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The square-lattice Hubbard and closely related $t$-$J$ models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group…
We study the largest-angle twisted homo-bilayer (LA-THB) systems, hosting Moir\'eless quasi-crystal (QC) structure. We propose to use these materials to generate high-angular-momentum (HAM) topological superconductivities (TSCs) protected…
Recent investigations of the magnetic properties and the discovery of superconductivity in quasi-one-dimensional triangular lattice organic charge-transfer solids have indicated the severe limitations of the effective 1/2-filled band…
Evidence for correlated insulating and superconducting phases around regions of high density of states was reported in the strongly spin-orbit coupled van-der Waals material twisted tungsten diselenide (tWSe$_2$). We investigate their…
We studied the real space structure of states in twisted bilayer graphene at the `magic angle' $\theta = 1.08^\circ$. The flat bands close to charge neutrality are composed of a mix of `ring' and `center' orbitals around the AA stacking…
Searching for triplet superconductivity has been pursued intensively in a broad field of material science and quantum information for decades. Nevertheless, these novel states remain rare. Within a simplified effective three-orbital model,…
The recent discovery of unconventional superconductivity has pointed to twisted WSe$_2$ bilayer as a versatile platform for studying the correlated and topological phases of matter. Here we analyze the effect of the displacement field and…
Artificially twisted heterostructures of semiconducting transition metal dichalcogenides (TMDs) offer unprecedented control over their electronic and optical properties via the spatial modulation of interlayer interactions and structural…
A half-filled-band Hubbard model on an anisotropic triangular lattice (t in two bond directions and t' in the other) is studied using an optimization variational Monte Carlo method, to consider the Mott transition and superconductivity…
Magic-angle twisted trilayer graphene (MATTG) recently emerged as a highly tunable platform for studying correlated phases of matter, such as correlated insulators and superconductivity. Superconductivity occurs in a range of doping levels…
Understanding the emergence of unconventional superconductivity, where the order parameter deviates from simple isotropic s-wave pairing, is a central puzzle in condensed matter physics. Transition-metal dichalcogenides (TMDCs), though…
It is now well established that superconducting cuprates support a charge density wave state in the so-called underdoped region of their phase diagram. We investigate the possibility of charge order in the square-lattice Hubbard model, both…
Recently, the observation of superconductivity (SC) with $T_c$ $\approx$ 3.6 K in the pressurized 1313 La$_3$Ni$_2$O$_7$ has attracted considerable interest. Here, we systematically investigate the electronic properties and superconducting…
Magic-angle twisted trilayer graphene (MATTG) has emerged as a novel moir\'e material that exhibits both strong electronic correlations and unconventional superconductivity. However, spectroscopic studies of its electronic properties are…
The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small `magic' twist angles has been linked to the existence of nearly-flat bands, which make TBG a fresh playground to…
It has been argued that inhomogeneity generally can enhance superconductivity in the cuprate high-Tc materials. To check the validity of this claim, we study d-wave superconductivity on the checkerboard Hubbard model on a square lattice…
Since the discovery of high-temperature superconductivity in 1986 by Bednorz and Mueller, great efforts have been devoted to finding out how and why it works. From the d-wave symmetry of the order parameter, the importance of…
Metallic transition metal dichalcogenides (TMDs), consisting of H-NbSe$_2$, H-NbS$_2$, H-TaSe$_2$ and H-TaS$_2$, remain superconducting down to a thickness of a single layer. In these materials, thickness affects a variety of properties,…
Heterostructures of two-dimensional transition metal dichalcogenides (TMDs) are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by…
Emergent quantum phases driven by electronic interactions can manifest in materials with narrowly dispersing, i.e. "flat", energy bands. Recently, flat bands have been realized in a variety of graphene-based heterostructures using the…