论文标题
二维电子自能力：远程库仑相互作用
The two-dimensional electron self-energy: Long-range Coulomb interaction
论文作者
论文摘要
远程库仑相互作用的电子能源在理解相互作用电子系统的多体物理学（例如，在金属和半导体中）起着至关重要的作用，并且已经对数十年进行了广泛的研究。实际上，它是物理学中最古老，最受欢迎的身体问题之一。但是，当能量$ \ varepsilon $和温度$ k_ {b} t $相对于彼此（而与Fermi Energy相比，均仍然很小），当能量$ \ varepsilon $和温度$ k_ {b} t $时，缺乏自我能量$ rece $ recreσ^{（r）}（\ Varepsilon，t）$的分析表达式。我们重新审视这个问题并在分析上计算出具有高密度限制的二维电子系统上的群壳上的自我能量|/e_f \ ll r_s $。我们为电子能源的真实和虚构部分提供了精确的高密度分析表达式，任意价值为$ \ varepsilon /k_ {b} t $，在无尺寸的库仑偶联常数$ r_s $中的领先顺序，以及比$ k_ {b} t /r_ r_ s e__ $ ef $ r_ s $ r_ $ r_s $ r_s $ r_s $ r_s $ r_s $ r_s $ r_s $和$ f的领先订单。我们还获得了自我能源的渐近行为$ | \ varepsilon | \ ll k_ {b} t $和$ | \ varepsilon | \ gg k_ {b} t $。高阶术语具有来自$ \ varepsilon $和$ t $的微妙且高度非平凡的化合物对数贡献，解释了为什么尽管有主题的重要性，但为什么从未计算过它们。
The electron self-energy for long-range Coulomb interactions plays a crucial role in understanding the many-body physics of interacting electron systems (e.g. in metals and semiconductors), and has been studied extensively for decades. In fact, it is among the oldest and the most-investigated many body problems in physics. However, there is a lack of an analytical expression for the self-energy $Re Σ^{(R)}( \varepsilon,T)$ when energy $\varepsilon$ and temperature $k_{B} T$ are arbitrary with respect to each other (while both being still small compared with the Fermi energy). We revisit this problem and calculate analytically the self-energy on the mass shell for a two-dimensional electron system with Coulomb interactions in the high density limit $r_s \ll 1$, for temperature $ r_s^{3/2} \ll k_{B} T/ E_F \ll r_s$ and energy $r_s^{3/2} \ll |\varepsilon |/E_F \ll r_s$. We provide the exact high-density analytical expressions for the real and imaginary parts of the electron self-energy with arbitrary value of $\varepsilon /k_{B} T$, to the leading order in the dimensionless Coulomb coupling constant $r_s$, and to several higher than leading orders in $k_{B} T/r_s E_F$ and $\varepsilon /r_s E_F$. We also obtain the asymptotic behavior of the self-energy in the regimes $|\varepsilon | \ll k_{B} T$ and $|\varepsilon | \gg k_{B} T$. The higher-order terms have subtle and highly non-trivial compound logarithmic contributions from both $\varepsilon $ and $T$, explaining why they have never before been calculated in spite of the importance of the subject matter.
