Room Temperature Superconductivity: the Roles of Theory and Materials Design

Abstract: For half a century after the discovery of superconductivity, materials exploration for better superconductors proceeded without knowledge of the underlying mechanism. The 1957 BCS theory cleared that up: the superconducting state occurs due to pairing of electrons over the Fermi surface. Over the following half century higher critical temperature T$c$ was achieved only serendipitously as new materials were synthesized. Meanwhile the formal theory of phonon-coupled superconductivity at the material-dependent level became highly developed: given a known compound, its value of T$_c$, the superconducting gap function, and several other properties of the superconducting state became available independent of further experimental input. More recently, density functional theory based computational materials design has progressed to a predictive level -- new materials can be predicted on the basis of various numerical algorithms. Taken together, these capabilities enable theoretical prediction of new superconductors. Here the process that resulted in three new highest temperature superconductors, predicted numerically, confirmed experimentally -- SH$_3$, LaH${10}$, and YH$_9$ -- is recounted. These hydrides have T$_c$ in the 200-280K range at megabar pressures, and here the development will be chronicled. Current activities and challenges are discussed, together with Regularities in compressed hydrides that can guide further exploration.

• The paper establishes a framework combining DFT and Eliashberg theory to predict superconductivity in hydrogen-rich compounds, validated by experimental breakthroughs in SH3, LaH10, and YH9.
• It shows that high-pressure experiments confirm superconductivity near room temperature, with critical temperatures reaching up to 260K under megabar pressures.
• The study outlines future challenges in stabilizing these superconductors at lower pressures, suggesting further computational and experimental efforts may unlock ambient superconductivity.

Room Temperature Superconductivity: The Roles of Theory and Materials Design

This document presents a detailed analysis of the theoretical and experimental advancements in achieving room-temperature superconductivity (RTS). The study focuses on recent developments within the sphere of superconductivity, particularly concerning hydrogen-rich compounds under high pressure. It encompasses a thorough overview of the milestones that have been achieved through a theoretical design and subsequent experimental validation.

Theoretical Foundations and Computational Advances

The primary theoretical framework for understanding superconductivity was established by the BCS theory in 1957, which proposed electron pairing mediated by phonons. Subsequent decades brought the Migdal-Eliashberg theory, extending superconductivity understanding to account for strong coupling effects up to the modern Density Functional Theory (DFT) implementations. DFT, particularly when combined with Eliashberg theory, allows for the prediction of electron-phonon coupling parameters and critical temperatures ($T_c$) for specific materials. The formulation of the superconducting density functional theory (SCDFT) extended these capabilities, providing a rigorous first-principles method to predict superconducting properties without empirical input.

Figure 1: A plot from the discovery of superconductivity in Hg in 1911 covering major advances in maximum $T_c$ over the years, illustrating the progression toward current hydride superconductors.

Experimental Milestones and Material Discovery

The exploration of hydrogen-rich compounds under megabar pressures has led to the discovery of superconductors with $T_c$ approaching room temperature. The three compelling discoveries highlighted are hydrogen sulfide (SH$_3$), lanthanum hydride (LaH$_{10}$), and yttrium hydride (YH$_9$). These hydrides, achieved through computational predictions validated by experimentation, exhibit superconductivity at remarkably high temperatures:

• SH$_3$: The superconductivity of hydrogen sulfide, predicted to occur around 200K at approximately 160 GPa, was a pivotal breakthrough, serving as the initial evidence supporting the feasibility of high $T_c$ transitions in hydrides at high pressures.
• LaH$_{10}$: Following SH$_3$, lanthanum hydride was experimentally confirmed to superconduct at temperatures up to 260K under pressures around 200 GPa, corroborating theoretical predictions and pushing the boundaries further toward RTS.
• YH$_9$: Yttrium hydride exhibited superconductivity around 240-260K, further cementing the potential for high-temperature superconductivity in metal hydrides.

  Figure 2: Bergmann and Rainer's plots showing $\delta T_c/\delta \alpha^2F(\omega)$, underscoring the critical contributions of higher-frequency phonons to $T_c$.

Implications and Future Directions

The implications of these developments are profound for both theoretical research and practical applications. The progress demonstrated here signifies a promising pathway toward achieving superconductivity at ambient conditions, presenting new opportunities for revolutionary applications in technology and energy.

The fundamental challenges remain multifaceted, requiring advances in understanding the coupling mechanisms in hydrogen-rich compounds and the development of techniques for synthesizing stable phases at lower pressures. Continued exploration through computational techniques and high-pressure experiments is expected to yield further insights and discoveries in the field.

Figure 3: McMillan's plot illustrating the remarkable agreement between experimental values and calculations, providing a foundation for understanding superconductivity in metal alloys.

Conclusion

The advancement toward room-temperature superconductivity is exemplified by the synthesis and characterization of compressed metal hydrides, substantiated by theoretical predictions and experimental validations. Researchers continue to face challenges related to stability, material selection, and pressure requirements. However, with ongoing innovations in computational materials design and experimental techniques, the realization of practical superconductors that operate at ambient conditions remains an attainable goal.

The collective efforts within this domain highlight the transformative potential of integrating theoretical frameworks with experimental breakthroughs, ushering in a new era of superconducting materials with unprecedented properties and applications.