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Motivated by recent advances in the realization of complex two-dimensional optical lattices, we investigate theoretically the quantum transport of ultracold fermions in an optical kagome lattice. In particular, we focus on its extensively…
Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…
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…
We study non-Hermitian photonic lattices that exhibit competition between conservative and non-Hermitian (gain/loss) couplings. A bipartite sublattice symmetry enforces the existence of non-Hermitian flat bands, which are typically embedded…
Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this…
Topological flat bands (FBs) offer an ideal platform for realizing exotic topological phases, such as fractional Chern insulators, yet their realization with both exact flatness and stable topology in local lattice models has been long…
Kagome metals offer a unique platform for investigating robust electron-correlation effects because of their lattice geometry, flat bands and multi-orbital nature. In the cases with active flat bands, recent theoretical studies have pointed…
Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In…
First-principles electronic structure calculations have been very useful in understanding some of the properties of the new iron-based superconductors. Further explorations of the role of the individual atomic orbitals in explaining various…
Non-Abelian physics, originating from noncommutative sequences of operations, unveils novel topological degrees of freedom for advancing band theory and quantum computation. In photonics, significant efforts have been devoted to developing…
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…
The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including…
We investigate how the multiple bands of fermions on a crystal lattice evolve if a magnetic field is added which does not increase the number of bands. The kagome lattice is studied as generic example for a lattice with loops of three…
Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe$_2$ and multilayer-graphene-based moir\'e heterostructures have captured a tremendous growth of interest. In this work, we propose that rhombohedral multilayer…
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…
Building on the principle of combinatorial gauge symmetry, lattice gauge theories can be formulated with only one- and two-body interactions that ensure the exact realization of the symmetry rather than its approximate emergence in a…
Non-Hermitian physics enriches the topological attributes of non-Abelian systems. Non-Abelian systems characterized by noncommutative braid patterns are associated with intriguing physical features and applications. Non-Abelian braiding of…
Strange metals arise in a variety of platforms for strongly correlated electrons, ranging from the cuprates, heavy fermions to flat band systems. Motivated by recent experiments in kagome metals, we study a Hubbard model on a kagome lattice…
Layered kagome-lattice materials with 3$d$ transition metals provide a fertile playground for studies on geometry frustration, band topology and other novel ordered states. A representative class of materials AV$_3$Sb$_5$ (A=K, Rb, Cs) have…
A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a…