Unusual renormalization group (RG) flow and temperature-dependent phase transition in strongly-insulating monolayer epitaxial graphene

By changing the measurement temperature (T), one can vary the effective sample size so as to study the renormalization group (RG) (or T-driven) flow of a semiconductor, a topological insulator, or a graphene device in the complex conductivity plane. Here we report RG flow of large-area, strongly disordered monolayer graphene epitaxially grown on SiC, which becomes insulating as T decreases for zero magnetic field. We observe cusp-like RG flow towards (σ_xy = e²/h, σ_xx = e²/h) where σ_xy and σ_xx are Hall conductivity and diagonal conductivity respectively. Such features, indicative of a fixed-temperature phase transition, have never been observed before and cannot be explained by existing RG models based on a modular symmetry group. Therefore, our results suggest the need for new theoretical models and experimental study leading to an understanding of strongly disordered two-dimensional materials such as graphene, few-layer black phosphorus, WSe₂, and so on.