LDOS of electron pair and the role of the Pauli exclusion principle.

IF 2.3 4区 物理与天体物理 Q3 PHYSICS, CONDENSED MATTER
Tomasz M Rusin
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Abstract

The local density of states (LDOS) for a pair of non-relativistic electrons, influenced by repulsive Coulomb forces, is expressed in term of one-dimensional integrals over Whittaker functions. The computation of the electron pair's LDOS relies on a two-particle Green's function (GF), a generalization of the one-particle GF applicable to a charged particle in an attractive Coulomb potential. By incorporating electron spins and considering the Pauli exclusion principle, the resulting LDOS consists of two components: one originating from an exchange-even two-particle GF and the other from an exchange-odd two-particle GF. The calculated LDOS reveals its dependence on both inter-electron distance and energy. The pseudo-LDOS, derived from the two-body contribution to the LDOS, is examined. This term ensures complete LDOS suppression atr = 0, exhibiting a limited spatial extent, and the reasons for its emergence are elucidated. It is shown that for energies exceeding the effective Hartree energy and inter-electron distances beyond the effective Bohr radius, the impact of many-body contributions to the LDOS can be disregarded. The induced LDOS for an electron pair subjected to an attractive contact potential in two dimensions is evaluated. At small distancesafrom the potential center, a predicted relative difference in LDOS between even and odd state pair reaches approximately 8%. The calculated LDOS is compared with available experimental findings from a two-dimensional electron gas (2DEG). Both exhibit similar oscillation periods; however, the LDOS of the electron pair decays as1/a3, significantly faster than the1/adecay observed for free electrons in a 2DEG.

电子对的 LDOS 和保利排斥原理的作用。
受库仑斥力影响的一对非相对论电子的局域态密度(LDOS)用惠特克函数的一维积分来表示。电子对 LDOS 的计算依赖于双粒子格林函数 (GF),这是适用于吸引力库仑势中带电粒子的单粒子格林函数的广义化。考虑到电子自旋和保利排斥原理,计算出的 LDOS 由两部分组成:一部分来自交换偶合的双粒子格林函数,另一部分来自交换偶合的双粒子格林函数。计算得出的 LDOS 揭示了它对电子间距离和能量的依赖性。研究还考察了从双体对 LDOS 的贡献推导出的伪 LDOS。该项能确保在 r = 0 时完全抑制 LDOS,但空间范围有限,并阐明了其出现的原因。研究表明,当能量超过有效哈特里能量和电子间距离超过有效玻尔半径时,可以忽略多体贡献对 LDOS 的影响。我们评估了一个电子对在二维空间中受到吸引力接触电势作用时的诱导 LDOS。在离电势中心较小的距离a处,预测偶态和奇态电子对的LDOS相对差异达到约8%。计算得出的 LDOS 与现有的二维电子气(2DEG)实验结果进行了比较。两者表现出相似的振荡周期;然而,电子对的LDOS衰减为1/a3,明显快于在二维电子气(2DEG)中观察到的自由电子的1/a衰减。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Physics: Condensed Matter
Journal of Physics: Condensed Matter 物理-物理:凝聚态物理
CiteScore
5.30
自引率
7.40%
发文量
1288
审稿时长
2.1 months
期刊介绍: Journal of Physics: Condensed Matter covers the whole of condensed matter physics including soft condensed matter and nanostructures. Papers may report experimental, theoretical and simulation studies. Note that papers must contain fundamental condensed matter science: papers reporting methods of materials preparation or properties of materials without novel condensed matter content will not be accepted.
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