Fractional Coulomb blockade for quasi-particle tunneling between edge channels

Measuring Topological Entanglement Entropy Using Maxwell Relations

Topological entanglement entropy (TEE) is a key diagnostic of topological order, allowing one to detect the presence of Abelian or non-Abelian anyons. However, there are currently no experimentally feasible protocols to measure TEE in condensed matter systems. Here, we propose a scheme to measure the TEE of chiral topological phases, carrying protected edge states, based on a nontrivial connection with the thermodynamic entropy change occurring in a quantum point contact (QPC) as it pinches off the topological liquid into two. We show how this entropy change can be extracted using Maxwell relations from charge detection of a nearby quantum dot. We demonstrate this explicitly for the Abelian Laughlin states, using an exact solution of the sine-Gordon model describing the universal crossover in the QPC. Our approach might open a new thermodynamic detection scheme of topological states also with non-Abelian statistics.

Spin-Selective Equilibration among Integer Quantum Hall Edge Channels

The equilibration between quantum Hall edge modes is known to depend on the disorder potential and the steepness of the edge. Modern samples with higher mobilities and setups with lower electron temperatures call for a further exploration of the topic. We develop a framework to systematically measure and analyze the equilibration of many (up to 8) integer edge modes. Our results show that spin-selective coupling dominates even for non-neighboring channels with parallel spin. Changes in magnetic field and bulk density let us control the equilibration until it is almost completely suppressed and dominated only by individual microscopic scatterers. This method could serve as a guideline to investigate and design improved devices, and to study fractional and other exotic states.

Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers

Quantum Hall interferometers have been used to probe fractional charge and statistics of quasiparticles. We present measurements of a small Fabry-Perot interferometer in which the electrostatic coupling constants which affect interferometer behavior can be determined experimentally. Near the center of the ν = 1/3 state this device exhibits Aharonov-Bohm interference interrupted by a few discrete phase jumps, and Φ0 oscillations at higher and lower magnetic fields, consistent with theoretical predictions for detection of anyonic statistics. We estimate the electrostatic parameters KI and KIL by two methods: using the ratio of oscillation periods in compressible versus incompressible regions, and from finite-bias conductance measurements. We find that the extracted KI and KIL can account for the deviation of the phase jumps from the theoretical anyonic phase θa = 2π/3. At integer states, we find that KI and KIL can account for the Aharonov-Bohm and Coulomb-dominated behavior of different edge states.