Observation of quantum hall effect in graphene using surface acoustic waves

Surface acoustic waves (SAWs) have been used to great effect in GaAs/AlGaAs heterostructures in the contactless measurement of length-scale dependent conductivity in high magnetic fields and low temperatures, where the system enters the QH and FQH regimes. SAWs would appear to be an ideal technique for two-dimensional (2D) heterostructures, where it can be difficult or impossible to make reliable electrical contact, and where there are emergent and engineered lengthscales such as charge density wavelengths and Moire periodicities. However, the quantum transport regime has been inaccessibe due to two main challenges. First, a piezoelectric substrate compatible with high-mobility 2D device fabrication and electrostatic gating needs to be identified. Second, the change in the SAW signal is directly proportional to the sample size, and high-quality exfoliated two-dimensional material devices are two to four orders of magnitude smaller than those used in semiconductor-based 2DESs studies. Here, we report the incorporation of a high-mobility, hexagonal boronitride (hBN)-encapsulated, graphene heterostructure into a SAW resonant cavity patterned on a piezoelectric LiNbO3 substrate. We show that the resonant cavity geometry increases signal-to-noise by two orders of magnitude over the traditional delay-line geometry. We observe strong quantum oscillations in both the cavity frequency and in the linewidth in the quantum Hall regime of graphene as a function of magnetic field and gate voltage. This establishes SAW resonant cavities as a viable technique for performing contactless, wavelength-dependent conductivity measurements in the quantum transport regime of 2D heterostructures.