Figures 1(a) and (c) are implausible. Usually something like this looks like this [0]. Note the gradual increase at low currents, this effect is to be expected especially with magnetic fields.
Fig. 1(d) cannot be correct either. At Tc ~ 400K the Meissner effect would displace a much stronger field than 10 Oe = 1 mT. I.e. the distinction between FC (field cooled) and ZFC (zero-field cooled) should not be that pronounced. It should look more like this [1].
What the authors might mean is that they are outside the Meissner range, which can occur at higher magnetic fields (keyword: Type II superconductors). It will look like that [2].
In this case, however, the temperature dependency does not agree at all with the critical currents of Figs. 1(a) and (c).
Also, that ALL the values in Fig. 1(d) are negative is extremely unusual, but that could perhaps be argued with.
The data set in Fig. 4(b) is also a treat. It is VERY unusual when the heat capacity decreases again at high temperatures. This can happen at low temperatures, but not at high temperatures.
I am very familiar with the described experimental setup / the cryostat. There is no good reason why the authors did not measure at higher temperatures to show that the behavior is markedly different above Tc ~ 400K. For example, a temperature dependency of the resistance would have been absolutely necessary.
In general, the paper is very poorly written. The data is under-discussed, the explanations are sparse, and the work cited is, shall we say, sparse. That doesn't exactly inspire confidence in what the authors measured and claim to have seen.
My personal assumption is that the authors measured an insulator, so no current flowed and therefore no voltage occurred (4-point measurement). Then it looks like a superconductor. But if you then turn up the current (i.e. the applied voltage), breakdowns may occur and a current begins to flow. That would explain the sharp increase.
Src: Max Planck Institute for Solid State Research
[0] https://www.researchgate.net/profile/Matthias-Graf-4/publica...
[1] https://www.researchgate.net/publication/370037045/figure/fi...
[2]https://www.europhysicsnews.org/images/stories/hl/472/Guo.jp...
