Investigation of the effect of electron correlation on the transport properties in the bilayer quantum Hall systems

在这项研究中，我们试图从理论上阐明实现什么样的基态，边缘如何行为，层与层间和层内的库仑相互作用如何影响双层系统的输运性质。我们还试图利用所获得的知识来提出实验，以阐明双层系统的基态性质。众所周知，双层体系的行为类似于具有自旋自由的体系。因此，我们首先研究了自旋系统中存在的、将在双层系统中起重要作用的Skyrmion，并得到了描述Skyrmion的波函数。接下来，我们建立了一套规则来描述量子霍尔效应的层次态中不同自旋极化之间的量子相变条件。在量子霍尔态中，边之间的隧穿决定了输运性质，而隧穿取决于基态。因此，我们研究了填充因子为1/(2p1)时隧道效应与基态的关系，得到了反映基态性质的电势依赖关系。这意味着在分数量子霍尔态中，两点电导、纵向电导和霍尔电导存在非线性，我们可以从中提取基态的性质。我们现在正在对层级状态和层间关联必不可少的状态进行研究。顺便说一句，对于单层和三维系统之间的隧穿情况，文的标准边理论与实验之间存在着差异，这种差异的原因还没有得到解释。在本研究中提出的实验中，使用了不同情况下的隧道效应。因此，如果拟议的实验得以进行，将有助于解决这一差异。

In this research we tried to clarify theoretically what kind of ground states are realized, how the edge behaves, how the tunneling between layers and the interlayer and intralayer Coulomb interactions affect the transport properties of the bilayer systems. We also tried to use the knowledge thus obtained to propose experiments to clarify the ground state properties of the bilayer systems. It is known that the bilayer systems behave similarly to that with spin freedom. Therefore, we first investigated skyrmion, which is known to exist in spin systems, and which will play an important role in the bilayer systems, and we obtained the wave function to describe the skyrmion. Next, we established a set of rules to describe the condition of the quantum phase transition between different spin polarization in the hierarchical states of the quantum Hall effect. In the quantum Hall states, tunneling between the edges determine the transport properties, and the tunneling depends on the ground state. So, we investigated how the tunneling depends on the ground states for the filling factor of 1/(2p+1), and we obtained the electric potential dependence, which reflects the properties of the ground state. This means that in the fractional quantum Hall states there are non-linearity in the two-point conductance, longitudinal conductance, and Hall conductance, from which we can extract the properties of the ground state. We are now pursuing investigations for hierarchical states and for the states where interlayer correlation is essential. By the way, there are discrepancies between the standard edge theory by Wen and experiments for the case of tunneling between single layer and three-dimensional system, the origin of the discrepancy being unexplained. In the experiment we have proposed in the present research tunneling in a different situation is used. Therefore, if the proposed experiment will be done, it will help to resolve the discrepancy.