The quantum anomalous Hall effect : uses in electrical metrology and understanding residual dissipation

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When a company manufactures and sells a resistor, they typically aim to traceably link its resistance value to a quantum Hall (QH) effect measurement. When a thin semiconductor is cooled to a low enough temperature and exposed to a large enough magnetic field, it exhibits zero longitudinal resistance and quantized Hall (transverse) resistance. This quantized resistance is a topological phenomenon, insensitive to sample details, and since 1990 has been used to define the ohm. Magnetic topological insulators exhibit the same resistance properties, but at zero magnetic field — this is the quantum anomalous Hall (QAH) effect. QAH materials offer significant advantages as possible replacements for QH resistance standards. Eliminating the need for large magnetic fields not only allows simplifying measurement infrastructure, but also allows a quantum resistance standard to be directly integrated with a Josephson voltage standard to produce a quantum current standard. However, all measurements of the QAH effect to date have observed non-zero longitudinal resistance despite quantization of the Hall resistance to h/e^2 (where h is Planck's constant and e the electron charge) being confirmed to within one part per billion. This residual dissipation is strongly temperature-dependent, lowering the temperature at which the QAH effect is well-quantized and thus limiting industrial applications. This dissertation will focus on our efforts to understand and find metrological applications for the QAH state of the canonical magnetic topological insulator — Cr-doped (Bi,Sb)2Te3. The nature of non-equilibrium dissipationless current flow in this system will be explored by comparing the measured potential profile in a QAH Hall bar to numerical simulations of the Poisson equation. Separately, residual dissipation will be studied by decoupling edge and bulk contributions using an annular geometry known as the Corbino disk. We will also show that despite their limitations, these materials are already useful within the field of electrical metrology. We will discuss how metrological measurements of resistance are made and highlight the construction of a novel quantum current sensor based on a single-cryostat combination of a QAH resistor with a programmable Josephson voltage standard.


Type of resource text
Form electronic resource; remote; computer; online resource
Extent 1 online resource.
Place California
Place [Stanford, California]
Publisher [Stanford University]
Copyright date 2023; ©2023
Publication date 2023; 2023
Issuance monographic
Language English


Author Rodenbach, Linsey Kathryn
Degree supervisor Goldhaber-Gordon, David
Thesis advisor Goldhaber-Gordon, David
Thesis advisor Feldman, Ben
Thesis advisor Kastner, Marc
Degree committee member Feldman, Ben
Degree committee member Kastner, Marc
Associated with Stanford University, School of Humanities and Sciences
Associated with Stanford University, Department of Physics


Genre Theses
Genre Text

Bibliographic information

Statement of responsibility Linsey K. Rodenbach.
Note Submitted to the Department of Physics.
Thesis Thesis Ph.D. Stanford University 2023.

Access conditions

© 2023 by Linsey Kathryn Rodenbach
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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