Smits, O. and Slingerland, Joost and Simon, Steven H.
(2014)
Tunnelling current through fractional quantum Hall interferometers.
Physical Review B, 89.
045308.
ISSN 1098-0121
Abstract
We calculate the tunnelling current through a Fabry-P�erot interferometer in the fractional quantum
Hall regime. Within linear response theory (weak tunnelling but arbitrary source-drain voltage)
we �nd a general expression for the current due to tunnelling of quasiparticles in terms of Carlson's
R function. Our result is valid for fractional quantum Hall states with an edge theory consisting of
a charged channel and any number of neutral channels, with possibly di�erent edge velocities and
di�erent chiralities. We analyse the case with a single neutral channel in detail, which applies for
instance to the edge of the Moore-Read state. In addition we consider an asymmetric interferometer
with di�erent edge lengths between the point contacts on opposite edges, and we study the
behaviour of the current as a function of varying edge length. Recent experiments attempted to
measure the Aharanov-Bohm e�ect by changing the area inside the interferometer using a plunger
gate. Theoretical analyses of these experiments have so far not taken into account the accompanying
change in the edge lengths. We show that the tunnelling current exhibits multiple osculations as a
function of this edge length, with frequencies proportional to the injected edge current and inversely
proportional to the edge velocities. In particular the edge velocities can be measured by looking at
the Fourier spectrum of the edge current. We provide a numerical scheme to calculate and plot the
R function, and include sample plots for a variety of edge states with parameter values which are
experimentally relevant.
| Item Type: |
Article
|
| Keywords: |
Tunnelling current; fractional quantum Hall interferometers; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematical Physics |
| Item ID: |
4795 |
| Depositing User: |
Dr. Joost Slingerland
|
| Date Deposited: |
05 Mar 2014 16:15 |
| Journal or Publication Title: |
Physical Review B |
| Publisher: |
American Physical Society |
| Refereed: |
Yes |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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