Observation of room-temperature universal conductance fluctuations in ultra-high-quality graphene

Near the Dirac point, graphene is expected to behave like a quantum critical Dirac fluid, the collective plasma of electrons and holes, where collective flow dominates over other momentum-relaxing individual scattering events. In the quantum critical regime, the electrical transport is governed by the electron-electron scattering at the Planckian rate. Here, in this work, we explore the universal conductance fluctuation (UCF) in the quantum critical regime, in contrast to what has been observed for disordered graphene at the low temperature limit. Our noise measurement reveals the quantized nature of conductance fluctuation ~ e²/h near the quantum-critical regime. This observed phenomenon is universal across a wide variety of ultra-clean graphene samples. The origin of the UCF in the high temperature limit is likely to be the collective quantum many-body modes, rather than a single-particle interference phenomenon. The statistics of conductance fluctuations are governed by the principles of random matrix theory. There have been several theoretical efforts made to describe the many-body quantum chaotic phase near the quantum critical point, but no direct experimental evidence has been achieved so far. Thus, our findings are critical towards the development of quantum many-body chaos in condensed matter systems.