From 701fe2f91798abbddd1082e21c760f69afc9ad31 Mon Sep 17 00:00:00 2001
From: mfm94 <mfm94@cornell.edu>
Date: Mon, 5 Aug 2019 20:41:53 +0000
Subject: Update on Overleaf.

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 main.tex | 24 ++++++++++++++++++------
 1 file changed, 18 insertions(+), 6 deletions(-)

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diff --git a/main.tex b/main.tex
index de38d17..aac94e5 100644
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@@ -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}
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