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Quantum particles on a lattice with competing long-range interactions are ubiquitous in physics. Transition metal oxides, layered molecular crystals and trapped ion arrays are a few examples out of many. In the strongly interacting regime,…
In the present work, we consider the excitonic effects in the twisted bilayer graphene (tBLG) within the rotated bilayer Hubbard model. Both, intralayer and interlayer Coulomb interactions have been considered and the half-filling condition…
The recently observed unconventional ferroelectricity in AB bilayer graphene sandwiched by hexagonal Boron Nitride (hBN) presents a new platform to manipulate correlated phases in multilayered van der Waals heterostructures. We present a…
The existence of band gaps in Mott insulators such as perovskite oxides with partially filled 3d shells has been traditionally explained in terms of strong, dynamic inter-electronic repulsion codified by the on-site repulsion energy U in…
We examine the influence of strong on-site Coulomb interactions on instabilities of the metallic state on the square lattice to general forms of bond order. The Mott correlations are accounted for by the auxiliary-boson method, and by…
We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the non-interacting theory at half-filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly…
Based on dynamical cluster approximation (DCA) quantum Monte Carlo simulations, we study the interaction-driven Mott metal-insulator transition (MIT) in the half-filled Hubbard model on the anisotropic two-dimensional triangular lattice,…
In this work, we study the synergistic correlated states in two distinct types of interacting electronic systems coupled by interlayer Coulomb interactions. We propose that this scenario can be realized in a type of Coulomb-coupled…
Manipulation of intrinsic magnetic and electronic structures of graphene nanoflakes is of technological importance. Here we carry out systematic study of the magnetic and electronic phases, and its manipulation in graphene nanoflakes…
The discovery of correlated insulating states in moir\'e heterostructures has renewed the interest in strongly-coupled electron systems where spin and valley (or layer) degrees of freedom are intertwined. In the strong-coupling limit, such…
We show that density-dependent synthetic gauge fields may be engineered by combining periodically modu- lated interactions and Raman-assisted hopping in spin-dependent optical lattices. These fields lead to a density- dependent shift of the…
We theoretically investigate the electronic structures of moir\'{e} superlattices arising in monolayer / bilayer graphene stacked on hexagonal boron nitride (hBN) in presence and absence of magnetic field. We develop an effective continuum…
Many-body effects in condensed matter yield novel quantum states when the electronic density of states is enhanced. A vivid example is flat bands, which suppress kinetic energy and let interactions dominate, when they are filled with an…
For a system of two spatially separated monoatomic graphene layers encapsulated in hexagonal boron nitride, we consider the drag effect between charge carriers in the Fermi liquid regime. Commonly, the phenomenon is described in terms of an…
We study the superlattice minibands produced by the interplay between moir\'e pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moir\'e…
In magic angle twisted bilayer graphene, transport, thermodynamic and spectroscopic experiments pinpoint at a competition between distinct low-energy states with and without electronic order. We use Dynamical Mean Field Theory (DMFT) on the…
We compute the phase diagram of twisted bilayer graphene near the magic angle where the occurrence of flat bands enhances the effects of electron-electron interactions and thus unleashes strongly-correlated phenomena. Most importantly, we…
Quantum geometry of electronic wavefunctions results in fascinating topological phenomena. A prominent example is the intrinsic anomalous Hall effect (AHE) in which a Hall voltage arises in the absence of an applied magnetic field. The AHE…
The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of un-doped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly…
Transition metal dichalcogenide (TMDC) moir\'e superlattices, owing to the moir\'e flatbands and strong correlation, can host periodic electron crystals and fascinating correlated physics. The TMDC heterojunctions in the type-II alignment…