Non-equilibrium Effects in Dissipative Strongly Correlated Systems
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Non-equilibrium phenomena in strongly correlated lattice systems coupling to dissipative environment are studied. Novel physics arises when strongly correlated system is driven out of equilibrium by external fields. Dramatic changes in physical properties, such as conductivity, are empirically observed in strongly correlated materials under high electric field. In particular, electric-field driven metal-insulator transitions are well-known as resistive switching effect in a variety of materials, such as VO 2 , V 2 O 3 and other transition metal oxides. To satisfactorily explain both the phenomenology and its underlying mechanism, it is required to model microscopically the out-of-equilibrium dissipative lattice system of interacting electrons. In this thesis, we developed a systematic method of modeling non-equilibrium steady state of dissipative lattice system by means of Non-equilibrium Green's function and Dynamical Mean Field Theory. We firstly establish a "minimum model" to formulate the strong-field transport in non-interacting dissipative electron lattice. This model is exactly soluble and convenient for discussing energy dissipation and steady-state properties. Non-equilibrium electron distribution and effective temperature naturally emerge as a result of competing electric power and Joule dissipation. Building on this model, we explore the non-equilibrium phase transition in dissipative Hubbard model. Our result verifies the importance of thermal effect in the non-equilibrium interacting system. Correlated metallic systems undergo metal-insulator transition at fields much lower than the quasiparticle energy scale. And the hysteretic $I-V$ relation shows the possibility of spatially inhomogeneous state during non-equilibrium phase transition. In addition, formation of filamentary structures have been widely reported by many experimental groups. In order to further examine the spatial inhomogeneity, we conduct finite-sample simulation in the dissipative Hubbard model with Hartree-Fock approximation. The calculation successfully explains the main experimental features of the non-equilibrium phase transitions, like formation of conductive filament and negative differential resistance, and reveals the underlying electronic mechanism. It also justifies the thermal description that non-equilibrium effective temperature approaches equilibrium transition temperature. Finally, we apply the formulation to strong-field transport of Dirac electrons in graphene, concentrating on current saturation due to electron-phonon interactions. We show the novel momentum distribution of Dirac electrons under strong electric field, which has its origin in Landau-Zener physics. We discuss in detail its relation to the experimentally observed phenomena.