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Charge density wave in hidden order state of URu$_2$Si$_2$

We argue that the hidden order state in URu$_2$Si$_2$ will induce a charge density wave. The modulation vector of the charge density wave will be twice that of the hidden order state, $Q_{CDW} = 2Q_{HO}$. To illustrate how the charge density wave arises we use a Ginzburg-Landau theory that contains a coupling of the charge density wave amplitude to the square of the HO order parameter $Δ_{HO}$. This simple analysis allows us to predict the intensity and temperature dependence of the charge density wave order parameter in terms of the susceptibilities and coupling constants used in the Ginzburg-Landau analysis.