CommunicationImportance of carbon in carbonaceous sulfur hydride room-temperature superconductor
Introduction
Very recently a team from the Universities of Rochester and Nevada, Las Vegas made history by raising the superconducting transition temperature, , to 287 K in carbonaceous sulfur hydride (CSH) at 267 GPa [1]. On the surface this achievement aligns with the use of hydrogen dominant metallic alloys, including sulfur hydride (SH) and lanthanum hydride (LH) in diamond anvil cells [2], [3], to replace metallic hydrogen resulting in high temperature superconductors [4], [5]. However, detailed analysis, together with a range of observational evidence, tell an interesting story about carbon.
In our analysis the characteristic temperature in the Bloch–Grüneisen formula, , which in most metals is close to the Debye temperature, [6], is found to be 6239 K. With the help of the Eliashberg–Nambu formalism and a generic model electron–phonon spectral density, , we have no difficulty to reproduce in CSH theoretically. On the other hand, is believed to be just 3500 K in metallic hydrogen [4], suggesting hydrogen may not be the main reason for the high values of both and in CSH.
Carbon appears to have played an important role in CSH, eclipsing the role of hydrogen, in accordance with a range of observational evidence. For example, in recent exhaustive surveys [7], [8], [9] is found to be K (14 K below freezing point) in any hydrides without carbon. Another example lies in the relatively low values of both and (203 and 1223 K) in SH, which is chemically similar to CSH (287 and 6239 K) apart from the absence of carbon [10]. In addition K in carbon in ambient [11] already comparable with in metallic hydrogen and could become higher under pressure to promote and in CSH.
The value of can be extracted with high precision from just a few measurements of electrical resistance, , over a narrow range of temperature, . We do not even have to know the size of the sample, in order to convert into electrical resistivity, , because the Bloch–Grüneisen formula applies to both and , and the latter is not routinely available in the literature [1], [2], [3]. More sophisticated measurements, such as infrared optical spectroscopy [12], are difficult to perform and may not be as quantitative and straightforward to interpret.
Our application of the Eliashberg–Nambu formalism aims at reducing the uncertainties usually in association with the formalism. We take advantage of interdependence among the defining properties of a conventional superconductor, including , , and for the strength of the electron–phonon interaction, the Coulomb repulsion, and the gap-to-temperature ratio respectively. We find these can be determined reasonably accurately from values of and and nothing else.
Our article is arranged as follows. In Section 2 we fit the Bloch–Grüneisen formula to find for lead, SH, and LH to demonstrate the applicability and reliability of our method. In Section 3 we evaluate the model to determine , , and again for lead, SH, and LH. In Section 4 we analyze CSH to reveal its unusual properties. In Section 5 we discuss observational evidence of the importance of carbon in CSH. Brief conclusions are placed in Section 6.
Section snippets
Fitting Bloch–Grüneisen formula
To illustrate the idea and verify its applicability and reliability, we apply our method first to a classical metallic superconductor, lead, which has been widely examined, leaving abundant experimental data to scrutinize with analysis. In lead K when the sample is measured at 298 K [13]. In the lower left corner of Fig. 1, the small circles represent exemplary lead resistivity from a sample of 14 measurements, K [14]. We fit the Bloch–Grüneisen formula to the sample and find
Evaluating electron–phonon spectral density
To extract superconducting properties from the sample we apply the following generic model of the electron–phonon spectral density: otherwise . Here is phonon frequency in eV, Boltzmann constant, and phonon exchange factor measuring the strength of the electron–phonon interaction. Eq. (1) is written in terms of which is more accessible experimentally in comparison with . We also have , correct by definition [15].
We must determine in
Analyzing carbonaceous sulfur hydride
Now we are adequately equipped to find the most likely values of , , and in CSH. There are a number of curves in [1] for the relation between and in CSH in the normal state. The curves in FIG. 1 in [1], measured below 265 K in the absence of a magnetic field, are somewhat chaotic. They show clearly when the superconducting transition takes place, but are hardly usable for the purpose of extracting . The curves at 174 and 210 GPa have kinks unusual to the dependence of on in for
Discussion
In 1968 Ashcroft applied the BCS theory to the proposed metallic modification of hydrogen and suggested it will be a high- superconductor on account of high in the material [4]. In 2003 Ashcroft argued that in hydrides the attainment of metallic states should be well within the current capabilities, but at pressures considerably lower than may be necessary for hydrogen [5]. The fascinating progress in this direction over the years has been summarized in a number of reviews [7], [8], [9].
Conclusions
In conclusion, in CSH the value of is extremely high but rather low, indicating an extremely high Debye temperature but weak electron–phonon interactions. This suggests that it is worthwhile to verify if is actually so high, by measuring more accurately, or directly measuring by other means. For example the accurate method to measure the - relation at 267 GPa, with superconductivity being suppressed, could be applied at other pressures, see FIGs. 1 and 2 in [1], in order to expose
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors wish to thank the late Professor David George Walmsley for his direction, inspiration, and help on this line of research.
References (23)
- et al.
A perspective on conventional high-temperature superconductors at high pressure: methods and materials
Phys. Rep.
(2020) - et al.
On distribution of superconductivity in mMetal hydrides
Curr. Opinion Solid State Mater. Sci.
(2020) - et al.
Prospects to attain room temperature superconductivity
Solid State Commun.
(2019) - et al.
Room-temperature superconductivity in a carbonaceous sulfur hydride
Nature
(2020) - et al.
Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system
Nature
(2015) - et al.
Superconductivity at 250 K in lanthanum hydride under high pressures
Nature
(2019) Metallic hydrogen: a high-temperature superconductor?
Phys. Rev. Lett.
(1968)Hydrogen dominent metallic alloys: high temperature superconductors?
Phys. Rev. Lett.
(2004)Electrons and Phonons, Vol. 366
(2001)- et al.
Structure and superconductivity of hydrides at high pressures
Natl. Sci. Rev.
(2017)
Debye temperature and stiffness of carbon and boron nitride polymorphs from first principles calculations
Phys. Rev. B
Cited by (4)
High-temperature superconductivity in hydrides
2022, Physics-UspekhiSuperconductivity in ternary hydrides at high pressure
2022, Modern Physics Letters BNew superconducting superhydride LaC<inf>2</inf>H<inf>8</inf>at relatively low stabilization pressure
2021, Physical Chemistry Chemical Physics