Direct measurements of inelastic scattering exponents of monolayer graphene on SiC

The scaling theory of localization provides a comprehensive framework for understanding the transition between the localized and the extended states in the vicinity of the quantum Hall (QH) regime. Prior studies or measurements of the inelastic scattering exponent p in two dimensions, which plays a crucial role in quantum dephasing, mostly extract a magnetic-field-independent p spanning a wide range (1 ≤ p ≤ 4) or determine p indirectly through the relation p=2κγ. Here κ and γ are the critical exponent and the universal exponent, respectively. Therefore, it is highly desirable to measure p at different magnetic fields directly. In this work, we study two different types of graphene devices over a wide range of magnetic fields in both the low and high current regimes. The latter allows us to determine p directly through the current-heating model. We show that p ≈ 2 using current-heating studies in all cases. At high fields, these results are consistent with those determined from p=2κγ in the low current regime. However, a vastly different inelastic scattering exponent p^' ≈ 1 is found in our analysis of weak localisation (WL) in the low-field region. Such an unexpected discrepancy may be explained as follows. In the WL analysis, the electron and phonon systems are in thermal equilibrium so that we probe p^' ≈ 1. In contrast, in the high current regime where there is a substantial difference between the electron effective temperature and the lattice (phonon) temperature, we extract the exponent p ≈ 2. Our results further add mysteries to the seemly well-understood QH systems and quantum dephasing in two dimensions.