2D materials such as graphene and hexagonal-boron nitride (h-BN), to name a few, when layered on top of each other offer a class of metamaterials with interesting properties. For example, the twisting degree of freedom between two layers has started the field of twistronics. The exceptional attributes of 2D materials like ultra-low mass, robustness, and high tunability make them very suitable for nanoelectromechanical systems (NEMS). Yet the mechanical properties of these heterostructures in the form of NEMS have not been studied extensively. Such 2D NEMS hold promise for various technological applications, namely, ultrafast sensors, actuators, etc. We report fabrication and characterization of h-BN graphene heterostructure-based circular nanoelectromechanical resonators on sapphire substrates. The devices are measured at cryogenic temperatures and exhibit multiple mode frequencies, which are highly tunable with gate voltage. A continuum mechanics model is employed to analyze the transmission (S21) data of the fundamental mode. Parameters like built-in tension obtained from the fit are used to identify the indices (m, n) of higher mechanical modes observed for the device, providing further device characterization. Such 2D NEMS could offer a way to study diverse electronic phenomena such as superconductivity in twisted bilayer graphene (tBLG) heterostructures.

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Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a $\rm{WS}_2$/$\rm{WSe}_2$ heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by measuring exciton diffusion, which remains constant upon increasing pumping intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.

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