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Nearly a century after Wigner's initial proposal, electron crystals are now a topic of intense experimental and theoretical interest. However, most proposed crystalline phases are commensurate and therefore become insulating in the presence…
When the Coulomb interaction dominates over kinetic energy, electrons can crystallize into a Wigner crystal (WC). This paradigmatic correlated electronic phase has been realized in two-dimensional electron gases with parabolic band…
Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent…
Recent experiments showing an integer quantum anomalous Hall effect in pentalayer rhombohedral graphene have been interpreted in terms of a valley-polarized interaction-induced Chern band. The resulting many-body state can be viewed as an…
The jellium model is a paradigmatic problem in condensed matter physics, exhibiting a phase transition between metallic and Wigner crystal phases. However, its vanishing Berry curvature makes it ill-suited for studying recent experimental…
The interplay of electronic interactions and nontrivial topology can give rise to a wealth of exotic quantum states. A notable example is the formation of Wigner crystals driven by strong electron-electron interactions. When these…
Graphene/h-BN has emerged as a model van der Waals heterostructure, and the band structure engineering by the superlattice potential has led to various novel quantum phenomena including the self-similar Hofstadter butterfly states. Although…
When the charge density is sufficiently low, interacting two-dimensional electron gas (2DEG) would undergo a phase transition from homogeneous Fermi liquid to an electronic crystal state, known as Wigner crystal. Besides conventional 2DEG,…
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two dimensional systems were predicted to spontaneously break continuous translation symmetry and form a quantum crystal. Efforts to observe this…
Wigner crystals are a paradigmatic form of interaction driven electronic order. A key open question is how Berry curvature and, more generally, quantum geometry reshape crystallization. The discovery of two-dimensional materials with…
In Bernal bilayer graphene (BBG), a perpendicular displacement field flattens the bottom of the conduction band and thereby facilitates the formation of strongly-correlated electron states at low electron density. Here, we focus on the…
Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moir\'e potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly,…
Transition metal dichalcogenide-based moire superlattices exhibit very strong electron-electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Theoretical studies predict…
Low-disorder two-dimensional electron systems in the presence of a strong, perpendicular magnetic field terminate at very small Landau level filling factors in a Wigner crystal (WC), where the electrons form an ordered array to minimize the…
We study the quantum dynamics of interstitials and vacancies in a two-dimensional Wigner crystal (WC) using a semi-classical instanton method that is asymptotically exact at low density, i.e., in the $r_s\to \infty$ limit. The dynamics of…
We employ large-scale density-matrix renormalization group (DMRG) simulations to investigate the quantum phase diagram of the hole-doped Hubbard model on square lattices. By implementing a diagonally oriented square lattice and…
Proximity orbital and spin-orbital effects of graphene on monolayer transition-metal dichalcogenides (TMDCs) are investigated from first-principles. The Dirac band structure of graphene is found to lie within the semiconducting gap of TMDCs…
Recently the graphene/SiC interface has emerged as a versatile platform for the epitaxy of otherwise unstable, monoelemental, two-dimensional (2D) layers via intercalation. Intrinsically capped into a van der Waals heterostructure with…
In multi-band systems, electrons from different orbitals coexist at the Fermi surface. An attractive interaction among these quasi-particles gives rise to inter-band or hybrid pairs which eventually condense in a superconducting state.…
Semimetals exhibit intriguing characteristics attributed to the coexistence of both electrons and holes. In rhombohedral multilayer graphene, a strong trigonal warping effect gives rise to a semi-metallic state near the Fermi surface,…