From 594beb4734708b8573e638bf9d5dc53424385ea0 Mon Sep 17 00:00:00 2001
From: mfm94 <mfm94@cornell.edu>
Date: Tue, 26 May 2020 17:48:52 +0000
Subject: Update on Overleaf.

---
 main.tex | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 6d133be..1296751 100644
--- a/main.tex
+++ b/main.tex
@@ -607,6 +607,25 @@ 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.
+}
+
 The coincidence of our theory's orthorhombic high-pressure phase and \urusi's
 \afm\ is compelling, but our mean field theory does not make any explicit
 connection with the physics of \afm. Neglecting this physics could be
-- 
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