Coupled nanomechanical resonators are interesting for both fundamental studies and practical applications as they offer rich and tunable oscillation dynamics. At present, the mechanical coupling in such systems is often mediated by a fixed geometry, such as a joint clamping point of the resonators or a displacement-dependent force. Here we show a graphene-integrated electromechanical system consisting of two physically separated mechanical resonators—a hybrid graphene comb-drive actuator system and a suspended silicon beam—that are tunably coupled by the integrated graphene membrane. The graphene membrane, moreover, provides a sensitive electrical read-out for the two resonating systems showing 16 different modes in the frequency range from 0.4 to 24 MHz. In addition, by pulling on the graphene membrane with an electrostatic potential applied to silicon beam resonator, we control the mechanical coupling, quantified by the g-factor, from 20 kHz to 100 kHz. Our results pave the way for coupled nanoelectromechanical systems requiring controllable mechanically coupled resonators.

We developed an impedance bridge that operates at cryogenic temperatures (down to 60 mK) and in perpendicular magnetic fields up to at least 12 T. This is achieved by mounting a GaAs HEMT amplifier perpendicular to a printed circuit board containing the device under test and thereby parallel to the magnetic field. The measured amplitude and phase of the output signal allows for the separation of the total impedance into an absolute capacitance and a resistance. Through a detailed noise characterization, we find that the best resolution is obtained when operating the HEMT amplifier at the highest gain. We obtained a resolution in the absolute capacitance of 6.4 aF/Hz at 77 K on a comb-drive actuator while maintaining a small excitation amplitude of 15 k_BT/e. We show the magnetic field functionality of our impedance bridge by measuring the quantum Hall plateaus of a top-gated hBN/graphene/hBN heterostructure at 60 mK with a probe signal of 12.8 k_BT/e.