We show that flat bands can be categorized into two distinct classes, is, singular and nonsingular bands, by exploiting the behavior of their Bloch wave functions in momentum space. In case a band, its function possesses immovable discontinuities generated band-crossing with other thus vector bundle associated band cannot defined. This singularity precludes compact localized states from forming complete set spanning band. Once degeneracy at crossing point is lifted, becomes dispersive...

We investigate Landau level structures of semimetals with nodal ring dispersions. When the magnetic field is applied parallel to plane in which lies, there exist almost nondispersive levels at Fermi (${E}_{F}=0$) as a function momentum along direction inside ring. show that each can be described by Hamiltonian for graphene bilayer fictitious interlayer couplings under tilted field. Near center where in-terlayer coupling negligible, we have Dirac explain appearance zero modes. Although...

The Zak phase $\gamma$, the generalization of Berry to Bloch wave functions in solids, is often used characterize inversion-symmetric 1D topological insulators; however, since its value can depend on choice real-space origin and unit cell, only difference between two regions believed be relevant. Here, we show that one extract an origin-independent part so-called inter-cellular $\gamma^{\mathrm{inter}}$, which as a bulk quantity predict number surface modes follows: neutral finite...

The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one quintessential ideas in physics topological quantum matter. Nevertheless, it has not been proven all generality and certain scenarios even shown to fail, depending on boundary profiles terminated system. Here, we introduce bulk numbers that capture exact number in-gap modes, without any such subtleties spatial dimension. Similarly, based these 1D numbers, define new 2D winding number, which...

We review recent progresses in the study of flat band systems, especially focusing on fundamental physics related to singularity band's Bloch wave functions. first explain that bands can be classified into two classes: singular and non-singular bands, based presence or absence The is generated by crossing with another dispersive band. In band, one find a special kind eigenmodes, called non-contractible loop states robust boundary modes, which exhibit nontrivial real-space topology. Then, we...

Topological properties of lattices are typically revealed in momentum space using concepts such as the Chern number. Here, we study unconventional loop states, namely, noncontractible states (NLSs) and robust boundary modes, mediated by nontrivial topology real space. While play a key role understanding fundamental physics flatband systems, their experimental observation has been hampered because challenge realizing desired conditions. Using laser-writing technique, optically establish...

We propose a band engineering scheme on the biphenylene network, newly synthesized carbon allotrope. illustrate that electronic structure of network can be significantly altered by controlling conditions affecting symmetry and destructive interference wave functions through periodic fluorination. First, we investigate mechanism for appearance type-II Dirac fermion in pristine network. show essential ingredients are mirror symmetries stabilization compact localized eigenstates via...

Abstract Magneto-nonlinear Hall effect is known to be intrinsic and requires time-reversal symmetry. Here we show that a new type of magneto-nonlinear can occur in the breaking materials within second-order response in-plane electric vertical magnetic fields. Such generated by oscillation electromagnetic field has quantum origin arising from geometric quantity associated with Berry curvature band velocity. We demonstrate massive Dirac model LaAlO3/LaNiO3/LaAlO3 well used detect this effect....

Motivated by recent experimental efforts on three-dimensional semimetals, we investigate the static and dynamic density response of nodal line semimetal computing polarizability for both undoped doped cases. The in absence doping is characterized a ring-shape zero energy contour momentum space, which may be considered as collection Dirac points. In case, Fermi surface has torus shape two independent processes transfer contribute to singular features even though only have single surface....

In this work, we develop a systematic method of constructing flat-band models with and without band crossings. Our construction scheme utilizes the symmetry spatial shape compact localized state (CLS) also singularity wave function obtained by Fourier transform CLS (FT-CLS). order to construct model systematically using these ingredients, first choose specific representation in given lattice. Then, FT-CLS indicates whether resulting flat exhibits crossing point or not. A tight-binding...

According to the Onsager's semiclassical quantization rule, Landau levels of a band are bounded by its upper and lower edges at zero magnetic field. However, there two notable systems where level spectra violate this expectation, including topological bands flat with singular crossings, whose wave functions possess some singularities. Here, we introduce distinct class anomalous spreading (LLS) appears outside zero-field energy bounds, although relevant function is nonsingular. The LLS...

Abstract Monolayer MX 2 (M = Mo, W; X S, Se) has recently been drawn much attention due to their application possibility as well the novel valley physics. On other hand, it is also important understand electronic structures of bulk for material applications since very challenging grow large size uniform and sustainable monolayer . We performed angle-resolved photoemission spectroscopy tight binding calculations investigate 2H-MX could extract all band parameters , including gap, direct gap...

We experimentally realize fractal-like photonic lattices by use of the cw-laser-writing technique, thereby observing distinct compact localized states (CLSs) associated with different flatbands in same lattice setting. Such triangle-shaped lattices, akin to first generation Sierpinski possess a band structure where singular non-degenerate and nonsingular degenerate coexist. By proper phase modulation an input excitation beam, we demonstrate not only simplest CLSs but also their...

Geometry of the wave function is a central pillar modern solid state physics. In this work, we unveil wave-function geometry two-dimensional semimetals with band crossing points (BCPs). We show that Berry phase BCPs are governed by quantum metric describing infinitesimal distance between states. For generic linear BCPs, corresponding determined either an angular integral metric, or equivalently, maximum Bloch This naturally explains origin $\pi$-Berry BCP. case quadratic can take arbitrary...

Abstract Noncontractible loop states (NLSs) are a recently realized topological entity in flatband lattices, arising typically from the band touching at point where flat intersects one or more dispersive bands. There exists also across plane, overlaps another all over Brillouin zone without crossing band. Such isolated plane‐touching bands remain largely unexplored. For example, what features associated with such degeneracy? Here, nontrivial NLSs and robust boundary modes system degeneracy...

Abstract A singular flat band (SFB), a distinct class of the band, has been shown to exhibit various intriguing material properties characterized by quantum distance. We present general construction scheme for tight-binding model hosting an SFB, where distance profile can be controlled. first introduce how build compact localized state (CLS), endowing with band-touching point and specific value maximum Then, we develop designing Hamiltonian SFB starting from obtained CLS, desired hopping...

Abstract The anomalous Hall conductivity (AHC) in magnetic materials, resulting from inverted band topology, has emerged as a key adjustable function spin‐torque devices and advanced sensors. Among systems with near‐half‐metallicity broken time‐reversal symmetry, cobalt disulfide (CoS 2 ) proven to be material capable of significantly enhancing its AHC. In this study, the AHC CoS is empirically assessed by manipulating chemical potential through Fe‐ (hole) Ni‐ (electron) doping. primary...

Abstract The bulk-boundary correspondence is an integral feature of topological analysis and the existence boundary or interface modes offers direct insight into structure Bloch wave function. While only topology function has been considered relevant to modes, we demonstrate that another geometric quantity, so-called quantum distance, can also host a bulk-interface correspondence. We consider generic class two-dimensional flat band systems, where parabolic band-crossing with dispersive band....

Flat bands have band crossing points with other dispersive in many systems including the canonical flat models Lieb and kagome lattices. Here we show that some of such degeneracy are unavoidable because symmetry representation (SR) under unitary symmetry. We refer to a point as SR-enforced crossing. is distinct from conventional protected by eigenvalues or topological charges its protection requires both specific flatness band, simultaneously. Even $n$-fold rotation $C_n$ ($n=2,3,4,6$)...

We report the low-frequency noise behaviors in quasi-two-dimensional (quasi-2D) electron systems based on complex oxide heterostructures. First, surface 2D gas (2DEG) SrTiO3 (STO) exhibits 1/fα-type current power spectral density (PSD) with α∼1.39. The non-unity exponent α indicates discrepancy between depth distributions of electrons and oxygen vacancies STO substrate. Second, amorphous LaAlO3/KTaO3 (LAO/KTO) interface, another quasi-2D system, shows Lorentzian components PSD at a...

We theoretically study the spin stiffness of graphene and nanoribbon based on Hubbard-type Hamiltonian. Using Hartree-Fock method with inclusion adiabatic twist, we have obtained effective energy functional investigated magnetic excitations two-dimensional zigzag (ZGNR). analyzed system varying temperature strength on-site Coulomb repulsion. For ZGNR, also studied effect lateral electric field stiffness. As increases, decreases reaches less than half zero-field value. However, remarkably...

Intricate interplay between the periodicity of lattice structure and that cyclotron motion gives rise to a well-known self-similar fractal energy eigenvalue, known as Hofstadter butterfly, for an electron moving in under magnetic field. Connected with $n=0$ Landau level, central band butterfly is especially interesting honeycomb lattice. While entire can be principle obtained by solving Harper's equations numerically, weak-field limit, most relevant experiment, intractable owing fact size...

Abstract We report on quantitative comparison between the electric dipole energy and Rashba band splitting in model systems of Bi Sb triangular monolayers under a perpendicular field. used both first-principles tight binding calculations p-orbitals with spin-orbit coupling. First-principles calculation shows systems. It also asymmetric charge distributions split bands which are induced by orbital angular momentum. calculated energies from coupling distribution external field compared it to...

Abstract In recent years, the spin Hall effect has received great attention because of its potential application in spintronics and quantum information processing storage. However, this is usually studied under external homogeneous electric field. Understanding how inhomogeneous field affects still lacking. Here, we investigate a two-dimensional two-band time-reversal symmetric system give an expression for intrinsic conductivity presence field, which shown to be expressed through geometric...