Path 1: Metallic Hydrogen & Superhydrides (Phonon-Mediated Route)

Idea: Attain very high T_c by maximizing the conventional electron–phonon coupling with light atoms.

Rationale: Since BCS theory, scientists predicted lattice vibrations (phonons) could mediate pairing at higher temperatures if phonon frequencies and coupling are extreme. Ashcroft’s classic 1968 paper proposed that solid metallic hydrogen under immense pressure might superconduct near room T. This proved prescient: in 2015–2019, H–S and H–La compounds under >150 GPa yielded T_c = 203 K and 250 K, respectively. These superhydrides effectively “pre-compress” hydrogen chemically, validating strong phonon coupling as a path. Ongoing predictions suggest ternary hydrides (e.g. ScH₁₂, Li₂MgH₁₆) could even surpass 300 K albeit still at high pressure.

Prerequisites: BCS theory and Eliashberg formalism; high-pressure techniques (diamond anvil cells) to create metastable metallic phases; crystal structure prediction and density-functional theory (DFT) for phonon spectra.

Dependencies: Advances in materials informatics (Path 8) strongly accelerate this route by identifying promising hydrogen-rich formulas, and fundamental phonon theory (Path 9) guides how far T_c can go.

Signs of Progress: Stepwise milestones would include synthesizing a hydride that superconducts at >273 K under some pressure (e.g. predicted ScH₁₂ ~350 K at <100 GPa), then reducing the required pressure via chemical tuning (e.g. finding a stable ambient-pressure variant or quenchable phase). Observable progress markers: a robust Meissner effect at warmer temperatures, successful trapping of high-T_c phases at lower pressures, and the eventual demonstration of zero resistance in a capsule without cryogenics.

Base Camp 1.1: SC Fundamentals

• Michael Tinkham. Introduction to Superconductivity. McGraw-Hill, 2nd ed., 1996. – Classic textbook covering superconducting fundamentals (London theory, BCS, Josephson effects) with clarity. Foundational across camps (Path 1 and Path 9), it builds the base for understanding conventional mechanisms.
• Charles P. Poole Jr., Horacio A. Farach, Richard J. Creswick, and Ruslan Prozorov. Superconductivity. Academic Press, 2nd ed., 2010. – Comprehensive reference (encyclopedic coverage of elements, alloys, and high-Tc materials). Useful for both theoretical background and experimental properties; sets stage for why room-Tc is challenging.
• J. F. Annett. Superconductivity, Superfluids and Condensates. Oxford University Press, 2004. – Concise and pedagogical introduction connecting BCS theory with real-world superconductors. Great for a first-year grad student to gain intuitive understanding of pairing and condensate physics.

Base Camp 1.2: Eliashberg & Strong Coupling

• P. B. Allen and B. Mitrović. “Theory of Strong-Coupling Superconductors.” Solid State Physics, vol. 37, 1982, pp. 1–92. – A definitive review of Eliashberg theory, presenting how strong electron-phonon coupling modifies T_c and other observables. Valuable to grasp limits of phonon-mediated superconductivity (relevant for hydrides).
• G. M. Eliashberg. “Interactions between Electrons and Lattice Vibrations in a Superconductor.” Soviet Physics JETP, vol. 11, 1960, pp. 696–702. – Seminal paper extending BCS to the strong-coupling regime. Though technical, it’s the basis for understanding how H₃S and LaH₁₀ achieve such high T_c.
• J. P. Carbotte. “Properties of Boson-Exchange Superconductors.” Reviews of Modern Physics, vol. 62, no. 4, 1990, pp. 1027–1157. – Extensive review that includes Eliashberg results and analysis of various bosonic glue scenarios. Helps connect theoretical equations with measurable effects (e.g. tunneling spectra), reinforcing understanding of λ and μ in high-Tc contexts.

Base Camp 1.3: High-Pressure Techniques & Metallic Hydrogen

• M. I. Eremets. High Pressure Experimental Methods. Oxford University Press, 1996. – Handbook by a pioneer in high-pressure physics. Details diamond anvil cell design, pressure calibration, and in situ measurement techniques. Essential for anyone aiming to create or measure superconductors at megabar pressures.
• Neil W. Ashcroft. “Metallic Hydrogen: A High-Temperature Superconductor?” Physical Review Letters, vol. 21, no. 26, 1968, pp. 1748–1749. – The classic one-page paper that predicted metallic hydrogen’s superconductivity at ~300 K. Inspiring rationale for Path 1; shows how high sound velocity and strong coupling in hydrogen could raise T_c.
• R. J. Hemley and H. K. Mao. “Recent Changes in the Landscape of High-Pressure Science and Technology.” MRS Bulletin, vol. 33, no. 6, 2008, pp. 614–623. – Overview of high-pressure science including techniques and materials synthesis. Useful to understand practical limits of DAC experiments and emerging methods (like dynamic compression) that might access metallic hydrogen or similar phases.

Base Camp 1.4: Superhydride Materials & DFT Design

• J. A. Flores-Livas, L. Boeri, A. Sanna, et al. “A Perspective on Conventional High-Temperature Superconductors at High Pressure: Methods and Materials.” Physics Reports, vol. 856, 2020, pp. 1–78. – Comprehensive review of the high-pressure hydride frontier. Surveys theoretical predictions and experimental results up to 2020, offering guidance on which elements and structures yield high T_c. A roadmap for Path 1 researchers.
• Alexander P. Drozdov, et al. “Superconductivity at 250 K in Lanthanum Hydride under High Pressures.” Nature, vol. 569, 2019, pp. 528–531. – Experimental paper that achieved 250 K in LaH₁₀. Important for learning how DFT predictions were validated and how to interpret data like superconducting critical fields and isotope shifts in these phases.
• V. V. Struzhkin, et al. “Superconductivity in La and Y Hydrides: Remaining Questions to Experiment and Theory.” Elements, vol. 15, no. 1, 2019, pp. 37–42. – A concise discussion piece summarizing where the community stood after the 2015–2019 hydride discoveries. It lists open questions (e.g., structure, anharmonicity, quantum zero-point effects) that are essential for new researchers to address.