Quantized Conductance and Arduinos

Quantized Conductance: An Advanced Lab About the Wave Nature of Matter

Khalid Eid

Department of Physics, Miami University

This immersion focuses on a simple, transport-based experiment about quantum mechanics. It can be easily employed in a sophomore modern physics (or higher) lab and is best understood using 1-dimensional infinite well-shaped potentials. It is a direct demonstration of the wave nature of matter (i.e. the conduction electrons) and that quantization emerges due to confinement at the nano- or atomic scale.

The effect is seen as a gold wire is stretched slowly until it breaks. Due to the ductile nature of gold, the wire elongates and gets extremely narrow (down to one atom) before it breaks. That corresponds to a diameter less than the de Broglei wavelength and consequently quantization emerges as a step-wise change in electrical conductance of the wire. A 'D-size' battery is used to apply a voltage across the wire in series with a 100K.Ohm resistor and the voltage across the wire is repeatedly measured using a voltmeter (i.e. a NI DAQ unit).

In the first day, we will: 1) prepare gold wires glued to a thin, elastic stainless steel sheet and let the glue harden overnight, 2) assemble the mechanical setup that will be used to measure the conductance of the wire, while it breaks and re-connects repeatedly, and 3) get an introduction to LabVIEW and 'build' a simple LabVIEW program to collect the conductance data of the wires.

In the second day, we will: 1) complete the preparation of the gold wires by creating a partial cut in each wire and 2) view, save, and analyze the quantized conductance data to deduce the number of quantized channels (quantum number of each energy level) from the data.

In the third day, we will explore using both manually-controlled and computer-controlled piezo-crystals to run the experiment.

Handout