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Hartree-Fock theory of a current-carrying two-dimensional homogeneous electron gas

机译：载流二维均质电子气的Hartree-Fock理论

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摘要

State-of-the-art simulation tools for nonequilibrium quantum transport systems typically take the current-carrier occupations to be described in terms of equilibrium distribution functions characterized by two different electrochemical potentials, while for the description of electronic exchange and correlation, the local density approximation (LDA) to density functional theory is generally used. However, this involves an inconsistency because the LDA is based on the homogeneous electron gas in equilibrium, while the system is not in equilibrium and may be far from it. In this paper, we analyze this inconsistency by studying the interplay between nonequilibrium occupancies obtained from a maximum entropy approach and the Hartree-Fock exchange energy, single-particle spectrum and exchange hole, for the case of a two-dimensional homogeneous electron gas. The current dependence of the local exchange potential is also discussed. It is found that the single-particle spectrum and exchange hole have a significant dependence on the current, which has not been taken into account in practical calculations since it is not captured by the commonly used functionals. The exchange energy and the local exchange potential, however, are shown to change very little with respect to their equilibrium counterparts. The weak dependence of these quantities on the current is explained in terms of the symmetries of the exchange hole.
机译：用于非平衡量子传输系统的最新仿真工具通常采用以两个不同的电化学势为特征的平衡分布函数来描述载流子的占据，而对于电子交换和相关性的描述则是局部密度通常使用密度泛函理论的近似（LDA）。但是，这涉及到一个不一致性，因为LDA是基于处于平衡状态的均质电子气，而系统并非处于平衡状态，并且可能离它很远。在本文中，我们通过研究二维均匀电子气情况下通过最大熵方法获得的非平衡占据与Hartree-Fock交换能，单粒子光谱和交换孔之间的相互作用来分析这种不一致。还讨论了本地交换潜力的当前依赖性。发现单粒子光谱和交换孔对电流有很大的依赖性，在实际计算中没有考虑到这一点，因为它没有被常用的功能捕获。但是，交换能和局部交换势相对于其平衡对应物变化很小。这些量对电流的弱依赖性通过交换孔的对称性来解释。

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