Unusual renormalization group (RG) flow in strongly-disordered monolayer epitaxial graphene

We present a magneto-transport study on highly disordered, large- area monolayer epitaxial graphene grown on SiC. Quantum Hall-like characteristics are observed even when the sample is in the strongly insulating regime in the sense that the longitudinal resistivity decreases with increasing temperature. Interestingly, the temperature ($T)$-driven (renormalization group (RG)) flow diagram shows unusual features- a cusp-like structure close to ($\sigma_{xy} =\sigma_{xx} ={e^{2}} \mathord{\left/ {\vphantom {{e^{2}} h}} \right. \kern-\nulldelimiterspace} h)$ where the unstable point in the context of modular group symmetry is predicted. Instead of a quantum phase transition characterized by a $T$-independent point, a magnetic-field-independent crossing is observed at diagonal conductivity $\sigma_{xx} \sim {e^{2}} \mathord{\left/ {\vphantom {{e^{2}} h}} \right. \kern-\nulldelimiterspace} h$. Our new experimental results cannot be explained by conventional modular group symmetry and thus suggests further theoretical studies are required.