Graphene nanomechanical resonators are the thinnest vibrating membranes imaginable, and as such they play an important role in the study of the dynamics of flexural vibrations in two-dimensional systems. This presentation will address two separate research works about graphene resonators that are ongoing in my lab.

The first work addresses the problem of graphene resonators with unconventional boundary conditions. These resonators are often firmly clamped to their supporting substrate, which means that the resonant frequencies of their vibrational modes are fixed. For graphene membranes of various sizes and substrates of various shapes, we often find that resonant frequencies exhibit a hysteretic behavior upon sweeping a dc gate voltage, both at room and at cryogenic temperatures. Having ruled out phase transitions in the membrane, we ascribe this phenomenon to a mechanical process where the resonator slowly and reversibly slides on the substrate. Our work may represent a novel approach to quantifying nanoscale friction between graphene and the substrate, especially at cryogenic temperatures where tribology measurements with an atomic force microscope are challenging.

The second work is about a simple data acquisition system we developed that allows us to perform a variety of nanomechanical measurements using a single platform. These include: (i) the measurement of weakly driven vibrations, including their cross-spectrum in the frequency domain and their vibrational amplitude ringdown in the time domain; (ii) the measurement of the cross-spectrum of vibrations actuated by a force noise; (iii) the measurement of the in-phase and quadrature components of vibrations; and (iv) the measurement in the time domain of vibrational phase modulation induced by high frequency strain modulation. In addition to its flexibility and its versatility, our simple data acquisition system allows us to emulate ordinary instruments that used to be a common occurrence in laboratories but are now difficult to find on the market. This is especially the case for cross-spectrum measuring instruments. Our system may also be useful where access to radio frequency equipment is restricted. As an illustration, we encode a video in a narrow band, digitally modulated radio frequency signal which we use to drive graphene vibrations. The nanomechanical signal is read out with a photo detector and demodulated in software, yielding what we believe may be the first nanomechanical television broadcast.