The quantum Hall effect is a marvelous thing, a microcosm of all that is strange and beautiful and quantum. The fractional quantum Hall effect supports quasiparticles of fractional charge and exotic statistics. These systems are not just a theorist's fancy and are measurable in lab. Even for properties that are still waiting for conclusive experimental confirmation, we have strong theoretical reasons to assume their existence, giving something for experimentalists to strive for as well. After nearly 40 years, the field isn't closed and can still yield surprises. In this thesis, a number of novel probes of the nature of the topological order existing in these systems are discussed, in particular focussing on the mystery of the \nu=5/2 filling factor. Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. A way is proposed to extract edge velocities from dc transport in a point contact geometry defined by narrow gates. The width of the gates assumes two different sizes at small and large distances from the point contact. The Coulomb interaction across the gates depends on the gate width and affects the conductance of the contact. The conductance exhibits two different temperature dependencies at high and low temperatures. The transition between the two regimes is determined by the edge velocity. An interesting feature of the low-temperature I-V curve is current oscillations as a function of the voltage. The oscillations emerge due to charge reflection from the interface of the regions defined by the narrow and wide sections of the gates. Numerical results suggest that the quantum Hall effect at \nu=5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at \nu=5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.
Zucker, Philip Thomas,
"Novel Probes of Topological Order in the Quantum Hall Effect"
(2017).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0959G17
