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Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively.…
The interplay of hopping parameters that can give rise to flat bands in consequence of quantum interference in electronic, photonic, and other interesting materials has become an extensively studied topic. Most of the recognized structures…
Flat band systems are currently under intense investigation in quantum materials, optical lattices, and metamaterials. These efforts are motivated by potential realization of strongly correlated phenomena enabled by frustration-induced flat…
Topological electronic flatten bands near or at the Fermi level are a promising avenue towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to the engineered…
We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied…
Flat band materials such as the kagome metals or moir\'e superlattice systems are of intense current interest. Flat bands can result from the electron motion on numerous (special) lattices and usually exhibit topological properties. Their…
When the electronic dispersion in a material is independent of momentum, it gives rise to strongly correlated flat bands, with the single particle energy, quenched. Though the notion of flat bands had been known since long, their…
Theoretical quest of flat-band tight-binding models usually relies on lattice structures on which electrons reside. Typical examples of candidate lattice structures include the Lieb-type lattices and the line graphs. Meanwhile, there can be…
Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive interference of Bloch wavefunctions encoded in pure lattice symmetry. Here, we develop a generic atomic/molecular orbital design principle for FBs in non-LG…
Periodic photonic structures enable precise control over the light-matter interaction through band structure engineering. Certain lattice geometries exhibit dispersionless flat bands, characterized by vanishing group velocity and diverging…
Materials in which atoms are arranged in a pyrochlore lattice have found renewed interest, as, at least theoretically, orbitals on those lattices can form flat bands. However, real materials often do not behave according to theoretical…
Certain lattices with specific geometries have one or more spectral bands that are strictly flat, i.e. the electron energy is independent of the momentum. This can occur robustly irrespective of the specific couplings between the lattices…
Flat electronic bands enhance electron-electron interactions and give rise to correlated states such as unconventional superconductivity or fractional topological phases. However, most current efforts towards flat-band materials discovery…
In recent years, materials with topological flat bands have attracted significant attention due to their association with extraordinary transport properties and strongly correlated electrons. Yet, generic principles linking lattice…
We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different…
Exotic phases of matter emerge from the interplay between strong electron interactions and non-trivial topology. Owing to their lack of dispersion at the single-particle level, systems harboring flat bands are excellent testbeds for…
Interaction in a flat band is magnified due to the divergence in the density of states, which gives rise to a variety of many-body phenomena such as ferromagnetism and Wigner crystallization. Until now, however, most studies of the flat…
The notion of an electronic flat band refers to a collectively degenerate set of quantum mechanical eigenstates in periodic solids. The vanishing kinetic energy of flat bands relative to the electron-electron interaction is expected to…
Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to…