Phase field modeling of metal-insulator transition dynamics in correlated electron materials

Metal insulator transition in correlated electron materials is a complex process which often involves multiple order parameters. In particular, almost all such electronic phase transitions are accompanied by structural distortions. Other degrees of freedom such as spins and orbitals also play an important role in the transformation from metal to insulating phases, and vice versa. The intricate interplay and competition between different ordering tendencies make the modeling of metal-insulator transition a very difficult task. Moreover, several recent nano-imaging experiments have revealed a highly inhomogeneous process for such phase transformations in correlated materials. A complete theoretical description of the metal-insulator transition dynamics thus requires theoretical efforts across multiple spatial and time scales. Macroscopically, the phase-field method has been widely used to investigate phase separation, pattern formation, and nucleation-and-growth phenomena in complex systems. The phase field approach is intimately related to the concept of order parameter for characterizing the different symmetry-breaking phases. However, unlike conventional phase transitions, metal-insulator transition describes a transition between different transport properties, which is not associated with a broken symmetry. Nonetheless, for correlation-driven Mott transition, an Ising-type field, similar to that used to describe liquid-gas transition, can serve as the order parameter, which corresponds to the local density of doubly-occupied atoms. In real materials, this Ising order-parameter couples to other dynamical variables such as elastic strain field. A complete phase-field modeling thus includes the dynamical equations for both the Ising field and other dynamical degrees of freedom.