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Flatbands play an important role in correlated quantum matter and have novel applications in photonic lattices. Synthetic magnetic fields and destructive interference in lattices are traditionally used to obtain flatbands. However, such…
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an…
Moir\'e superlattices created by the twisted stacking of two-dimensional crystalline monolayers can host electronic bands with flat energy dispersion in which interaction among electrons is strongly enhanced. These superlattices can also…
Electrons in periodic potentials exhibit oscillatory motion in presence of an electric field. Such oscillations are known as Bloch oscillations. In this article we theoretically investigate the emergence of Bloch oscillations for systems…
We propose a scheme to control and enhance atomic Bloch oscillations via photon-mediated interactions in an optical lattice supported by a standing-wave cavity with incommensurate lattice and cavity wavelengths. Our scheme uses…
Superflow of Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results on the interaction effects in the energy dispersion of the…
We propose a tunable optical setup to engineer topologically nontrivial flat bands in twisted bilayer graphene under circularly polarized light. Using both analytical and numerical calculations, we demonstrate that nearly flat bands can be…
We study the appearance of topological Floquet flat bands in alternating-twist multilayer graphene, which has alternating relative twist angle $\pm\theta$ near the first magic angle. While the system hosts both flat bands and a steep Dirac…
We use a coherent Bragg diffraction method to impart an external momentum to ultracold bosonic atoms trapped in a one-dimensional optical lattice. This method is based on the application of a single light pulse, with conditions where…
Motivated by the observation of polarization superlattices in twisted multilayers of hexagonal boron nitride ($h$-BN), we address the possibility of using these heterostructures for tailoring the properties of multilayer graphene by means…
Photonic flat bands are crucial for enabling strong localization of light and enhancing light-matter interactions, as well as tailoring the angular distribution of emission from photonic structures. These unique properties open pathways for…
The engineering of synthetic dimensions allows for the construction of fictitious lattice structures by coupling the discrete degrees of freedom of a physical system, such as the quantized modes of an electromagnetic cavity or the internal…
Flat bands, characterized by zero group velocity and strong energy localization, enable interaction-enhanced phenomena across both quantum and classical systems. Existing photonic flat-band implementations were limited to evanescent-wave…
Motivated by the recent discovery of Mott insulating phase and unconventional superconductivity due to the flat bands in twisted bilayer graphene, we propose more generic ways of getting two-dimensional (2D) emergent flat band lattices…
The paper presents results of numerical experiments simulating Bloch oscillations of solitons in a deformable molecular chain in a constant electric field. By the example of a homogeneous polynucleotide chain it is shown that the system…
We examine the high-frequency differential conductivity response properties of semiconductor superlattices having various miniband dispersion laws. Our analysis shows that the anharmonicity of Bloch oscillations (beyond tight-binding…
Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strong correlation phenomena. In certain lattices with built-in geometrical frustration, electronic…
We study the effect of twisting on bilayer graphene. The effect of lattice relaxation is included; we look at the electronic structure, piezo-electric charges and spontaneous polarisation. We show that the electronic structure without…
We theoretically investigate the emergence of quantum nonlinearities in the optical response of lattices of two-level quantum emitters coherently driven by a laser. For subwavelength lattice periods, where the system behaves as a quantum…
Existing Quantum Monte Carlo studies have investigated the properties of fermions on a Lieb (CuO$_2$) lattice interacting with an on-site, or near-neighbor electron-electron coupling. Attention has focused on the interplay of such…