Emergent symmetries in quantum impurity experiments
Abstract/Contents
- Abstract
- In systems involving a continuum of energy scales, one can imagine that under renormalization an effective Hamiltonian valid at low energies could possess a symmetry that the bare Hamiltonian does not. We are interested in the extent to which measurements of a physical system may reflect such emergent symmetries. Localized spins coupled to reservoirs of electrons are a natural domain to study these phenomena. Such "quantum impurity" systems can be realized using quantum dots. We report transport measurements of two lithographically patterned quantum dot systems in GaAs/AlGaAs heterostructures: 1. In a capacitively-coupled double quantum dot, gate voltage can be used to tune the system so that it is equally favorable for either dot to hold one electron. The effective Kondo Hamiltonian valid at low energies has been predicted to have an emergent SU(4)-symmetric exchange interaction based on the spin and orbital degrees of freedom. We provide evidence for emergent SU(4) symmetry by carefully comparing temperature-dependent conductance with numerical renormalization group calculations. In our device, conductance may be measured through each dot individually, uniquely enabling orbital state-resolved spectroscopy of the Kondo state. 2. A quantum dot tunnel-coupled to a metallic grain can host a non-Fermi liquid two-channel Kondo state, where a spin-1/2 impurity is exchange-coupled to two independent electron reservoirs. It occurs at the critical point of a second-order quantum phase transition, which surprisingly has exact theoretical descriptions both at and away from the critical point, even at finite temperature. We confirm transport signatures of quantum criticality as first reported by Potok, et al. (Nature 446, 167 (2007)), and then go further by quantitatively validating a universal theory for the crossover to a Fermi liquid. The universality of this crossover in the presence of arbitrary symmetry-breaking perturbations is a consequence of emergent symmetry at the non-Fermi liquid fixed point.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2015 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Keller, Andrew Joseph |
|---|---|
| Associated with | Stanford University, Department of Physics. |
| Primary advisor | Goldhaber-Gordon, David, 1972- |
| Thesis advisor | Goldhaber-Gordon, David, 1972- |
| Thesis advisor | Fisher, Ian |
| Thesis advisor | Qi, Xiaoliang |
| Advisor | Fisher, Ian |
| Advisor | Qi, Xiaoliang |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Andrew Joseph Keller. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2015. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2015 by Andrew Joseph Keller
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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