Kinetic arrest of a disordered first-order phase transition in strained V2O3 thin films

We develop a continuum phenomenological theory for the kinetic arrest (KA) of a first-order phase transition (FOPT), taking the thermal and electric field-driven metal-insulator transition (MIT) in epitaxial V2O3 thin films as a prototype. By defining a coarse-grained mesoscopic order parameter φ(r, t) ≡ 1 − θ(r, t)/θ0 representing the metallic volume fraction coupled to the primary structural monoclinic distortion θ, we formulate a Time-Dependent Ginzburg-Landau (TDGL) framework integrated with a non-local elastic interaction kernel and an Imry-Wortis quenched disorder landscape. We derive an explicit dynamic criterion for the kinetic arrest boundary TK(E) by analyzing the divergence of the intrinsic order-parameter relaxation time relative to experimental observation timescales. Our framework rigorously decouples the thermodynamic driving force from the kinetic activation barrier. We demonstrate that epitaxial substrate-induced clamping elevates local elastic barriers, pinning domain boundaries and stabilizing an arrested, inhomogeneous mosaic of metallic and insulating phases down to cryogenic temperatures. The simulated transformation kinetics exhibit an Avrami exponent suppression to values n < 1, reflecting slow, hindered domain-wall propagation. Furthermore, we examine the effect of an external electric field as an isothermal mechanism that lowers this kinetic barrier, providing a phenomenological description of threshold de-arrest and multi-level resistance states. We critically discuss this electronic barrier-lowering mechanism in comparison with electrothermal Joule heating, establish diagnostic criteria to distinguish them, and contextualize these non-equilibrium dynamics with related phenomena in disordered superconducting films.