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

我们已经知道，偶极型量子霍尔态是在以下两种情况下实现的：(I)朗道能级填充因子为1/2的单层系统和(Ii)总填充因子为1的双层系统。在本研究中，我们研究了这两种情况，并进一步发现，还有其他情况实现偶极型关联。我们得到了以下结果：1.利用密度矩阵重整化群(DMRG)技术发现，随着双层之间距离的减小，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跃迁，以理解输运性质。由于一个小问题没有得到很好的解决，这项调查尚未公布，但我们已经取得了几个结果，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。电荷分布依赖于结合能，这一行为由扫描隧道谱(STS)观察到。我们计算了两个系统的波函数、束缚能和局域态密度，一个是普通抛物线色散的，另一个是在石墨烯中实现的线性色散的。澄清了由于色散不同而产生的差异，并与实验结果进行了比较，得到了合理的一致性。对于具有不同密度的双层系统，使得两层中的费米能级处于不同的朗道能级，在更大的填充因子下，偶极关联的发展和新的基态成为可能。到目前为止，我们只取得了定性的结果。为了获得量化结果，平均场分析正在进行中。一旦我们得到了结果，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.