Superconductor discovery in the emerging paradigm of Materials Informatics

TL;DR

This review surveys the computational discovery of hydride superconductors through Migdal-Éliashberg theory and first-principles methods, highlighting how structure prediction and electron-phonon calculations yield Tc estimates that, in several landmark cases (e.g., H$_3$S, LaH$_{10}$), align with experimental realizations under high pressure. It then outlines the emergence of materials informatics as a complementary framework, detailing data resources, predictive models from formula and structure, ML-assisted structure screening, and accelerated structure prediction using ML potentials. The piece emphasizes both the substantial achievements in predicting record Tc values at high pressure and the critical gaps—data scarcity, model interpretability, and domain shift—that currently limit ambient-condition discovery. Finally, it articulates concrete future directions where data generation, physics-informed deep learning, and ML-guided design could synergistically advance the search for ambient-pressure superconductors.

Abstract

The last two decades have witnessed a tremendous number of computational predictions of hydride-based (phonon-mediated) superconductors, mostly at extremely high pressures, i.e., hundreds of GPa. These discoveries were heavily driven by Migdal-Éliashberg theory (and its first-principles computational implementations) for electron-phonon interactions, the key concept of phonon-mediated superconductivity. Dozens of predictions were experimentally synthesized and characterized, triggering not only enormous excitement in the community but also some debates. In this Article, we review the computational-driven discoveries and the recent developments in the field from various essential aspects, including the theoretical, computational, and, specifically, artificial intelligence (AI)/machine learning (ML) based approaches emerging within the paradigm of materials informatics. While challenges and critical gaps can be found in all of these approaches, AI/ML efforts specifically remain in its infant stage for good reasons. However, opportunities exist when these approaches can be further developed and integrated in concerted efforts, in which AI/ML approaches could play more important roles.

Figures (15)

• Figure 1: The time evolution of $T_{\rm c}$ for some classes of superconductors.
• Figure 2: Typical computational (a) and experimental (b) workflows for superconductor discovery. ML efforts are categorized in 5 groups (see Sec. \ref{['sec:ML']}), three of them are (iii) predicting superconductivity-related properties, (iv) accelerate the structure predictions by ML potentials, and (v) deriving new formulae of $T_{\rm c}$. Some computational predictions were advanced to experimental synthesis and characterization.
• Figure 3: An incompleted snapshot of the phonon-mediated superconductors discovered computationally. For some of them, e.g., H$_3$S and LaH$_{10}$, experimental data are available and also shown. Highlighted in the figure, data for MgB$_2$ at 0 GPa, Li$_2$MgH$_{16}$ at 250 GPa, H at 700 GPa, and SiH$_4$ at 800 GPa are taken from Refs. nagamatsu2001superconductivity, sun2019route, zhong2022prediction, and zhang2015high, respectively. Part of the data used for this Fig. has been used for Fig. 2c of Ref. tran2023machine.
• Figure 4: (a) The predicted $C2/c$ structure of silane SiH$_4$yao2007superconductivity, (b) the spectral function $\alpha^2F(\omega)$ and accumulated $\lambda (\omega)$ of the $C2/c$ structure, (c) the fabricated sample placed within the four-point probe, (d) a representative superconducting step in measured resistance, and (e) pressure-dependent $T_{\rm c}$ measured for silane. Panels (b) and (c, d, e) were reprinted with permission from Ref. yao2007superconductivity (Copyright 2007, IOP Publishing) and Ref. eremets2008superconductivity (Copyright 2008, The American Association for the Advancement of Science), respectively.
• Figure 5: (a) The predicted $Im\overline{3}m$ structure of H$_3$S, (b) phonon band structure, the spectral function $\alpha^2F(\omega)$, and accumulated $\lambda (\omega)$ of the $Im\overline{3}m$ structure at 200 GPa, (c) four Ti electrodes sputtered on a diamond anvil, i.e., a four-point probe, at the center of them is the sample, (d) $R$-$T$ dependence measured for H$_3$S at different pressures, (e) $R$-$T$ dependence measured for H$_3$S and H$_3$D, which reveals the isotope effect, and (f) the magnetization measured as functions of external field, showing the diamagnet and paramagnet characteristics below and above $T_{\rm c}\simeq 203$ K, respectively. Panels (b) and (c, d, e, f) were reprinted with permission from Ref. duan2014pressure (under a Creative Commons license) and Ref. Drozdov15 (Copyright 2015, Springer Nature), respectively.