Attempt to make poster less wordy and bold important sentences.

1 files changed, 120 insertions, 77 deletions

diff --git a/poster_aps_mm_2020.tex b/poster_aps_mm_2020.tex
index 84d0496..d63be44 100644
--- a/poster_aps_mm_2020.tex
+++ b/poster_aps_mm_2020.tex
@@ -11,8 +11,6 @@
 \usepackage[export]{adjustbox}
 \renewcommand*\familydefault{\sfdefault}
 
-\mathtoolsset{showonlyrefs=true}
-
 \setlength\textwidth{194pc}
 \begin{document}
 
@@ -80,33 +78,43 @@
 
 \noindent\hspace{176pc}\includegraphics[width=18pc]{CULogo-red120px.eps}
 \vspace{-24.5pc}\\
-\Huge \textbf{Elastic properties of hidden order in URu$_{\text2}$Si$_{\text2}$ are reproduced by\\ staggered nematic order}\hspace{37.5pc}\textbf{\LARGE arXiv:1910.01669 [cond-mat.str-el]}
+\Huge \textbf{Elastic properties of hidden order in URu$_{\text2}$Si$_{\text2}$ are reproduced by\\ staggered nematic order}
+\hspace{37.5pc}\textbf{\LARGE arXiv:1910.01669 [cond-mat.str-el]}
 \bigskip\\
-\huge \textbf{Jaron~Kent-Dobias, Michael Matty \& B J Ramshaw}\hspace{7pc}\ding{81}\hspace{7pc}\textbf{Cornell University}
+\huge \textbf{Jaron~Kent-Dobias, Michael Matty \& B J Ramshaw}
+\hspace{7pc}\ding{81}\hspace{7pc}\textbf{Cornell University}
 
 \begin{multicols}{2}
   \Large
-  \urusi\ is a heavy fermion material with a continuous transition into a `hidden
-  order' (\ho) phase whose broken symmetry is unknown. Under sufficient
-  pressure it instead transitions into an antiferromagnet (\afm), with phase
-  diagram in Fig.~\ref{phase_diagram}(a). \urusi\ also has a lower-temperature
-  superconducting phase within \ho\ that is destroyed by the \afm.
-
-  Resonant ultrasound spectroscopy measures anomalous softening in its stiffness
-  tensor over several hundred Kelvin approaching the \ho\ transition. Starting
-  with a general Ginzburg--Landau theory of \urusi, we show that only one
-  order parameter symmetry is consistent with both this softening and the
-  topology of the phase diagram. This choice reproduces other \urusi\ phenomena and motivates new experiments.
+  \hspace{1em}
+  \textbf{ \urusi\ is a heavy fermion material with a continuous
+    transition into a `hidden order' (\ho) phase whose broken symmetry is
+    unknown.
+  } Under sufficient pressure it instead transitions into an antiferromagnet
+  (\afm), with phase diagram in Fig.~\ref{phase_diagram}(a). It also has a
+  superconducting phase within \ho\ that is destroyed by \afm.
+
+  \hspace{1em}
+  The modulus tensor of \urusi\ anomalously softens over several hundred
+  Kelvin and is cut off by the \ho\ transition.
+  \textbf{
+    We show that only one order parameter symmetry is consistent with this
+    softening and the topology of the phase diagram.
+  }
+  This choice reproduces other \urusi\ phenomena and motivates new experiments.
 
   \section{Resonant ultrasound spectroscopy \&\\ irreducible strains}
   \Large
 
-  \Rus\ drives material with sound and measures the response. Resonances
-  produced by driving at the natural frequency of a normal mode are visible as
-  spikes in the response amplitude. The stiffness tensor $C$ is uniquely
-  determined by the frequencies of sufficiently many normal modes and the
-  sample geometry. The structure of the stiffness tensor and its behavior as a
-  function of temperature yield a lot of information about symmetry breaking.
+  \hspace{1em}
+  Resonant ultrasound spectroscopy drives a sample with sound and measures its
+  resonances by looking for spikes in the response. Using the sample geometry
+  and the location of sufficiently many resonances, the modulus tensor $C$
+  can be calculated.
+  \textbf{
+    The structure of the modulus tensor and its temperature dependence yield
+    a lot of information about symmetry breaking.
+   }
 
   \begin{figure}
     \centering
@@ -114,50 +122,66 @@
     \includegraphics[width=0.5\textwidth]{rus_resonances.jpg}
     \hfill\raisebox{2em}{\includegraphics[width=0.48\textwidth]{urusi_modes.png}}
     \captionof{figure}{
-      \textbf{Left:} Response amplitude versus driving frequency for a sample at some
+      \textbf{Left:}
+      Response versus driving frequency for a sample at some
       temperature. The spikes correspond to resonances, and the strains
       corresponding to a few dominant modes are depicted in the cartoons.
       \textbf{Right:}
       The crystal structure of \urusi\ and the influence of the irreducible
-      strains of \Dfh\ on it.
+      strains of \Dfh.
     }
     \label{fig:rus}
     \vspace{1em}
   \end{figure}
 
-  The strain tensor $\epsilon$ has six independent components that can be
-  divided into tuples upon which symmetry transformations act with irreducible
-  representations of the crystallographic point group. \urusi's point group is \Dfh\ and has
-  five `irreducible' strains, depicted in Fig.~\ref{fig:rus}. Of these, four
-  are one-tuples (single-component) and one is a two-tuple (multi-component). 
+  \hspace{1em}
+  The strain tensor $\epsilon$ has six independent components. These components can be
+  divided into tuples that symmetry transformations of the crystal act on with irreducible
+  representations (irreps) of its point group.
+  \textbf{
+    \urusi's point group \Dfh\ yields five `irreducible' strains, shown in
+    Fig.~\ref{fig:rus}.
+  }
+  Four are one-tuples (single-component). These are uniform compression in and
+  out of the plane ($\Aog$) and in-plane shear along the faces and diagonals of
+  the unit cell ($\Bog$ and $\Btg$). One is a two-tuple (multi-component), and
+  corresponds to out of plane shears ($\Eg$).
+
 
 
   \section{Landau--Ginzburg theory}
   \Large
 
-  Symmetry transformations must act trivially on the free energy, so all its
-  terms must correspond to $\Aog$ irreps. An order parameter can only linearly
-  couple to a strain that shares its irrep. Any other coupling must be
-  higher-order, which leads to thermodynamic discontinuities but not diverging
-  responses. The anomalous softening seen in \urusi\ suggests the \ho\ order
-  parameter $\eta$ couple linearly to a strain.
-
-  Of the irreps found in strains, $\Aog$ yields a first-order transition and
-  therefore can't describe \ho.  For any of those remaining, the effective free
-  energy has three components: the bare elastic energy of the strain
-  $f_\e=\sum_\X C^0_\X\epsilon_\X\epsilon_\X$, the bare energy of the order
-  parameter $\eta$
+  \hspace{1em}
+  The free energy must be invariant under symmetry transformations. This
+  constrains the way fields can couple together. Two fields can linearly couple
+  only if they correspond to the same irrep. Higher order couplings lead to
+  thermodynamic discontinuities but not diverging responses.
+  \textbf{
+    The anomalous softening of \urusi\ suggests the hidden order parameter
+    couples linearly to strain.
+  }
+
+  \hspace{1em}
+  An $\Aog$ order parameter results in first-order transitions and can't
+  describe hidden order. If the order parameter $\eta$ corresponds to any of
+  the remaining irreps $\X$ present in strain, the free energy is
+  $f=f_\e+f_\i+f_\op$, where
   \begin{equation}
-      f_\op=\frac12\big[r\eta^2+c_\parallel(\nabla_\parallel\eta)^2
+    \begin{aligned}
+      & \hspace{2em}f_\e=\sum_\X C^0_\X\epsilon_\X\epsilon_\X
+        \hspace{4em} f_\i=-b\epsilon_\X\eta \\ 
+      & f_\op=\frac12\big[r\eta^2+c_\parallel(\nabla_\parallel\eta)^2
         +c_\perp(\nabla_\perp\eta)^2
-        +D_\perp(\nabla_\perp^2\eta)^2\big]+u\eta^4,
+        +D_\perp(\nabla_\perp^2\eta)^2\big]+u\eta^4
+    \end{aligned}
     \label{eq:fo}
   \end{equation}
-  and the coupling between them $f_\i=-b\epsilon_\X\eta$. Tracing out the
-  strain gives an effective free energy with the form of \eqref{eq:fo} but with
-  $r\to\tilde r$.
+  The strain $\epsilon$ can be traced out exactly, which results in a free
+  energy density with the form of $f_\op$ but with $r\to\tilde
+  r=r-b^2/2C^0_\X$.
 
-  \vfill\null
+  \vfill
 
   \begin{wrapfigure}{R}{0.6\columnwidth}
     \centering
@@ -168,55 +192,74 @@
     \includegraphics[width=0.51\columnwidth]{paper/phases_scalar}\hspace{-0.75em}
     \includegraphics[width=0.51\columnwidth]{paper/phases_vector}
     \captionof{figure}{
-      Phase diagrams for (a) \urusi\ from Phys Rev B \textbf{77} 115117 (2008) (b) mean
-      field theory of a one-component ($\Bog$ or $\Btg$) Lifshitz point (c) mean
-      field theory of a two-component ($\Eg$) Lifshitz point. Solid lines denote
-      continuous transitions, while dashed lines denote first order transitions.
+      Phase diagrams for (a) \urusi\ from Phys Rev B \textbf{77} 115117 (2008)
+      (b) theory for a one-component order ($\Bog$ or $\Btg$) (c) theory for a
+      two-component order ($\Eg$). Solid lines denote continuous transitions,
+      while dashed denote first order.
     }
     \label{phase_diagram}
   \end{wrapfigure}
 
-   This is the theory of a \emph{Lifshitz point} at $\tilde r=c_\perp=0$. This
-   triple point lies where three phases meet: an unordered phase with $\eta=0$,
-   a uniform ordered phase with $\eta\neq0$, and a modulated ordered phase with
-   $\eta\propto\cos q_*x_3$. Phase diagrams are shown in Fig.~\ref{phase_diagram}(b--c). The type of transition between the ordered phases
-   depends on how many components $\eta$ has: a one-component theory is first
-   order while a two-component one is continuous. The irreps
-   consistent with the first order transition between \ho\ and \afm\ in \urusi\
-   are $\Bog$ and $\Btg$.
+  \hspace{1em}
+  \textbf{
+    This theory has a \emph{Lifshitz triple point} at $\tilde r=c_\perp=0$.
+  }
+  The three phases that meet are
+  \begin{itemize}
+    \item\hspace{0.25em}unordered ($\eta=0$)
+    \item\hspace{0.25em}uniform ($\eta\neq0$)
+    \item\hspace{0.25em}modulated ($\eta\propto\cos q_*x_3$)
+  \end{itemize}
+  Phase diagrams are in Fig.~\ref{phase_diagram}(b--c). The order of the
+  transition between the uniform and modulated phases depends on the number of
+  order parameter components: one-component theories have a first order
+  transition while two-component theories are continuous.
+  \textbf{
+    The only order parameter irreps consistent with the first order transition
+    between \ho\ and \afm\ in \urusi\ are $\Bog$ and $\Btg$.
+  }
 
-  \section{Anomalous stiffness response}
+  \section{Anomalous modulus response}
   \Large
 
-  The stiffness $C$ can be calculated like any other response
-  function. Approaching the modulated phase, the strain stiffness with the same
-  symmetry $\X$ of the order parameter is
+  \hspace{1em}
+  The modulus $C$ can be calculated like any other response function.
+  Approaching the modulated phase, the modulus with the symmetry irrep
+  $\X$ of the order parameter is
   \begin{equation}
     C_\X=C_\X^0\bigg[1+\frac{b^2}{C_\X^0}\big(D_\perp q_*^4+|\Delta\tilde r|\big)^{-1}\bigg]^{-1}
     \label{eq:static_modulus}
   \end{equation}
-  which has the form of an inverted cusp at the critical point. Compared with
-  experimental \rus\ measurements, this doesn't resemble the $\Btg$ stiffness
-  in Fig.~\ref{fig:plots}(a), but fits the $\Bog$ stiffness in
-  Fig.~\ref{fig:plots}(b). This suggests \ho\ is a $\Bog$ nematic modulated along the $c$-axis.
-
-  This theory explains the presence of the 0.4--0.5 inverse lattice constant scattering peak seen in some experiments and is consistent with $\Bog$ symmetry breaking observed in the \afm\ phase. \Rus\ experiments at pressure might resolve the divergence of the modulation wavevector $q_*$ and the vanishing of the $\Bog$ stiffness at the Lifshitz point.
+  \hspace{1em}
+  \textbf{
+    At the critical point the modulus with the symmetry of the order parameter
+    has an inverted cusp.
+  }
+  Compared with experiments, this doesn't resemble the $\Btg$ modulus in
+  Fig.~\ref{fig:plots}(a) but fits the $\Bog$ modulus in
+  Fig.~\ref{fig:plots}(b). \textbf{This suggests hidden order is a $\Bog$
+  nematic modulated along the \textit{c}-axis.}
+
+  \hspace{1em}
+  This theory explains the presence of the 0.4--0.5 inverse lattice constant
+  scattering peak seen in some experiments and is consistent with $\Bog$
+  symmetry breaking observed in the \afm\ phase. \Rus\ experiments at pressure
+  might resolve the divergence of the modulation wavevector $q_*$ and the
+  vanishing of the $\Bog$ modulus at the Lifshitz point.
 
   \begin{figure}
-    \vspace{1pc}
+    \vspace{1em}
     \centering
     \includegraphics[width=\columnwidth]{paper/fig-stiffnesses.pdf}
     \captionof{figure}{
-     \Rus\ measurements of the elastic moduli of \urusi\ at ambient pressure
-     as a function of temperature from \texttt{arXiv:1903.00552
-     [cond-mat.str-el]} (blue, solid) alongside fits to theory (magenta,
-     dashed). The solid yellow region shows the location of the \ho\ phase.
-     (a) $\Btg$ modulus data and a fit to the standard form. (b) $\Bog$
+     \Rus\ measurements of \urusi's moduli as a function of temperature from
+     \texttt{arXiv:1903.00552 [cond-mat.str-el]} (blue, solid) alongside fits
+     to this theory (magenta, dashed). The solid yellow region shows the \ho\
+     phase.  (a) $\Btg$ modulus data and a fit to standard form. (b) $\Bog$
      modulus data and a fit to \eqref{eq:static_modulus}. (c) $\Bog$ modulus
      data and the fit of the \emph{bare} $\Bog$ modulus. (d) $\Bog$ modulus
-     data and the fit transformed by $[C^0_\Bog(C^0_\Bog/C_\Bog-1)]]^{-1}$,
-     which is predicted from \eqref{eq:static_modulus} to equal $D_\perp
-     q_*^4/b^2+a/b^2|T-T_c|$, e.g., an absolute value function. 
+     data and fit transformed in way predicted from \eqref{eq:static_modulus}
+     to be an absolute value function. 
     }
     \label{fig:plots}
     \vspace{1pc}