Motivated by the ground-breaking discovery of near room-temperature superconductivity in high-pressure superhydrides, in this project we will combine state-of-the art computational methods for ab-initio material design and data science to search for new materials that could superconduct under liquid nitrogen cooling at ambient pressure. We will focus on ternary hydrides and light element compounds, which are too promising venues to find covalent metals that could exhibit high-Tc conventional superconductivity. Compared to just ten years ago, the progress of ab-initio methods is such, that it is now possible to predict the superconducting phase diagram of an arbitrary combination of elements on a computer. The complexity of the chemical space is however too large for a brute-force exploration; machine learning methods will be employed to steer the search into promising direction. The synergy of different computational methods for targeted material discovery is one of the emerging trends in condensed matter research (material
State of the Art and own Preliminary work
The hope of identifying superconductotrs (SC) that can operate at, or close to, ambient temperature, was revamped five years ago by the discovery of superconductivity in a sulfur superhydride (SH3) at Megabar pressure. Not only did SH3, and, later, LaH10 (fig. 1a), set new Tc records (203 and 260 K, respectively), but also indicated a new avenue for SC discovery: in fact, for the first time in over one century, the experimental reports were anticipated by accurate theoretical predictions. Crucial developments in abinitio methods for Xtal structure prediction and superconductivity in the last 10 years – fig. 1(b)-1(c) – had permitted to calculate on a computer phase diagrams and Tc of most conventional SC with an accuracy which is often comparable to experiments. The SH3 discovery has been followed by a “hydride rush”, in which more than 100 new H-based binary SC have been predicted and, in many cases, experimentally synthesized. The discovery of superhydrides is of great fundamental, but little practical, importance, due to the high pressures involved (1 Mbar=10^6 atmospheres). Therefore, the next challenge in the field is to identify materials, where high-Tc superconductivity may be realized at ambient pressure1. This is the goal of the present project, where the problem will be tackled using a combination of stateof- the-artl ab-initio (DFT-based) and machine learning methods (Material Informatics). Our group is perfectly placed to meet this challenge, having a recognized experience in ab-initio calculations for SC and Xtal structure prediction. In the last 5 years, we have published more than 15 papers on superconductivity at high pressures, including an invited review , and have been invited to present our results at more than 10 international conferences, including the APS March Meeting 2020 and
Superhydrides represent an unprecedented starting point to understand the key factors underlying high-Tc superconductivity. At variance with other classes of high-Tc superconductors, such as Fe pnictides and cuprates, for which no universally-accepted theory of SC exists, superhydrides are phonon-mediated (conventional) superconductors, described in broad terms by Migdal-Eliashberg theory. Several anomalies exist, concerning the role of anharmonicity, non-adiabatic corrections to electron-phonon interaction, Coulomb interaction. , which need to be addressed for a quantitative theory of superconductivity. -> Q1: How good is our current description of high-Tc superconductivity in high-pressure hydrides? Superhydrides form highly symmetric hydrogen sublattices, held together by metallic covalent bonds, which are key factors to boost the Tc. After five yers, binary hydrides have been fully explored computationally, and it is clear that these conditions can only be realized at extreme pressures (> 100 GPa), and only for a few elements, which lie in two “sweet spots” of the periodic table. However, it is reasonable to assume that the same factors leading to high-Tc superconductivity
in superhydrides may be realized in other systems, which require lower stabilization pressures. Strong candidates are ternary hydrides (Q2 Can ternary hydrides improve over binary hydrides?), or light-element compounds (Q3: Is it possible to find other compounds that realize high-Tc conventional superconductivity? ). In fact, light electronegative elements like boron, carbon, nitrogen can form covalent metals, with high phonon frequencies, such as MgB2, alkali-doped fullerites, graphane, LiBC, and for some of these Tc’s as high as 120 K have been predicted. Using computational methods for XSP and SC it is in principle possible to verify whether any of these systems could host high-Tc SC, and propose meaningful synthesis routes, with inexpensive computer experiments. However, it is unthinkable to perform a brute-force scan of all possible compositions, because the complexity of the chemical space, even for a limited set like ternary hydrides, is too large. Machine learning methods will be employed to reveal patterns and correlations in the data generated by computational experiments, to help and steer the search in promising directions (Q4: What are the descriptors of high-Tc conventional
Computational SC design will follow a simple four-step procedure. feedback loop: (1) The phase diagrams for selected elemental combinations will be constructed using state-of-the-art computational methods for XSP, such as evolutionary algorithms and minima hopping. XSP algorithms use efficient methods to sample the free energy surface of a system and locate the (local)global minima, corresponding to its (meta)stable structures.
(2) Superconducting properties will then be computed from first-principles at different levels of theory, eventually including anharmonic, non-adiabatic or Coulomb corrections, employing ab-initio Migdal-Eliashberg theory and/or Superconducting Density Functional Theory.  (3) The data thus generated will be organized into DB, which also contain other physical and structural properties of the structures, which may be indicators (descriptors) of Tc, using ad-hoc developed scripts. (4) Once a sufficiently large DB has been generated, we will employ standard python libraries for data handling and machine learning (panda, sci-kit learn), to perform a statistical analysis of the database. This information will be used to identify the most promising regions to explore in the chemical space.
-  A. P. Drozdov et al., Nature 525, (2015);
-  J.A.Flores-Livas, L. B., A. Sanna, G.
Profeta, R. Arita and M. Eremets, Physics Reports 856, 1-78 (2020) and refs therein;
-  L Pietronero, L. B., E. Cappelluti, L Ortenzi, Quantum Studies: Mathematics and Foundations 5, 5 (2018);
-  A. Sanna, C. Pellegrini, and E. K. U. Gross, Phys. Rev. Lett. 125, 057001 (2020);
-  S. Saha, S. Di Cataldo, M. Amsler, W. von der Linden, and L. B., Phys. Rev. B 102, 024519 (2020).
Lilia Boeri, Dipartimento di Fisica, Sapienza Università di Roma
Giovanni Battista Bachele, Dipartimento di Fisica, Sapienza Università di Roma