Strarted response to referees.

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+> Re: BN13654
+>     Elastic properties of hidden order in URu 2Si 2 are reproduced by a
+>     staggered nematic
+>     by Jaron Kent-Dobias, Michael Matty, and B. J. Ramshaw
+> 
+> Dear Jaron Kent-Dobias,
+> 
+> The above manuscript has been reviewed by two of our referees.
+> Comments from the reports appear below.
+> 
+> These comments suggest that the present manuscript is not suitable for
+> publication in the Physical Review.
+> 
+> Yours sincerely,
+> 
+> Sarma Kancharla
+> Associate Editor
+> Physical Review B
+> Email: prb@aps.org
+> https://journals.aps.org/prb/
+> 
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+> ----------------------------------------------------------------------
+> Report of the First Referee -- BN13654/Kent-Dobias
+> ----------------------------------------------------------------------
+> 
+> The work deals with a purely phenomenological model for the “hidden” 
+> order parameter if URu2Si2, with particular emphasis on the expected 
+> elastic properties. The work might eventually be suitable for Phys. 
+> Rev. B, but some aspects are not clear to me. 
+> 
+> The main result is Fig. 2, where the behavior around TN is difficult 
+> to see. I suggest to add zooms on that crucial T-range, where it seems 
+> to me that there is a qualitative difference between model and 
+> experiments. The justification given by the Authors (“mean field 
+> theory—which is based on a small-eta expansion—will not work 
+> quantitatively far below the transition where eta has a large nonzero 
+> value and higher powers in the free energy become important”) does not 
+> look plausible as the disagreement does not appear to develop slowly 
+> as T decreases, but appears immediately below TN, where eta is small. 
+
+The disagreement between the theory at low temperature is resolved by the
+addition of an additional interaction in the mean-field free energy of the form
+ε²η², now shown in Fig. 2 as a thin black line.
+
+> Is it not clear how discriminatory is the agreement above TN in 2a, 2b 
+> and 2c. Are calculation results robust over a wide range of fitting 
+> parameters, or does the agreement result from a fine-tuning? (e.g., 
+> the presence of a maximum at 120 K in 2b). 
+
+[Not exactly sure what this means.]
+
+> Is it possible to say something about the c/a ratio, which displays a 
+> non-trivial T-dependence? 
+
+[Not sure what this means either. Is this asking about the ratio of lattice constants?]
+
+> At last, I understand that the model is meant to be purely 
+> phenomenological, but given the plethora of publications on URu2Si2 
+> over 30 years, where any conceivable order parameter has been proposed 
+> as candidate, the Authors should make a connection between their 
+> abstract OP and possible physical realizations. For instance, in the 
+> simplest framework of localized f-electrons, what ionic moments would 
+> fit the present proposal?
+
+[Mike, can you help with this?]
+
+> ----------------------------------------------------------------------
+> Report of the Second Referee -- BN13654/Kent-Dobias
+> ----------------------------------------------------------------------
+> 
+> In this paper, possible elastic properties of URu2Si2 are studied with 
+> focusing on the long-standing hidden order (HO) problem. The authors 
+> introduce a generic form of the free energy density for the elastic 
+> energy, a modulated order parameter, and their mutual coupling, and 
+> analyze the temperature dependences of the elastic constants by 
+> minimizing the free energy. It is shown that the B1g component 
+> exhibits a remarkable softening with decreasing temperature and a cusp 
+> singularity at the HO transition point, and these results are compared 
+> with recent ultrasound experiments. From the comparison, the authors 
+> conclude that the HO phase of URu2Si2 originates from the modulated 
+> B1g order parameter. 
+> 
+> In the course of evaluation, the referee does not recommend the paper 
+> to be published in PRB, mainly based on the following reason. 
+> 
+> 1) The scheme for the coupled strains in this paper is quite standard 
+> within the mean-field treatment and does not provide a novel 
+> theoretical advance. 
+> 
+> 2) One can generically expect several sources for softening elastic 
+> constants. For example, the authors in ref.25 also succeeded in the 
+> quantitative fits in the framework of a 4f crystal field model for T > 
+> T_HO. Thus, the fitting is not regarded as the decisive evidence on 
+> the validity of the model. 
+
+[Not sure how to respond to this; Brad?]
+
+> 3) The agreement of C[B1g] in the region T<T_HO is poor, though only 
+> the cusp at T_HO seems qualitatively consistent with the experiment. 
+> Moreover, the referee expects that even a cusp structure in the 
+> elastic constants is not unique to this model; it can be obtained from 
+> more general models beyond the linear coupling (4), within the 
+> mean-field level. Therefore, the referee thinks that this analysis 
+> does not lead uniquely to the authors' arguments on the realization of 
+> the B1g order parameter. 
+
+The disagreement between the theory at low temperature is resolved by the
+addition of an additional interaction in the mean-field free energy of the form
+ε²η², now shown in Fig. 2 as a thin black line.
+
+While terms like this provide cusp-like features in the modulus for each strain
+symmetry, they cannot explain the 1/ΔT softening seen in the high-temperature
+phase, since their contribution to the response function is zero above T_c.
+
+> 4) The most important point in the HO problem is the microscopic 
+> identification of symmetry breaking and the order parameter. In spite 
+> of the long history in research over almost 40 years, there is no 
+> experimental evidence of the formation of any superlattice structure 
+> at least at ambient pressure. So, the proposed modulated order is not 
+> consistent with the absence or identification of symmetry breaking. 
+> The authors do not provide any resolution on that point which is the 
+> most relevant in this problem.
+
+The articles below provide experimental evidence for the formation of
+superlattice structure along the c-axis at ambient pressure.
+
+[I pulled these from our citation on the estimate for q_*. Do they actually provide the evidence we need?]
+
+https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.127002
+https://journals.aps.org/prb/abstract/10.1103/PhysRevB.43.12809
+https://journals.jps.jp/doi/10.1143/JPSJ.79.064719
+https://www.nature.com/articles/nphys522
+