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Imaging Fractal Conductance Fluctuations and Scarred Wave Functions in a Quantum Billiard

R. Crook·C. G. Smith·A. C. Graham·I. Farrer·H. E. Beere·D. A. Ritchie
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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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R. Crook, C. G. Smith, A. C. Graham, I. Farrer, H. E. Beere, D. A. Ritchie. 2003-10-27. Imaging Fractal Conductance Fluctuations and Scarred Wave Functions in a Quantum Billiard. https://doi.org/10.1103/physrevlett.91.246803

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