From 36c91821da6d19a72cb676920c2c4d6fa850ecaf Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 21 Aug 2019 14:43:31 -0400
Subject: added some citations and discussion of xrays

---
 main.tex | 20 +++++++++-----------
 1 file changed, 9 insertions(+), 11 deletions(-)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index c7b31a1..0a31ff4 100644
--- a/main.tex
+++ b/main.tex
@@ -98,7 +98,7 @@ the order parameter, i.e. the symmetry of the ordered state.
 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?]
+hidden order (HO) \cite{hassinger_temperature-pressure_2008}, 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 \cite{kambe_odd-parity_2018, haule_arrested_2009,
@@ -117,7 +117,7 @@ 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].
+electronic phase transition due to electron-phonon coupling \cite{shekhter_bounding_2013}.
 Ref.~\cite{ghosh_single-component_2019} 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
@@ -133,7 +133,7 @@ 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
+comparison with recent x-ray scattering experiments \cite{choi_pressure-induced_2018}.  Finally, we
 discuss our conclusions and the future experimental and theoretical work motivated
 by our results.
 
@@ -355,12 +355,11 @@ r_c|^\gamma$ for $\gamma=1$.
 
 We have seen that mean field theory predicts that whatever component of strain
 transforms like the order parameter will see a $t^{-1}$ softening in the
-stiffness that ends in a cusp. Ultrasound experiments \textbf{[Elaborate???]}
+stiffness that ends in a cusp. Ultrasound experiments \cite{ghosh_single-component_2019}
 yield the strain stiffness for various components of the strain; this data is
 shown in Figure \ref{fig:data}.  The $\Btg$ and $\Eg$ stiffnesses don't appear
 to have any response to the presence of the transition, exhibiting the expected
-linear stiffening with a low-temperature cutoff \textbf{[What's this called?
-Citation?]}. The $\Bog$ stiffness has a dramatic response, softening over the
+linear stiffening with a low-temperature cutoff \cite{varshni_temperature_1970}. The $\Bog$ stiffness has a dramatic response, softening over the
 course of roughly $100\,\K$. There is a kink in the curve right at the
 transition. While the low-temperature response is not as dramatic as the theory
 predicts, mean field theory---which is based on a small-$\eta$ expansion---will
@@ -420,7 +419,7 @@ Experiments give $\Delta c_V\simeq1\times10^5\,\J\,\m^{-3}\,\K^{-1}$
 \cite{fisher_specific_1990}, and our fit above gives $\xi_{\perp0}q_*=(D_\perp
 q_*^4/aT_c)^{1/4}\sim2$. We have reason to believe that at zero pressure, very
 far from the Lifshitz point, $q_*$ is roughly the inverse lattice spacing
-\textbf{[Why???]}. Further supposing that $\xi_{\parallel0}\simeq\xi_{\perp0}$,
+\cite{meng_imaging_2013}. Further supposing that $\xi_{\parallel0}\simeq\xi_{\perp0}$,
 we find $t_\G\sim0.04$, so that an experiment would need to be within
 $\sim1\,\K$ to detect a deviation from mean field behavior. An ultrasound
 experiment able to capture data over several decades within this vicinity of
@@ -430,14 +429,13 @@ Our analysis has looked at behavior for $T-T_c>1\,\K$, and so it remains
 self-consistent.
 
 There are two apparent discrepancies between the phase diagram presented in 
-[cite] and that predicted by our mean field theory. The first is the apparent
+\cite{choi_pressure-induced_2018} and that predicted by our mean field theory. The first is the apparent
 onset of the orthorhombic phase in the HO state prior to the onset of AFM. 
-As ref.[cite] notes, this could be due to the lack of an ambient pressure calibration
+As ref.\cite{choi_pressure-induced_2018} notes, this could be due to the lack of an ambient pressure calibration
 for the lattice constant. The second discrepancy is the onset of orthorhombicity 
-at higher temperatures than the onset of AFM. We expect that this could be due to the
+at higher temperatures than the onset of AFM. Susceptibility data sees no trace of another phase transition at these higher temperatures \cite{inoue_high-field_2001}, and therefore we don't in fact expect there to be one. We do expect that this could be due to the
 high energy nature of x-rays as an experimental probe: orthorhombic fluctuations
 could appear at higher temperatures than the true onset of an orthorhombic phase. 
-This is similar to the situation seen in [cite cuprate x-ray source]. 
 
 \begin{acknowledgements}
 
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