电子双层中量子电容的涨落电动力学
Fluctuation electrodynamics of quantum capacitance in electron bilayers
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中文总结 AI 辅助
本文建立电子双层量子电容的涨落电动力学理论，揭示层间关联通过耦合等离激元贡献电容，且石墨烯双层的层间修正因带间屏蔽异常，可作为层间配对探针。
中文摘要 AI 辅助
电容是相互作用电子的热力学探针，用于测量导体间电荷转移的能量代价，在低维系统中，该代价由交换、关联效应与静电学共同决定。本文针对电子双层（包括半导体量子阱、单层及双层石墨烯器件）的量子电容建立理论，重点研究层间关联的贡献。在泛函积分框架内，研究表明基态能量中与层间距相关的部分，在环图近似下恰好是两张导电片范德瓦尔斯能量的非延迟Lifshitz表达式，其反射振幅由层极化率构成。逆电容的层间修正为该能量对密度的二阶导数，即卡西米尔压缩率。产生镜面间卡西米尔力的零点涨落，在此对应双层的耦合等离激元，其对电容的贡献以闭合形式给出，具有普适系数；该系数的符号表明，层间关联在高密度下会阻碍电荷积累。Gell-Mann-Brueckner分析给出了普适函数形式的精确高密度极限。对于石墨烯，研究发现单层遵循电子气体模型，而双层石墨烯表现反常：在实验相关的层间距范围内，带间屏蔽使修正量降低数个数量级并反转其符号。本文明确了该理论的适用范围，指出在稀薄维格纳晶体区及激子凝聚附近的电子-空穴双层区，电容可作为层间配对的探针。
英文摘要
Capacitance is a thermodynamic probe of interacting electrons: it measures the energy cost of moving charge between conductors, and in low-dimensional systems this cost is shaped by exchange and correlation as much as by electrostatics. We develop a theory of the quantum capacitance of electron double layers, semiconductor quantum wells as well as monolayer and bilayer graphene devices, focusing on the contribution generated by interlayer correlations. Within a functional-integral formulation we show that the separation-dependent part of the ground-state energy is, at the level of ring diagrams, exactly the nonretarded Lifshitz expression for the van der Waals energy of two conducting sheets, with reflection amplitudes built from the layer polarizabilities. The interlayer correction to the inverse capacitance is the second density derivative of this energy: a Casimir compressibility. The zero-point fluctuations that generate Casimir forces between mirrors are here the coupled plasmons of the bilayer, and their contribution to the capacitance is obtained in closed form, with a universal coefficient; its sign shows that interlayer correlations oppose charging at high density. A Gell-Mann-Brueckner analysis gives the exact high-density limit in terms of universal functions. For graphene we find that monolayers follow the electron-gas template, while bilayer graphene is anomalous: interband screening suppresses the correction by orders of magnitude and reverses its sign in the experimentally relevant range of separations. We delineate the limits of the theory, identifying the dilute Wigner-crystal regime and electron-hole double layers near exciton condensation as regimes where the capacitance becomes a probe of interlayer pairing.
