Abstract

We have studied the effect of temperature and electron–hole mass-asymmetry on pair-correlation functions (PCFs) of a coupled electron–hole bilayer, treating correlations dynamically using the dynamical self-consistent mean-field approach of Singwi, Tosi, Land, and Sjölander. Taking a fixed electron–hole effective mass ratio \(m_h^*/m_e^*=5\), both intra- and interlayer static PCFs are calculated for their dependence on carrier density \(r_{se}\), temperature \(\tau _e\), and interlayer spacing d. Besides, the static wavevector-dependent density susceptibility is obtained to probe the role of these effects on the hitherto existence of density-modulated phases in the bilayer. We find that thermal effects in overall make correlations weaker, but the mass-asymmetry results in stronger correlations both within and across the layers, with the effect being most pronounced in the holes layer. In the strong coupling regime (i.e., large \(r_{se}/\tau _e d\)), the intra- and interlayer PCFs show pronounced in-phase periodic oscillations, typical of a spatially localized phase in the bilayer. Correspondingly, the in-phase component of static density susceptibility is seen to exhibit in the close approach of two layers an apparently diverging peak at a wavevector coincident with the location of sharp peak in the static structure factor, implying the emergence of a density-modulated phase in the bilayer. Parallel to the zero-temperature study, the charge-density-wave (CDW) phase is found to dominate at higher densities, with a cross-over to the Wigner crystal (WC) phase below a critical density. As an interesting result, we find that while thermal effects tend to oppose the formation of density-modulated phase, the electron–hole mass-asymmetry boosted correlations favour it, with the two effects almost cancelling out at \(\tau _e=0.125\), thus resulting in the CDW-WC cross-over at nearly the same critical density as for a zero-temperature mass-symmetric electron–hole bilayer. Our prediction of coupled WC phase is found to be in qualitative agreement with path-integral Monte Carlo simulations.

Graphic abstract

中文翻译：

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电子-空穴双层中的对相关函数和密度调制态：热和质量不对称效应

摘要

我们研究了温度和电子-空穴质量不对称性对耦合的电子-空穴双层的对相关函数（PCF）的影响，使用Singwi，Tosi，Land，和舍兰德。取固定的电子-空穴有效质量比\（m_h ^ * / m_e ^ * = 5 \），就计算层内和层间静态PCF取决于载流子密度\（r_ {se} \），温度\（ \ tau _e \）和层间距d。此外，获得了依赖于静波矢量的密度磁化率，以探讨这些效应对双层中迄今存在的密度调制相的作用。我们发现整体上的热效应使相关性变弱，但质量不对称导致层内和跨层的相关性更强，该效应在空穴层中最为明显。在强耦合状态下（即大\（r_ {se} / \ tau _e d \）），层内和层间PCF表现出明显的同相周期性振荡，这是双层中空间局部相的典型特征。相应地，静态密度敏感性的同相分量在两层的接近中表现出在波矢量处的明显发散峰，与静态结构因子中尖峰的位置重合，这暗示了密度调制的出现。双层中的相。与零温度研究平行，发现电荷密度波（CDW）相在较高密度下占主导地位，在临界密度以下与Wigner晶体（WC）相交叉。有趣的结果是，我们发现，尽管热效应倾向于与密度调制相的形成相反，但电子-空穴质量不对称性增强了相关性，\（\ tau _e = 0.125 \），因此导致CDW-WC穿越的临界密度几乎与零温度质量对称电子-空穴双层的临界密度相同。我们发现耦合的WC相的预测与路径积分的Monte Carlo模拟在质量上是一致的。

图形摘要