From 7c75479e374836f292475a8a1b9364661a11fc7a Mon Sep 17 00:00:00 2001
From: mfm94 <mfm94@cornell.edu>
Date: Tue, 16 Jun 2020 20:29:07 +0000
Subject: Update on Overleaf.

---
 main.tex | 40 ++++++++++++++++++++++++----------------
 1 file changed, 24 insertions(+), 16 deletions(-)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 1296751..79d436a 100644
--- a/main.tex
+++ b/main.tex
@@ -607,23 +607,31 @@ is characterized by uniform $\Bog$ order. The staggered nematic of \ho\ is
 similar to the striped superconducting phase found in LBCO and other
 cuperates.\cite{Berg_2009b}
 
+% {\color{blue}
+% We can also connect our abstract order parameter to a physical picture of multipolar
+% ordering.
+% The U-5f electrons in URu$_2$Si$_2$ exhibit a moderate degree of localization [cite], which is
+% reflected in partial occupancy of many electronic states. Motivated by the results of refs [cite],
+% we assume that the dominant U state consists of $j = 5/2$ electrons in the U-5f2 configuration, which has 
+% total angular momentum $J = 4$. Within the $J=4$ multiplet, the precise energetic ordering
+% of the $D_{4h}$ crystal field states still remains a matter of debate [cite]. In a simple
+% framework of localized $j = 5/2$ electrons in the 5f2 configuration, our phenomenological theory
+% is consistent with the ground state being the B$_{1g}$ crystal field state with
+% order parameter 
+% \[
+%     H = \eta (J_x^2 - J_y^2)
+% \]
+% corresponding to hexadecapolar orbital order,
+% where here $\eta$ is taken to be modulated at $\vec{Q} = (0, 0, 1)$. 
+% The result of non-zero $\eta$ is a nematic distortion of the B1g orbitals, alternating along the c-axis.
+% }
 {\color{blue}
-We can also connect our abstract order parameter to a physical picture of multipolar
-ordering.
-The U-5f electrons in URu$_2$Si$_2$ exhibit a moderate degree of localization [cite], which is
-reflected in partial occupancy of many electronic states. Motivated by the results of refs [cite],
-we assume that the dominant U state consists of $j = 5/2$ electrons in the U-5f2 configuration, which has 
-total angular momentum $J = 4$. Within the $J=4$ multiplet, the precise energetic ordering
-of the $D_{4h}$ crystal field states still remains a matter of debate [cite]. In a simple
-framework of localized $j = 5/2$ electrons in the 5f2 configuration, our phenomenological theory
-is consistent with the ground state being the B$_{1g}$ crystal field state with
-order parameter 
-\[
-    H = \eta (J_x^2 - J_y^2)
-\]
-corresponding to hexadecapolar orbital order,
-where here $\eta$ is taken to be modulated at $\vec{Q} = (0, 0, 1)$. 
-The result of non-zero $\eta$ is a nematic distortion of the B1g orbitals, alternating along the c-axis.
+We can also connect our results to the large body of work concerning various multipolar
+orders as candidate states for HO (e.g. refs.~\cite{Haule_2009,Ohkawa_1999,Santini_1994,Kiss_2005,Kung_2015,Kusunose_2011_On}).
+Physically, our phenomenological order parameter could correspond to $\Bog$\ multipolar
+ordering originating from the localized component of the U-5f electrons. For the crystal
+field states of \urusi, this could correspond either to electric quadropolar or
+hexadecapolar order based on the available multipolar operators \cite{Kusunose_2011_On}.
 }
 
 The coincidence of our theory's orthorhombic high-pressure phase and \urusi's
-- 
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