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Imaging fractal conductance fluctuations and scarred wave functions in a quantum billiard
R Crook1, C G Smith, A C Graham
1Department of Physics, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
Abstract:
We present scanning-probe images and magnetic-field plots which reveal fractal conductance fluctuations in a quantum billiard. The quantum billiard is drawn and tuned using erasable electrostatic lithography, where the scanning probe draws patterns of surface charge in the same environment used for measurements. A periodicity in magnetic field, which is observed in both the images and plots, suggests the presence of classical orbits. Subsequent high-pass filtered high-resolution images resemble the predicted probability density of scarred wave functions, which describe the classical orbits.
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