Screening-controlled dynamical criticality in the quantum Hall regime

At continuous electronic phase transitions, Coulomb interactions can modify the relation between length, energy, and temperature, but experimentally disentangling their effects on spatial versus dynamical criticality has remained difficult, since finite-temperature scaling alone measures only the combined exponent $\kappa = 1/(z\gamma)$. Here, we introduce two advances that resolve this limitation. First, by combining temperature scaling with independent current scaling, we separately extract the dynamical exponent $z$ and the localization-length exponent $\gamma$ at the quantum Hall plateau transition -- rather than inferring one from an assumed value of the other. Second, using dual-graphite-gated graphene devices in which the effective Coulomb interaction range is tuned geometrically by the ratio of the magnetic length $l_B$ to the graphite-gate distance $d$, we track this separation across both screened and unscreened interaction regimes within the same device platform. Temperature scaling gives $\kappa \simeq 0.21$ in the screened regime and $\kappa \simeq 0.41$ in the unscreened regime; combining this with current scaling reveals that screening changes $z$ from $\simeq 1$ in the unscreened regime to $\simeq 2$ in the screened regime. In contrast, $\gamma$ remains close to $2.4$ throughout. Our results establish that gate-controlled screening selectively modifies the interaction-dependent dynamical sector of the quantum Hall transition, leaving the localization-length exponent $\gamma$ unchanged within experimental uncertainty. More broadly, this work establishes geometric screening as a versatile tool for controlling interactions and disentangling interaction and disorder effects in correlated two-dimensional systems, including fractional quantum Hall states, moir\'e materials, and other strongly localized electronic phases.