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| -rw-r--r-- | library.bib | 31 | ||||
| -rw-r--r-- | main.tex | 24 | ||||
| -rw-r--r-- | phase_diagram.png | bin | 0 -> 94427 bytes |
3 files changed, 48 insertions, 7 deletions
diff --git a/library.bib b/library.bib index dcc98ec..c944258 100644 --- a/library.bib +++ b/library.bib @@ -2,13 +2,42 @@ %% http://bibdesk.sourceforge.net/ -%% Created for Michael Matty at 2019-06-19 12:30:22 -0400 +%% Created for Michael Matty at 2019-08-05 15:24:37 -0400 %% Saved with string encoding Unicode (UTF-8) +@article{harrison:apa2019a, + Author = {Neil Harrison and Marcelo Jaime}, + Date-Added = {2019-08-05 15:23:30 -0400}, + Date-Modified = {2019-08-05 15:24:17 -0400}, + Journal = {arXiv preprint arXiv:1902.06588}, + Title = {Hidden valence transition in URu2Si2?}, + Year = {2019}, + Bdsk-File-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhXxBIZG9jcy9oYXJyaXNvbi9oYXJyaXNvbl8oMjAxOWEpX2hpZGRlbiB2YWxlbmNlIHRyYW5zaXRpb24gaW4gdXJ1MnNpMj8ucGRmTxECPAAAAAACPAACAAAMTWFjaW50b3NoIEhEAAAAAAAAAAAAAAAAAAAAAAAAAEJEAAH/////H2hhcnJpc29uXygyMDE5YSlfaCNGRkZGRkZGRi5wZGYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////8AAAAAAAAAAAAAAAAAAQAEAAAKIGN1AAAAAAAAAAAAAAAAAAhoYXJyaXNvbgACAHYvOlVzZXJzOm1pY2hhZWxtYXR0eTpEcm9wYm94OmNpdGF0aW9uX2xpYnJhcnk6ZG9jczpoYXJyaXNvbjpoYXJyaXNvbl8oMjAxOWEpX2hpZGRlbiB2YWxlbmNlIHRyYW5zaXRpb24gaW4gdXJ1MnNpMj8ucGRmAA4AdgA6AGgAYQByAHIAaQBzAG8AbgBfACgAMgAwADEAOQBhACkAXwBoAGkAZABkAGUAbgAgAHYAYQBsAGUAbgBjAGUAIAB0AHIAYQBuAHMAaQB0AGkAbwBuACAAaQBuACAAdQByAHUAMgBzAGkAMgA/AC4AcABkAGYADwAaAAwATQBhAGMAaQBuAHQAbwBzAGgAIABIAEQAEgB0VXNlcnMvbWljaGFlbG1hdHR5L0Ryb3Bib3gvY2l0YXRpb25fbGlicmFyeS9kb2NzL2hhcnJpc29uL2hhcnJpc29uXygyMDE5YSlfaGlkZGVuIHZhbGVuY2UgdHJhbnNpdGlvbiBpbiB1cnUyc2kyPy5wZGYAEwABLwAAFQACABP//wAAAAgADQAaACQAbwAAAAAAAAIBAAAAAAAAAAUAAAAAAAAAAAAAAAAAAAKv}} + +@article{ikeda:np2012a, + Author = {Ikeda, Hiroaki and Suzuki, Michi-To and Arita, Ryotaro and Takimoto, Tetsuya and Shibauchi, Takasada and Matsuda, Yuji}, + Date = {2012/06/03/online}, + Date-Added = {2019-08-05 15:21:55 -0400}, + Date-Modified = {2019-08-05 15:22:06 -0400}, + Day = {03}, + Journal = {Nature Physics}, + Keywords = {URu2Si2}, + L3 = {10.1038/nphys2330; https://www.nature.com/articles/nphys2330#supplementary-information}, + Month = {06}, + Pages = {528 EP -}, + Publisher = {Nature Publishing Group SN -}, + Title = {Emergent rank-5 nematic order in URu2Si2}, + Ty = {JOUR}, + Url = {https://doi.org/10.1038/nphys2330}, + Volume = {8}, + Year = {2012}, + Bdsk-Url-1 = {https://doi.org/10.1038/nphys2330}, + Bdsk-File-1 = {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}} + @article{zhang:apa2018a, Author = {Zhang, Yi and Mesaros, A and Fujita, K and Edkins, SD and Hamidian, MH and Ch'ng, K and Eisaki, H and Uchida, S and Davis, JC and Khatami, E and others}, Date-Added = {2019-06-19 12:29:40 -0400}, @@ -94,28 +94,39 @@ transition, the physics of the OP can often be described in the context of Landa mean field theory. However, to construct such a theory, one must know the symmetries of the order parameter, i.e. the symmetry of the ordered state. -One quintessential case where the symmetry of an ordered phase remains unknown is in \urusi. +A paradigmatic example where the symmetry of an ordered phase remains unknown is in \urusi. \urusi is a heavy fermion superconductor in which superconductivity condenses out of a symmetry broken state referred to as hidden order (HO) [cite pd paper], and at sufficiently large [hydrostatic?] pressures, both give way to local moment antiferromagnetism. -Despite over thirty years of effort, the symmetry of the hidden order state remains unknown, and -modern theories [big citation chunk] propose a variety of possibilities. +Despite over thirty years of effort, the symmetry of the hidden order state remains unknown, and modern theories +\cite{kambe:pr2018a, haule:np2009a, kusunose:jpsj2011a, kung:s2015a,cricchio:prl2009a,ohkawa:jpcm1999a,santini:prl1994a,kiss:ap2004a,harima:jpsj2010a,thalmeier:pr2011a,tonegawa:prl2012a,rau:pr2012a,riggs:nc2015a,hoshino:jpsj2013a,ikeda:prl1998a,chandra:n2013a,harrison:apa2019a,ikeda:np2012a} +propose a variety of possibilities. Many [all?] of these theories rely on the formulation of a microscopic model for the HO state, but without direct experimental observation of the broken symmetry, none have been confirmed. -One case that does not rely on a microscopic model is recent work [cite RUS paper] +One case that does not rely on a microscopic model is recent work \cite{ghosh:apa2019a} that studies the HO transition using resonant ultrasound spectroscopy (RUS). RUS is an experimental technique that measures mechanical resonances of a sample. These resonances contain information about the full elastic tensor of the material. Moreover, the frequency locations of the resonances are sensitive to symmetry breaking at an electronic -phase transition due to electron-phonon coupling [cite]. Ref. [RUS paper] uses this information +phase transition due to electron-phonon coupling [cite]. Ref.~\cite{ghosh:apa2019a} uses this information to place strict thermodynamic bounds on the symmetry of the HO OP, again, independent of any microscopic model. Motivated by these results, in this paper we consider a mean field theory of an OP coupled to strain and the effect that the OP symmetry has on the elastic response in different symmetry channels. Our study finds that a single possible OP symmetry reproduces the experimental strain susceptibilities, and fits the experimental data well. +We first present a phenomenological Landau-Ginzburg mean field theory of strain coupled to an +order parameter. We examine the phase diagram predicted by this theory and compare it +to the experimentally obtained phase diagram of \urusi. +Then we compute the elastic response to strain, and examine the response function dependence on +the symmetry of the OP. +We proceed to compare the results from mean field theory with data from RUS experiments. +We further examine the consequences of our theory at non-zero applied pressure in comparison +with recent x-ray scattering experiments [cite]. +Finally, we discuss our conclusions and future experimental and theoretical work that our results motivate. + The point group of \urusi is \Dfh, and any coarse-grained theory must locally respect this symmetry. We will introduce a phenomenological free energy density in three parts: that of the strain, the order parameter, and their interaction. @@ -414,6 +425,7 @@ self-consistent. \end{acknowledgements} -\bibliography{hidden_order} +\bibliographystyle{apsrev4-1} +\bibliography{hidden_order,library} \end{document} diff --git a/phase_diagram.png b/phase_diagram.png Binary files differnew file mode 100644 index 0000000..aa07be6 --- /dev/null +++ b/phase_diagram.png |
