Generalization of Anderson's theorem for disordered superconductors
Abstract/Contents
- Abstract
- The real world is imperfect, and disorder is an inherent feature of condensed matter systems. Whether or not the associated physical effects are of consequence for the properties we are interested in is a separate question. For example, conventional superconductors exhibit a robustness of the critical temperature and energy gap to non-magnetic impurities. This can be understood through Anderson's "theorem" of pairing exact time-reversed states; however, the theorem is not applicable to unconventional superconductors, such as the cuprates, with a sign-changing order parameter where the dirty limit is not well-defined. Moreover, the perturbative and effective medium approximations typically employed to treat the suppression of superconductivity are only valid under certain assumptions about the disorder ensemble and coherence length. While the simultaneous treatment of disorder and interactions typically requires numerical methods without uncontrolled approximations, there are interesting questions that emerge if we restrict ourselves to an exact treatment of disorder within BCS theory. The first part of the thesis focuses on the effect of disorder on the mean-field transition temperature Tc. In particular, we argue that mean-field Tc is always increased in the presence of disorder independent of order parameter symmetry, disorder strength, and spatial dimension. This can be understood through an analogy with Lifshitz tails is disordered semiconductors where rare regions conducive to bound states produce exponential tails in the density of states. While this is valid as a strict mathematical statement, the physical content only becomes relevant for short-coherence length superconductors. We then revisit the conventional wisdom that the overdoped cuprate phase diagram can be described entirely by dirty d-wave BCS theory. An extensive mutual inductance experiment probing the superconducting dome and overdoped quantum critical point has provided compelling evidence for a vanishing superfluid stiffness as Tc --> 0 in the ultra-clean limit. The drop in superfluid density without the usual signatures of pair-breaking disorder suggests a simple mean-field approach is at least partially incomplete. To address the applicability of dirty d-wave BCS theory in the overdoped regime, we compute the superfluid density for various disorder ensembles that are microscopically motivated by the chemistry of the cuprates. We find that the disorder models can capture some features observed the experiments, but typically require unrealistically high impurity concentrations. The latter part of this thesis involves other projects on strongly correlated systems including computations for thermal conductivity and spin susceptibility for chiral p-wave models of strontium ruthenate 214, a DMRG study of the t1-t2-J1-J2 model on a 4-leg ladder, and a phenomenological model of twisted bilayer graphene.
Description
| 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 | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Dodaro, John Fitzgerald |
|---|---|
| Degree supervisor | Kivelson, Steven |
| Thesis advisor | Kivelson, Steven |
| Thesis advisor | Hwang, Harold Yoonsung, 1970- |
| Thesis advisor | Raghu, Srinivas, 1978- |
| Degree committee member | Hwang, Harold Yoonsung, 1970- |
| Degree committee member | Raghu, Srinivas, 1978- |
| Associated with | Stanford University, Department of Physics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | John F. Dodaro. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by John Fitzgerald Dodaro
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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