Examining Hirsch's Criticism of Superconductivity in Carbonaceous Sulfur Hydride (C-S-H)


    Recently, a paper on high-pressure superconductivity in the C-S-H system [1] by R. Dias et al. has been published in Nature as the first room-temperature superconductor. There are still several problems to be clarified, such as the identification of the superconducting material, follow-up tests by other groups, and identification of the crystal structure. However, one of the reasons for the attention is that the paper has been exposed to criticism such as "Is the data reported in Nature real?". 

    This criticism has been made mainly by the American physicist, J. E. Hirsch, who has made various criticisms, including that "the transition in electrical resistance is not broadened by applying the magnetic field", "the behavior of the magnetic susceptibility is similar to previously reported results for Eu high-pressure superconductivity", and "raw verification data was not provided to Dias et al." [2]. On the other hand, Dias et al. also made various objections, such as that "We had no data to provide to Hirsch, a troll who criticized the BCS theory, the standard theory of superconductivity", and "Hirsch did not understand experiments under high pressure" [3]. This debate has been fiercely contested, with Hirsch's critical paper being withdrawn because he took the liberty of including his private correspondence with Dias et al. in his critical paper, and the Eu high-pressure superconductivity paper [4], in which Dias's collaborators were involved, being retracted.
    In this article, I would like to focus on the latest critical paper by Hirsch [5].

[Contents of the latest critical paper]

    Since the first reports of C-S-H superconductivity, Hirsch has criticized the interpretation of the data. Aside from the validity of Hirsch’s claim, Dias and others responded to the criticism by submitting a rebuttal paper [6] to Arxiv at the end of 2021, which included details of the experiment and the raw magnetic susceptibility data. In the latest paper, Hirsch analyzed the raw data and pointed out the possibility that the data had been manipulated.
    Let's take a look at the contents. First, the following figure 1 shows the results of the magnetic susceptibility reported in the Nature paper and the magnetic susceptibility from the raw data in the rebuttal paper. The behavior of the magnetic susceptibility is very similar, so we can confirm that it is indeed the raw data.
    However, there is one embarrassing aspect of this reproduction. This is because the raw data in the rebuttal paper was pasted as a figure, not a table, and Hirsch et al. had to read each value and convert it into tabular data (Fig. 2 and 3). It is interesting to note that only the 160 GPa data is pasted as a figure, while the other pressure data is in tabular form and can be copied and pasted. The reason for Dias et al.'s apparently nonsensical response is not well understood.
Figure 1, row data of magnetic susceptibility (left) and the data published in Nature(right).

Figure, 2 this is a table data. OK.

Figure 3, This is a figure. Why???

    Hirsch et al. pointed out that there was an unnatural jump in the raw data by trying to differentiate it from the neighboring temperature data (fig. 4). Furthermore, since this jump is an integer multiple of the value 0.1655, Hirsch et al. point out that this may be the result of an unusual background subtraction from the raw data, and that it may be a "Manipulation" of the actual data. In other words, they may be doing something other than the linear background subtraction claimed in the rebuttal paper.
Figure 4, the magnetic susceptibility @ 160GPa (left top) and 
the original row data reproduced by Hirsch (left bottom).

    To see if Hirsch et al. were right, I tried to check the difference in the same way with the raw data of other pressures reported by Dias et al. The reason for this is that if the other data also shows anomalous spikes, it could be a characteristic of the equipment.
 The figure 5 (top) shows the raw data of the magnetic susceptibility at 189 GPa, a copy-and-pasteable pressure from the rebuttal paper by Dias et al [6]. It is stated in the paper that the magnetic susceptibility is obtained by subtracting the linear background from this raw data. Figure 5 (middle) is the result of subtracting the straight line background from figure (top), and indeed, it shows a superconducting transition similar to that of 160 GPa, which is read as Tc=198 K. The temperature difference of the data is shown in fig. 5 (bottom). From the figure, we can't see any spikes, as Hirsch pointed out. In other words, it doesn't seem that the deviation of the data is a characteristic of the device.

Figure 5 (top)、the row data @ 189GPa.
(middle), the linear back ground substracted data. 
(bottom), the data with the difference from the neighboring temperature.

    The 160 GPa data may contain errors because Hirsch et al. did their best to create the table data by reading from the figure. I should have tried to do it myself, but I gave up because it was too tedious to input the data manually. I guess this is what Dias et al. are aiming for...?
 In any case, I could not deny the possibility that only the 160 GPa data had been mysteriously "manipulated".


 I tried to do a verification similar to the one done in the critical paper on C-S-H high pressure superconductivity by Hirsch et al. In one of the raw data that I could copy and paste, I could not confirm the mysterious spikes in the data found by Hirsch et al. This is not enough to say anything, but it will be interesting to see what the authors of the C-S-H system of high-pressure superconductivity will show again in their rebuttal.


[1] Snider, E., Dasenbrock-Gammon, N., McBride, R. et al. Room-temperature superconductivity in a carbonaceous sulfur hydride. Nature 586, 373–377 (2020).
[2] Jorge E Hirsch, On the ac magnetic susceptibility of a room temperature superconductor: anatomy of a probable scientific fraud, arXiv:2110.12854
[3] Breakthrough or bust? Claim of room-temperature superconductivity draws fire, doi: 10.1126/science.acx9428
[4] M. Debessai, et al., Retraction: Pressure-Induced Superconducting State of Europium Metal at Low Temperatures [Phys. Rev. Lett. 102, 197002 (2009)], Phys. Rev. Lett. 127, 269902 – Published 23 December 2021
[5] Dirk van der Marel, Jorge E Hirsch, Comment on Nature 586, 373 (2020) by E. Snider et al., arXiv:2201.07686
[6] Ranga P. Dias, Ashkan Salamat, Standard Superconductivity in Carbonaceous Sulfur Hydride, arXiv:2111.15017