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We demonstrate from a fundamental perspective the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. Remarkably, we find a robust presence and connection with pairs of…
We propose loading trapped ions into microtraps formed by an optical lattice. For harmonic microtraps, the Coulomb coupling of the spatial motions of neighboring ions can be used to construct a broad class of effective short-range…
We give an overview of recent work on charge degrees of freedom of strongly correlated electrons on geometrically frustrated lattices. Special attention is paid to the checkerboard lattice, i.e., the two-dimensional version of a pyrochlore…
Correlated electron systems with topological flat bands show great promise in exploring exotic quantum phenomena. However, such crystalline materials remain rare. Here we report the discovery of a novel material, Cs$_3$V$_9$Te$_{13}$, which…
This paper presents a theory of interaction-induced band-flattening in strongly correlated electron systems. We begin by illustrating an inherent connection between flat bands and index theorems, and presenting a generic prescription for…
Correlated ad-atom systems on the Si(111) surface have recently attracted an increased attention as strongly correlated systems with a rich phase diagram. We study these materials by a single band model on the triangular lattice including…
Strongly correlated materials exhibit exotic electronic states arising from the strong correlation between electrons. Dimensionality provides a tuning knob because thinning down to atomic thickness reduces screening effects and enhances…
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…
We study a system of ultra-cold atoms possessing long range interaction (e.g. dipole-dipole interaction) in a one dimensional optical lattice in the presence of a confining harmonic trap. We have shown that for large enough on-site and…
In nearly free electron theory the imposition of a periodic electrostatic potential on free electrons creates the bandstructure of a material, determined by the crystal lattice spacing and geometry. Imposing an artificially designed…
We show that in layered systems with electronic phase separation tendency, the long-range Coulomb interaction can drive the spontaneous formation of unidirectional superlattices of electronic charge in a completely homogeneous crystalline…
We treat elementary excitations, the spin-liquid state, and the anomalous Hall effect (including the quantum one in purely 2D situation) in layered highly correlated systems. The mechanisms of the formation of a topological state associated…
The field of topological electronic materials has seen rapid growth in recent years, in particular with the increasing number of weakly interacting systems predicted and observed to host topologically non-trivial bands. Given the broad…
Electronic flat bands represent a paradigmatic platform to realize strongly correlated matter due to their associated divergent density of states. In common instances, including electron-electron interactions leads to magnetic instabilities…
Kagome lattice has been actively studied for the possible realization of frustration-induced two-dimensional flat bands and a number of correlation-induced phases. Currently, the search for kagome systems with a nearly dispersionless flat…
Recent ultracold atomic gas experiments implementing synthetic spin-orbit coupling allow access to flatbands that emphasize interactions. We model spin-orbit coupled fermions in a one-dimensional flatband optical lattice. We introduce an…
Electronic correlation effects are manifested in quantum materials when either the onsite Coulomb repulsion is large or the electron kinetic energy is small. The former is the dominant effect in the cuprate superconductors or heavy fermion…
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…
Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on…
The Dirac bands and flat bands are difficult to coexist because they represent two extreme ends of electronic properties. However, in this paper, we propose a carbon-Kagome-lattice (CKL) family based on first-principles calculations, and…