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

TL;DR

This paper uses scanning-probe imaging to reveal fractal conductance fluctuations and scarred wave functions in a quantum billiard, linking classical orbits with quantum behavior.

Contribution

It introduces a novel method of using electrostatic lithography and scanning probes to visualize quantum and classical phenomena in a quantum billiard.

Findings

Detection of fractal conductance fluctuations

Observation of classical orbit signatures in magnetic-field plots

Visualization of scarred wave functions resembling theoretical predictions

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.