耗散强关联系统的非平衡效应
Non-equilibrium Effects in Dissipative Strongly Correlated Systems
摘要：
当强关联系统被外场驱动而脱离平衡时，新的物理学就出现了。在强相关材料中，在高电场下，根据经验观察到物理性质（如电导率）的显著变化。特别地，电场驱动的金属-绝缘体转变作为各种材料中的阻变效应是公知的，所述材料例如VO $_2$、V $_2$ O $_3$和其它过渡金属氧化物。为了更好地解释这一现象及其内在机制，需要对相互作用电子的非平衡耗散晶格系统进行微观建模。本文利用非平衡格林函数和动力学平均场论建立了一个系统的方法来模拟耗散格点系统的非平衡定态。我们首先建立了一个“最小模型”来描述非相互作用耗散电子晶格中的强场输运。该模型是精确可解的，便于讨论能量耗散和稳态性质。然后将该形式与动态平均场理论相结合，提供了描述相关材料的非平衡稳态的系统框架。利用该方法研究了石墨烯中关联材料、莫特绝缘体和狄拉克电子的强场输运性质。我们集中在电阻开关的微观描述。特别感兴趣的是动态相变过程中的灯丝形成，这已被解释为耗散和莫特物理之间微妙的相互作用的结果。我们还将研究$IV$特性，特别是石墨烯中狄拉克电子的电流饱和。arXiv版本已更新，并进行了微小修改和更正。
英文摘要：
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 the 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 states for dissipative lattice systems 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. The formalism is then combined with Dynamical Mean Field Theory to provide a systematic framework describing the nonequilibrium steady-state of correlated materials. We use the formalism to study the strong-field transport properties of correlated materials, Mott insulators and Dirac electrons in graphene. We concentrate on the microscopic description of resistive switching. Of particular interest is the filament formation during the dynamical phase transition, which has been interpreted as a result of the delicate interplay between dissipation and Mott physics. We will also examine $IV$ characteristics and particularly the current saturation of Dirac electrons in graphene. The arXiv version has been updated with minor modifications and corrections.
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