| Research Abstract |
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.
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