Room temperature superconductivity at near ambient pressure has recently been claimed for a Lu-H-N compound [1]. In this paper, we question the validity of that claim on the basis of analysis of some of the reported measurement results that show anomalous features and discuss the implications of this analysis.

Fig. 1
figure 1

Resistance versus temperature for N-doped lutetium hydride at pressure \(\sim 10 kbar\), as reported in Ref. [1] ED Fig. 13a and associated reported raw data. The blue and red curves were measured under cool down and warm up conditions, respectively [1]

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In Extended Data (hereafter ED) Fig. 15 of Ref. [1], the authors show resistance versus temperature in the absence and presence of a magnetic field. The relative width of the resistive transition \(\Delta T/T_c\) shown in the inset of their figure is 0.13 for zero field. The superconducting transition width is defined as [1] \(\Delta T_c=T_{90\%}-T_{10\%}\), where \(T_{90\%}\) and \(T_{10\%}\) are the temperatures corresponding to \(90\%\) and \(10\%\) of what they assumed to be the critical temperature, \(T_c=292 K\). The authors explain the considerable width by stating “The large transition width at zero field indicates sample inhomogeneities, which is typical for high-pressure experiments.”, which is not implausible. However, in the data for resistance versus temperature in ED Fig. 13a of Ref. [1], shown here in Fig. 1, the width of the resistive transitions is only 0.04K, so the relative width is \(\Delta T/T_c=0.00014\), at comparable pressures (10 kbar vs 15 kbar, respectively). For the resistance curves shown in Fig. 2 of Ref. [1], at pressures 10 kbar and 16 kbar, the relative width is in-between those two extremes, \(\Delta T/T_c\sim 0.008\), 60 times larger than for ED Fig. 13a, 16 times smaller than for ED Fig. 15.

Following the logic of the authors, the sample used for ED Fig. 13a is 1000 times more homogeneous than the sample used for ED Fig. 15, and the samples used for their Fig. 2 are in-between. The protocol used in preparing these samples was presumably similar, as described in the “Methods” section of Ref. [1]. It is not understandable why superconducting samples prepared similarly would exhibit a degree of inhomogeneity that differs by three orders of magnitude. The fact that the transitions shown in Fig. 1 show hysteresis is also in conflict with what is expected for a superconductor and is not explained in the paper.

Fig. 2
figure 2

Resistance versus temperature for N-doped lutetium hydride at pressure 15kbar. Left panel: with background subtraction, as reported in Ref. [1] ED Fig. 15. Right panel: same without background subtraction, obtained from the raw data given in Ref. [1]. The black, blue, and red curves are for applied magnetic fields 0T, 1T, and 3T respectively [1]

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It should also be noted that the authors say “In some cases, small residual resistance from the instrument offsets was subtracted from the measured voltage”, but do not specify whether “some cases” include the resistance data shown in their Fig. 2 and ED Fig.13a. For ED Fig. 15, it is explicitly stated that a background resistance is subtracted out [1]. When plotting the raw data without background subtraction, the curves shown in Fig. 2 right panel result [4]. There is no hint of a superconducting transition in Fig. 2 right panel.

Fig. 3
figure 3

Top panel: voltage versus current from source data for Fig. 2b of Ref. [1]. Bottom panel: voltage versus current data for a known superconductor, from Ref. [7]

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In addition, the width of the transitions shown in Fig. 1 is unreasonably small. No other known superconductor exhibits such sharp transitions even at ambient pressure, and under pressure additional broadening of the transition should result from pressure gradients. In Ref. [2], we pointed out that the narrow width of the transitions reported in Ref. [3] for another room temperature superconductor under pressure, CSH, was unreasonably small, \(\Delta T/T_c=0.005\), and that was 35 times larger than the width seen in Fig. 1. Other anomalies in the resistance curves of Ref. [3] were noted in Ref. [5]. Reference [3], which has six coauthors in common with Ref. [1], was recently retracted [6].

Furthermore, the voltage-current characteristic shown in Fig. 2b of Ref. [1], reproduced here in Fig. 3 top panel, is not consistent with what is expected for a superconductor at temperature well below its critical temperature \(T_c\). There is no evidence of any region of zero resistance in Fig. 3 top panel, in contrast with the typical behavior shown in Fig. 3 bottom panel for a known superconductor [7], showing zero voltage up to a critical current that increases as the temperature decreases. Other such measurements for known superconductors showing how this behavior varies with temperature and magnetic field are shown in Refs. [8–11]. If one nevertheless insisted to infer a non-zero critical current from Fig. 3 top panel, it would be certainly smaller than 0.5 mA, at temperature \(T/T_c\sim 0.1\). According to the authors, “On average, sample sizes are on the order of 70–100 \(\mu\)m in diameter and 10–20 \(\mu\)m thick.” Assuming the smallest cross-sectional area in that range, A\(\sim\) 10 \(\mu\)m \(\times\) 70 \(\mu\)m, yields a critical current density \(J_c<\) 72 A/cm\(^2\) (or smaller if larger dimensions are assumed). That would be five orders of magnitude smaller than critical current densities reported for \(LaH_{10}\) and \(H_3S\) at temperature \(T/T_c\sim 0.5\) [13] and inconsistent with the magnetization measurements shown in Fig. 3 of Ref. [1].

Fig. 4
figure 4

Voltage versus current for Lu-H-N. Left panel: Fig. 2b of Ref. [1]. Right panel: another example reported by Dias, Ref. [12]

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Fig. 5
figure 5

Three holy grails. The top three panels show resistance versus temperature for three different compounds at pressure ranges \(\sim 200 GPa\) (Refs. [3, 16, 17]), \(\sim 20 GPa\) (Ref. [14, 15]), and \(\sim 2GPa\) (Ref. [1]), respectively, all showing room temperature superconductivity. The bottom three panels show \(T_c\) versus pressure for the three different compounds as reported in Refs. [1, 3, 14, 15]. Note that even though Ref. [3] was retracted [6], all the authors disagreed with the retraction

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Furthermore, the values of the normal state resistance at room temperature inferred from Fig. 2b of Ref. [1], and for another example of voltage current-characteristics presented by the lead author of Ref. [1] in Ref. [12], shown on the left and right panels of Fig. 4, are anomalously small: R\(\sim\) 1.12 m\(\Omega\) for the left panel, R\(\sim\) 0.05 m\(\Omega\) for the right panel. From the van der Pauw formula \(\rho \sim \pi d R /ln(2)\) (d = thickness, R = resistance), assuming the largest d = 20 \(\mu\)m yields \(\rho \sim\) 10 \(\mu \Omega\)-cm for the left panel of Fig. 4 and \(\rho \sim\) 0.4 \(\mu \Omega\)-cm for the right panel. These values are six times and 130 times smaller that the room temperature resistivity of lutetium metal. These discrepancies point to the behavior reported [1, 12] as voltage versus current for Lu-H-N both at room temperature and at low temperatures being due to experimental artifacts rather than superconductivity. It is notable that for other samples that showed a resistance drop from much larger room temperature resistance values (Fig. 2a and ED Fig. 13 a of Ref. [1]), consistent with what could be expected, no voltage-current characteristics were shown in Refs. [1, 12].

We also point out that the ac susceptibility data shown in ED Fig. 5 of Ref. [1] before background subtraction show a background dependence on temperature that has positive slope, negative slope, and zero slope, for the same or comparable pressures. The background ac susceptibility is expected to reflect the physical properties of the environment of the sample, which should not drastically change for different measurements.

Fig. 6
figure 6

Resistance versus temperature for various hydrides under pressure claimed to be high temperature superconductors. The name of the last author in the reference is shown in each panel. From upper left to lower right: LuHN [1],CSH [3], \(YH_9\) [30], \(LaH_{10}\) [31], \(LaH_{10}\) [32], \(YH_n\) [33], \(CeH_{10}\) [34], \(H_3S\) [35], \(CaH_6\) [36]

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We also point out that the lead author of Ref. [1] R. P. Dias and some of its coauthors have previously reported room temperature superconductivity in other compounds, at pressures one [14, 15] and two [3, 16, 17] orders of magnitude larger than reported in Ref. [1], as shown in Fig. 5. In the 112 years since superconductivity was discovered, no room temperature superconductivity has been conclusively established by other researchers in any compound at any pressure despite intensive searches. The probability that the same research group would hit this holy grail three separate times is insignificant.

Finally, we point out that experimental attempts to reproduce the results reported in Ref. [1] have shown no indication of superconductivity in samples prepared by following the sample preparation method described in Ref. [1, 18–23], and theoretical attempts to calculate \(T_c\) in this system within the conventional theory of superconductivity have found values of \(T_c\) two orders of magnitude smaller [24–27] than reported in Ref. [1].

In conclusion, the extreme sharpness of the resistive transition curves shown in Fig. 1, together with the facts that the width of the resistive transition changes by three orders of magnitude between different samples, that resistance data versus temperature plotted without background subtraction show no hint of superconductivity, that voltage-current characteristics do not show evidence for a finite critical current, that normal state resistances measured are anomalously small, that the background ac susceptibility changes drastically in different measurements, and that several experimental and theoretical studies have not been able to reproduce the results reported in Ref. [1], indicate that the behavior observed reported in Ref. [1] is not due to superconductivity.

If the resistance drops seen in Fig. 5 and other figs. of Refs. [1, 3, 16, 17] are not due to superconductivity, they must be due to other reasons unrelated to superconductivity, either physical phenomena or/and experimental artifacts associated with performing resistance measurements on very small hydrogen-rich samples under high pressure in diamond-anvil cells, with the expectation grounded in the conventional theory of superconductivity that superconductivity will be found [29]. The resistance versus temperature curves shown in Fig. 5 above and in other figs. of Refs. [1, 3, 16, 17] look similar to resistance versus temperature curves for other hydrides under high pressure that have been claimed to be high temperature superconductors in recent years [28], as shown in Fig. 6. This raises the possibility that those same other reasons unrelated to superconductivity that may account for the resistance drops in Refs. [1, 3, 16, 17] reported by Dias and coworkers could account for the resistance drops seen in all hydrides under high pressure claimed to be high temperature superconductors [28], in contradiction with the predictions of Ref. [29] and in agreement with other theoretical predictions [37]. Magnetic evidence claimed to support high temperature superconductivity in sulfur and lanthanum hydrides under pressure has been called into question elsewhere [38–41].