Electronic correlations and fluctuating lattice distortions in vanadium dioxide

Abstract

Metal-insulator transitions in correlated materials are often accompanied by a change of crystal structure. They are commonly described within a coherent lattice approximation, which combines a correlated treatment of the electrons with a lattice represented by one or a few classical distortion coordinates fixed by minimizing an energy. The structural degrees of freedom then carry no entropy of their own, even though the partition of the transition entropy between electrons and lattice is often what decides the transition temperature. Here we develop a stochastic semiclassical extension of dynamical mean-field theory in which correlated electrons and fluctuating lattice distortions are evolved together, extending previous formulations from linear to nonlinear electron-phonon interactions and from a single to several coupled lattice modes. The resulting non-conservative Langevin equations have deterministic forces, damping, and correlated noise generated self-consistently by the interacting electronic subsystem. Applying the approach to a minimal two-orbital model containing the two symmetry-distinct distortions of the monoclinic phase of vanadium dioxide, we find that the two distortions melt at well separated temperatures, giving an insulating, an intermediate metallic, and a high-symmetry phase. The two transitions have different origins: the melting of the dimerization is driven by the coupling to the correlated electrons and is captured already within the coherent lattice approximation, whereas the restoration of the undistorted structure requires the entropy of the fluctuating lattice. Since the electronic subsystem is treated within nonequilibrium dynamical mean-field theory, the framework can be extended in future work to photoexcited systems with nonthermal electronic distributions.