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Research on the ground state of non-quantized quantum Hall systems

非量子化量子霍尔系统基态研究

基本信息

批准号：
12640308
负责人：
YOSHIOKA Daijiro
金额：
$ 1.47万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640308/
关键词：
two-dimensional electrons strong magnetic field quantum Hall effect stripe states density matrix renormalization method pairing state by-layer quantum Hall system 半導体電荷密度波状態ウィグナー結晶密度行列繰り込み群法

项目摘要

The first aim of the research was to obtain an comprehensive understanding as to why states at the same even-denominator filling factor have different ground states at various Landau levels. For this aim we performed investigations using the Hartree-Fock meanfield theory and the density matrix renormalization group (DMRG) study, which gives the most include Fermi liquid state, pairing state, and stripe state. Furthermore we clarified how the ground state evolves as we change the filling factor in the third and fourth lowest Landau levels.The second aim of the research was to obtain an understanding of the orientation of the stripe phase. For this aim we performed Hartree-Fock calculation in the presence of an external periodic potential. We clarified that when the external periodic potential that is originated from the surface morphology has period that is longer than that of the stripe state, the stripes orient themselves perpendicular to the external potential. As the cause of the orientation we identified the tendency towards the Wigner crystallization as the origin. Namely, it causes modulation of the stripe, and forms an energy gap at the Fermi level. Then compressibility acquires anisotropy that causes the orientation of the stripe.Furthermore, we investigated how the pairing state in the second lowest Landau level evolves when the layer separation is increased in a bi-layer systems. Thus we obtained an phase diagram on the layer-separation and the inter-layer tunneling strength.Apart from these investigations, we investigated the ground state at total filling one. For these investigations we obtained various new findings. We are planning to publish these results in the near future.

研究的第一个目的是获得一个全面的理解，为什么在相同的偶数分母填充因子的国家有不同的基态在不同的朗道水平。为此，我们使用Hartree-Fock平均场理论和密度矩阵重整化群（DMRG）研究进行了调查，其中最包括费米液态，配对状态，和条纹状态。此外，我们还阐明了在第三和第四最低朗道能级上，当我们改变填充因子时，基态是如何演变的。研究的第二个目的是了解条纹相的取向。为此，我们进行了Hartree-Fock计算中存在的外部周期性的潜力。我们澄清，当源自表面形态的外部周期性电位的周期长于条纹状态的周期时，条纹本身垂直于外部电位取向。作为取向的原因，我们确定了维格纳结晶的趋势作为起源。也就是说，它引起条纹的调制，并在费米能级处形成能隙。此外，我们还研究了在双层系统中，当层间距增大时，次低朗道能级对态的演化。得到了层间分离和层间隧穿强度的相图。此外，我们还研究了完全填充时的基态。在这些研究中，我们获得了各种新的发现。我们计划在不久的将来公布这些结果。