Electronic Structures and Optical Properties of Aluminum in Bulk, Thin Film and Nanoparticulate Forms

The electronic structures of aluminum in bulk, thin film and nanoparticle forms were calculated and compared in order to understand how the optical properties change with the dimensionality of the system. The band structure calculations were performed using the Vienna ab initio simulation package (VASP) based on the density functional theory (DFT)[1] and the projector augmented wave (PAW)-method.[2] We used an exchange-correlation potential Vxc within the generalized gradient approximation (GGA), where Vxc depends on the total electron density ρ(r) and the gradient of ρ(r), namely the Perdew-Burke-Ernzerhof (PBE) functional.[3] The calculated band structure diagrams for each of the three forms are shown in Figure 1. The z-direction was chosen as the direction along which periodicity of the lattice breaks down in going from bulk to thin film structure. In order to describe how the electronic structures of a periodic system evolve with spatial confinement, we have used tetragonal unit cells constructed from the lattice parameters of the conventional fcc unit cell in these calculations. Due to the absence of any bound d-like states, the progression from bands in the bulk to subbands in thin films and discrete energy levels in nanoparticles could be easily followed. Every energy band from the bulk splits into multiple bands for the thin films, referred to as subbands and discrete energy levels for nanoparticles. These subbands of the thin films can be noticed on comparing the lowest band between M and Γ points in the band structure plots of states associated with the bulk and thin films in Figure 1. The discrete structure of the energy levels along the kz -direction can be seen from the dispersion of the subbands along the Γ-Z direction. The nearly parabolic band along the Γ-Z direction in the bulk is replaced by a number of flat bands corresponding to discrete energy levels resulting from the confinement along the Z-direction. The density of states (DOS) and partial density of states (PDOS) were also calculated and will be discussed from the perspective of optical properties of this metal. Figure 2 shows the calculated values of the imaginary part of the dielectric function, ε 2 , as the system changes from bulk to thin film to particle. The free electron contribution is not included, and the peaks are due to interband transitions entirely. For the bulk case, the minor peaks at E > 2 eV appear to be varying randomly and are probably artifacts of calculation. Most likely there are only two meaningful peaks, one being at 0.5 eV and the other at 1.5 eV. For the thin film in the x-direction, ε 2 has a form that is somewhat similar to that seen in the bulk with a slight shift in the lower energy peak. This similarity is expected since the system in not confined in the x- or y-direction. On the other hand, ε 2 for the thin film in the z-direction exhibits a broad peak at ~1 eV and another peak at ~2 eV, which is significantly different from either the bulk or thin film in the x-direction. Finally, Figure 2 also shows ε 2 for the nanoparticles, and with confinement in all directions, the shape of the function differs from both the bulk or thin film case. In this talk, we will discuss the optical properties of this interesting metal based on our calculations, and the effect of spatial confinement.