Unusual renormalization group (RG) flow and temperature-dependent phase transition in strongly-insulating monolayer epitaxial grapheneElectronic supplementary information (ESI) available. See DOI: 10.1039/c7ra05463g

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 = e 2 / h , σ xx = e 2 / 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, WSe 2 , and so on. 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.