Issue |
Europhys. Lett.
Volume 49, Number 4, February II 2000
|
|
---|---|---|
Page(s) | 417 - 423 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2000-00165-4 | |
Published online | 01 September 2002 |
An investigation of Weierstrass self-similarity in a semiconductor billiard
1
School of Physics, University of New South Wales - Sydney, NSW, 2052, Australia
2
Physics Department, University of Oregon - Eugene, OR 97403-1274, USA
3
Physics Department, Nottingham University - Nottingham NG7 2RD, UK
Corresponding author: mico@phys.unsw.edu.au
Received:
7
May
1999
Accepted:
5
December
1999
We present a model for the self-similar magneto-conductance recently observed in the low-temperature measurement of a semiconductor Sinai billiard. To model the self-similar behaviour, we investigate the scaling properties observed over more than three orders of magnitude in magnetic field. The magneto-conductance is found to be composed of a summation of damped cosines scaled according to a Weierstrass function —a known generator of self-similar behaviour. Our preliminary model, based on a single hierarchy of oscillations with magnetic flux periods of h/2e, provides a close match to the experimental data. However, a refined model featuring co-existing h/e and h/2e hierarchies matches the features of the data with remarkable accuracy.
PACS: 05.45.Df – Fractals / 73.23.Ad – Ballistic transport / 72.20.My – Galvanomagnetic and other magnetotransport effects
© EDP Sciences, 2000
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