Inelastic scattering exponents in two dimensions

The integer quantum Hall (QH) effect is one of the most widely studied physical phenomena in two dimensions. The plateau-plateau transition within this effect can be comprehensively described by the scaling theory, which encompasses three pivotal exponents: the critical exponent κ, the inelastic scattering exponent p and the universal exponent γ. Prior studies have focused on measuring κ and estimating γ, assuming a constant value of 2 across magnetic fields. Here, our work marks an advancement by measuring all three exponents within a single graphene device and a conventional two-dimensional electron system. Our study uniquely determines p across both low and high magnetic fields in the QH regime. Employing a comprehensive analytical approach that includes weak localization, plateau-plateau transitions, and variable range hopping, we have directly determined γ and κ. Our findings reveal a distinct variation in p, shifting from 1 in the low magnetic field regime to 2 near the QH regime in graphene on SiC.