Distinguishing particle-hole conjugated fractional quantum Hall states using quantum-dot-mediated edge transport

We study theoretically edge transport of a fractional quantum Hall liquid, in the presence of a quantum dot inside the Hall bar with well-controlled electron density and Landau-level filling factor and show that such transport studies can help reveal the nature of the fractional quantum Hall liquid. In our first example we study the v = 1/3 and v = 2/3 liquids in the presence of a v = 1 quantum dot. When the quantum dot becomes large, its edge states join those of the Hall bar to reconstruct the edge states configuration. Taking randomness around the edges into account, we find that in the disorder-irrelevant phase the two-terminal conductance of the original v = 1/3 system vanishes at zero temperature, while that of the v = 2/3 case remains finite.