Importance of carbon in carbonaceous sulfur hydride room-temperature superconductor

doi:10.1016/j.ssc.2021.114295

Solid State Communications

Volume 331, May 2021, 114295

https://doi.org/10.1016/j.ssc.2021.114295 Get rights and content

Highlights

•
Tc reaches room-temperature in carbonaceous sulfur hydride (CSH) under pressure.
•
The experimental R–T relation in CSH is fitted to the Bloch–Gruneisen formula.
•
The characteristic temperature in CSH is found to be extremely high, suggesting high Debye temperature vastly exceeding that in metallic hydrogen.
•
Observational evidence indicates Tc may never exceed the freezing point in hydrides without carbon.
•
Importance of carbon may eclipse that of hydrogen in the pursuit of room-temperature superconductivity in ambient.

Abstract

In the new carbonaceous sulfur hydride superconductor, with $T_{c} = 287$ K at 267 GPa, the characteristic temperature is found to be 6239 K, implying a Debye temperature vastly exceeding that of metallic hydrogen. With the help of the Eliashberg–Nambu formalism and a generic model for the electron–phonon spectrum density, $0.92 < λ < 1.01$ , $0.125 < μ^{*} < 0.179$ , and $3.90 < 2 Δ_{0} ∕ k_{B} T_{c} < 3.92$ are shown to be the most likely defining properties of the superconductor. The extraordinarily high Debye temperature and relatively low $λ$ indicate the importance of carbon may be comparable to or even eclipsing that of hydrogen in the pursuit of higher $T_{c}$ in ambient.

Introduction

Very recently a team from the Universities of Rochester and Nevada, Las Vegas made history by raising the superconducting transition temperature, $T_{c}$ , 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, $Θ$ , which in most metals is close to the Debye temperature, $T_{D}$ [6], is found to be 6239 K. With the help of the Eliashberg–Nambu formalism and a generic model electron–phonon spectral density, $α^{2} F (ν)$ , we have no difficulty to reproduce $T_{c}$ in CSH theoretically. On the other hand, $T_{D}$ 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 $Θ$ and $T_{c}$ 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] $T_{c}$ is found to be $\leq 259$ K (14 K below freezing point) in any hydrides without carbon. Another example lies in the relatively low values of both $T_{c}$ and $Θ$ (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 $T_{D} = 2240$ K in carbon in ambient [11] already comparable with $T_{D}$ in metallic hydrogen and could become higher under pressure to promote $Θ$ and $T_{c}$ in CSH.

The value of $Θ$ can be extracted with high precision from just a few measurements of electrical resistance, $R$ , over a narrow range of temperature, $T$ . We do not even have to know the size of the sample, in order to convert $R$ into electrical resistivity, $ρ$ , because the Bloch–Grüneisen formula applies to both $R$ and $ρ$ , 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 $λ$ , $μ^{*}$ , and $2 Δ_{0} ∕ k_{B} T_{c}$ 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 $T_{c}$ and $Θ$ and nothing else.

Our article is arranged as follows. In Section 2 we fit the Bloch–Grüneisen formula to find $Θ$ for lead, SH, and LH to demonstrate the applicability and reliability of our method. In Section 3 we evaluate the model $α^{2} F (ν)$ to determine $λ$ , $μ^{*}$ , and $2 Δ_{0} ∕ k_{B} T_{c}$ 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 $T_{D} = 87$ 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, $1.30 \leq T \leq 88.56$ 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: $α^{2} F (ν) = λ {(ν ∕ k_{B} Θ)}^{2} when ν < k_{B} Θ,$ otherwise $α^{2} F (ν) = 0$ . Here $ν$ is phonon frequency in eV, $k_{B}$ Boltzmann constant, and $λ$ phonon exchange factor measuring the strength of the electron–phonon interaction. Eq. (1) is written in terms of $Θ$ which is more accessible experimentally in comparison with $T_{D}$ . We also have $2 \int α^{2} F (ν) d ν ∕ ν = λ$ , correct by definition [15].

We must determine $λ$ in

Analyzing carbonaceous sulfur hydride

Now we are adequately equipped to find the most likely values of $Θ$ , $λ$ , and $μ^{*}$ in CSH. There are a number of curves in [1] for the relation between $R$ and $T$ 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 $Θ$ . The curves at 174 and 210 GPa have kinks unusual to the dependence of $R$ on $T$ in for

Discussion

In 1968 Ashcroft applied the BCS theory to the proposed metallic modification of hydrogen and suggested it will be a high- $T_{c}$ superconductor on account of high $T_{D}$ 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 $Θ$ is extremely high but $λ$ rather low, indicating an extremely high Debye temperature but weak electron–phonon interactions. This suggests that it is worthwhile to verify if $T_{D}$ is actually so high, by measuring $Θ$ more accurately, or directly measuring $T_{D}$ by other means. For example the accurate method to measure the $R$ - $T$ 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)

Flores-LivasJ.A. et al.
A perspective on conventional high-temperature superconductors at high pressure: methods and materials
Phys. Rep.
(2020)
SemenokD.V. et al.
On distribution of superconductivity in mMetal hydrides
Curr. Opinion Solid State Mater. Sci.
(2020)
ZhengX.H. et al.
Prospects to attain room temperature superconductivity
Solid State Commun.
(2019)
SniderE. et al.
Room-temperature superconductivity in a carbonaceous sulfur hydride
Nature
(2020)
DrozdovA.P. et al.
Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system
Nature
(2015)
DrozdovA.P. et al.
Superconductivity at 250 K in lanthanum hydride under high pressures
Nature
(2019)
AshcroftN.W.
Metallic hydrogen: a high-temperature superconductor?
Phys. Rev. Lett.
(1968)
AshcroftN.W.
Hydrogen dominent metallic alloys: high temperature superconductors?
Phys. Rev. Lett.
(2004)
ZimanJ.M.
Electrons and Phonons, Vol. 366
(2001)
DuanD. et al.
Structure and superconductivity of hydrides at high pressures
Natl. Sci. Rev.
(2017)

ToheiT. et al.

Debye temperature and stiffness of carbon and boron nitride polymorphs from first principles calculations

Phys. Rev. B

(2006)

Cited by (4)

High-temperature superconductivity in hydrides
2022, Physics-Uspekhi
Superconductivity in ternary hydrides at high pressure
2022, Modern Physics Letters B
Crystal structures and superconductivity of carbonaceous sulfur hydrides at pressures up to 300 GPa
2022, Physical Review B
New superconducting superhydride LaC<inf>2</inf>H<inf>8</inf>at relatively low stabilization pressure
2021, Physical Chemistry Chemical Physics

View full text

CommunicationImportance of carbon in carbonaceous sulfur hydride room-temperature superconductor

Highlights

Abstract

Introduction

Section snippets

Fitting Bloch–Grüneisen formula

Evaluating electron–phonon spectral density

Analyzing carbonaceous sulfur hydride

Discussion

Conclusions

Declaration of Competing Interest

Acknowledgment

Phys. Rep.

Curr. Opinion Solid State Mater. Sci.

Solid State Commun.

Room-temperature superconductivity in a carbonaceous sulfur hydride

Nature

Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system

Nature

Superconductivity at 250 K in lanthanum hydride under high pressures

Nature

Metallic hydrogen: a high-temperature superconductor?

Phys. Rev. Lett.

Hydrogen dominent metallic alloys: high temperature superconductors?

Phys. Rev. Lett.

Electrons and Phonons, Vol. 366

Structure and superconductivity of hydrides at high pressures

Natl. Sci. Rev.

Debye temperature and stiffness of carbon and boron nitride polymorphs from first principles calculations

Phys. Rev. B

Communication
Importance of carbon in carbonaceous sulfur hydride room-temperature superconductor