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@@ -609,6 +609,25 @@ 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 |