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

研究的第一个目的是全面了解为什么具有相同偶数分母填充因子的态在不同的朗道能级上具有不同的基态。为此，我们使用了Hartree-Fock平均场理论和密度矩阵重整化群(DMRG)研究，给出了最多的包括费米液态态、配对态和条纹态。此外，我们还阐明了当我们改变第三和第四最低朗道能级的填充因子时，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，我们在存在外周期势的情况下进行了Hartree-Fock计算。我们阐明了当源于表面形态的外周期势的周期比条纹态的周期长时，条带的取向与外势垂直。作为取向的原因，我们确定了Wigner结晶的趋势是起源。也就是说，它导致条带的调制，并在费米能级上形成能隙。此外，我们还研究了双层系统中第二低朗道能级的配对态是如何随着层间距的增加而演化的。由此，我们得到了层分离和层间隧道强度的相图。在这些研究的基础上，我们研究了全填充基态。对于这些调查，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。

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.