Imaging fractal conductance fluctuations and scarred wave functions in a quantum billiard

Phys Rev Lett. 2003 Dec 12;91(24):246803. doi: 10.1103/PhysRevLett.91.246803. Epub 2003 Dec 11.

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.