Research on the Ground State and Transport Properties of Dipole-Type Quantum Hall States

已知偶极型量子霍尔态在以下两种情况下实现，（i）朗道能级填充因子为1/2的单层系统，和（ii）总填充为1的双层系统。在目前的研究中，我们调查了这些情况，而且，我们发现，还有其他的情况下，偶极型相关实现。我们得到了以下结果。1.我们用密度矩阵重整化群（DMRG）方法发现，随着双层膜之间距离的减小，偶极关联不断地从层内关联转变为层间关联。我们试图用平均场理论来描述这些连续的跃迁，以理解其输运性质。由于一个小问题没有得到满意的解决，这项调查还没有发表，但我们已经得到了一些结果，并希望能够在不久的将来发表。在正杂质周围，形成偶极束缚态。电荷分布取决于结合能，并且通过STS（扫描隧道光谱）观察到这种行为。我们计算了两个系统的波函数，结合能和局域态密度，一个是普通的抛物色散和另一个是在石墨烯中实现的线性色散。我们澄清了由于色散的不同而导致的差异，并与实验结果取得了合理的一致.对于密度不同的双层体系，当两层体系的费米能级处于不同的朗道能级时，在较宽的填充因子范围内，偶极关联的发展和新的基态的出现成为可能。到目前为止，我们只得到了定性的结果。为了获得定量结果，正在进行平均场分析。一旦我们获得结果，我们就进行DMRG计算。平均场分析的结果将在不久的将来发表。

It has been known that the dipole-type quantum Hall states are realized in the following two situations,(i) single layer system at Landau level filling factor 1/2, and(ii) bilayer system at total filling 1. In the present investigation We investigated these situations, and furthermore, We found that there are other situations in which the dipole-type correlation is realized. We obtained the following results.1. We have found by DMRG (density matrix renormalization group) technique that the dipolar correlation continuously changes from intralayer correlation to interlayer correlation as the distance between the bilayer is decreased. We tries to describe these continuous transition by a mean field theory to understand the transport properties. Because of a minor problem which is not satisfactorily solved, this investigation has not been published, but We have obtained several results, and hoping to be able to publish in near future.2. Around a positive impurity, dipolar bound states are formed. The charge distribution depends on the binding energy, and this behavior is observed by STS (scanning tunneling spectroscopy). We have calculated wave function, binding energy and local density of states for two systems, one with ordinary parabolic dispersion and the other with linear dispersion realized in graphene. We clarified the difference due to the difference in dispersion, and obtained reasonable agreement with experiment.3. For bilayer systems with different density so that the Fermi level is at different Landau levels in the two layers, dipolar correlation developes and new kind of ground state becomes possible in wider filling factors. Until now we obtained only qualitative results. To obtain quantitaitve results, mean field analysis is underway. Once we obtained the results we proceed to DMRG calculation. The results by the mean field analysis will be published in near future.