Renyi–Wehrl mutual information and phase-space indicators of topological criticality in Xenes under a perpendicular electric field

In this work we develop a phase-space–based information-theoretic framework to quantify delocalization and correlations in two-dimensional Dirac states. The construction relies on the Husimi representation, obtained from canonical coherent states, which associates to each quantum state a positive, normalized quasiprobability distribution in phase space. Within this setting we introduce delocalization diagnostics derived from the Rényi–Wehrl family of entropies, complemented by marginal indicators for each quadrature, and we further propose the second-order Rényi-type mutual information as a direct measure of Husimi non-separability. We apply the formalism to silicene and related Xene systems, where a perpendicular electric field externally controls the effective Dirac mass and drives the transition between topological-insulator and band-insulator phases. We show that the mutual-information indicator exhibits a sharp step-like variation at the electrically tuned critical point, thereby providing a clear informational signature of topological criticality and a unified phase-space characterization of the system’s electrically induced spectral reorganization.