Merge branch 'master' of https://git.overleaf.com/5cf56f861d72e9071d1a343c

2 files changed, 43 insertions, 31 deletions

diff --git a/main.tex b/main.tex
index 66459b6..fb36846 100644
--- a/main.tex
+++ b/main.tex
@@ -609,23 +609,31 @@ 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
diff --git a/ref_response.tex b/ref_response.tex
index 9df15f7..f02cbc3 100644
--- a/ref_response.tex
+++ b/ref_response.tex
@@ -109,23 +109,27 @@ The behaviour of c/a is indeed interesting, but our model only considers the cou
     fit the present proposal?
 }\\
 
-We thank the referee for bringing up this point. We have added a discussion of possible physical 
+We thank the referee for bringing up this point. We have added a statement about possible physical 
 realizations to the conclusion section of our manuscript, which we believe broadens the appeal of our
 work by connecting it to the large body of research concerning microscopic theories of hidden order.
-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.\\
+As we now say in the manuscript, physically, our phenomenological order parameter could correspond 
+to B$_{1g}$ multipolar ordering originating from the localized component of the U-5f electrons. 
+For the crystal field states of URu$_2$Si$_2$, this could correspond either to electric quadropolar or
+hexadecapolar order based on the available multipolar operators.
+% 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.\\
 
 \ruleline{Report of the Second Referee -- BN13654/Kent-Dobias}\\