Determining Planck's Constant by Measuring the Integer Quantum Hall effect in Graphene
Christopher O'Driscoll and Jonathan Brashear
Advisor: Ke Wang
Spring 2019
What is the Quantum Hall effect?
The Hall effect occurs when a sample with a current running through it is placed in a magnetic field. The magnetic field deflects charge carriers to the edge of the sample, so an electric field builds up across the sample width. The electric field causes a voltage drop across the sample. This voltage is called the Hall voltage. In the presence of strong magnetic fields, the Hall voltage becomes quantized. This is called the Quantum Hall Effect. The Hall voltage is often expressed as a resistance or conductance by dividing by the current through the sample. For a more detailed description of the phenomena, see the Theory section.
Why study the Quantum Hall effect?
The National Institute of Standards and Technology (NIST) defines units of measurement based on fundamental constants. The Quantum Hall effect is used to define the Ohm because the quantized Hall resistances are precisely measurable and multiples of e2/h, relating resistance to the electron charge and Planck's constant. This relation is independent of the bulk properties of the material used. This independence is called exact quantization [1]. For this experiment, rather than using the accepted Planck's constant and electron charge to measure the Ohm, we used the accepted electron charge and Ohm to measure Planck's constant.
What is Graphene?
Graphene is a form of carbon in which the honeycomb lattices stacked on each other are only a few atoms thick. For example, we used both monolayer and bilayer graphene, in which the carbon lattices were one and two atoms thick, respectively.
How do we make something so thin?
The process, called scotch tape exfoliation, is explained in the Sample Preparation section.
How were the measurements taken?
The sample was cooled to 2 K using a Physical Properties Measurement System. The Hall voltage was measured while sweeping over the applied magnetic field and charge carrier density. The equipment used and the methods of measuring the voltage are explained in more detail in the Apparatus and Procedures section.
What were the results of the experiment?
We measured Planck's Constant to be h = (6.559 ± 0.005) * 10-34 Js. This deviated from the accepted value of h = 6.626 * 10-34 Js by 5.3 σ but just 0.4%. The complete analysis is given in the Data and Analysis section.
Concluding thoughts
The conclusions of our experiment and some recommendations for improvement are provided in the Looking Forward section.
References:
1. Boutin, Chad. “Developing a 'Gold Standard' for Hall Resistance.” NIST, NIST, 8 Jan. 2018, www.nist.gov/news-events/news/2014/04/developing-gold-standard-hall-resistance.