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Physics Reports a Perspective on Conventional High Physics Reports 856 (2020) 1–78 Contents lists available at ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep A perspective on conventional high-temperature superconductors at high pressure: Methods and materials José A. Flores-Livas a, Lilia Boeri a, Antonio Sanna b, Gianni Profeta c, ∗ Ryotaro Arita d,e, , Mikhail Eremets f a Department of Physics, Sapienza Universita' di Roma, Italy b Max-Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany c Department of Physical and Chemical Sciences and SPIN-CNR, University of L'Aquila, Via Vetoio 10, I-67100 L'Aquila, Italy d Department of Applied Physics, Hongo Bunkyo-ku 113-8656, Japan e RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, 351-0198, Japan f Max-Planck Institute for Chemistry, Hahn-Meitner-Weg 1 55128 Mainz, Germany article info a b s t r a c t Article history: Two hydrogen-rich materials, H3S and LaH10, synthesized at megabar pressures, have Received 14 May 2019 revolutionized the field of condensed matter physics providing the first glimpse to Received in revised form 5 February 2020 the solution of the hundred-year-old problem of room temperature superconductivity. Accepted 6 February 2020 The mechanism underlying superconductivity in these exceptional compounds is the Available online 15 February 2020 conventional electron–phonon coupling. Here we describe recent advances in experi- Editor: N. Nagaosa mental techniques, superconductivity theory and first-principles computational methods Keywords: which have made possible these discoveries. This work aims to provide an up-to-date High-pressure chemistry compendium of the available results on superconducting hydrides and explain how the Hydrides synergy of different methodologies led to extraordinary discoveries in the field. Besides, Conventional superconductivity in an attempt to evidence empirical rules governing superconductivity in binary hydrides Density-functional theory under pressure, we discuss general trends in the electronic structure and chemical Structure prediction bonding. The last part of the Review introduces possible strategies to optimize pressure and transition temperatures in conventional superconducting materials as well as future directions in theoretical, computational and experimental research. ' 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents 1. Introduction...............................................................................................................................................................................................2 2. Experimental methods: High pressure physics ....................................................................................................................................6 2.1. The diamond anvil cell................................................................................................................................................................7 2.1.1. Diamond anvils.............................................................................................................................................................8 2.1.2. Gasket preparation.......................................................................................................................................................9 2.1.3. Pressure measurements............................................................................................................................................... 10 2.1.4. Low-temperature loading............................................................................................................................................ 11 2.2. Superconductivity in sulfur-hydrogen compounds.................................................................................................................. 11 2.2.1. Sample preparation...................................................................................................................................................... 12 2.2.2. Raman measurements ................................................................................................................................................. 13 2.2.3. Electrical measurements.............................................................................................................................................. 13 ∗ Corresponding author at: RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, 351-0198, Japan. E-mail address: [email protected] (R. Arita). https://doi.org/10.1016/j.physrep.2020.02.003 0370-1573/' 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/ licenses/by/4.0/). 2 J.A. Flores-Livas, L. Boeri, A. Sanna et al. / Physics Reports 856 (2020) 1–78 2.2.4. Measurements in magnetic field................................................................................................................................ 14 2.3. Superconductivity in P-H and La-H hydrides........................................................................................................................... 16 3. Theoretical methods for superconductivity........................................................................................................................................... 18 3.1. Phonons and electron–phonon coupling................................................................................................................................... 18 3.1.1. Phonons......................................................................................................................................................................... 18 3.1.2. Density functional theory............................................................................................................................................ 19 3.1.3. Electron–phonon interaction ...................................................................................................................................... 19 3.1.4. Anharmonic effects ...................................................................................................................................................... 20 3.1.5. Dielectric screening in metals .................................................................................................................................... 22 3.2. Formalism for conventional superconductivity........................................................................................................................ 23 3.2.1. BCS theory..................................................................................................................................................................... 23 3.2.2. Éliashberg Theory......................................................................................................................................................... 24 3.2.3. Morel–Anderson theory............................................................................................................................................... 27 3.2.4. Empirical models for Tc .............................................................................................................................................. 28 3.3. Density functional theory for superconductors ....................................................................................................................... 29 3.3.1. SCDFT Hamiltonian and OGK theorem...................................................................................................................... 29 3.3.2. The Kohn–Sham system .............................................................................................................................................. 30 3.3.3. Electron–phonon interaction ...................................................................................................................................... 32 3.3.4. Plasmon-assisted superconductivity .......................................................................................................................... 33 4. Computational methods for structural prediction................................................................................................................................ 34 4.1. Ab initio crystal structure prediction........................................................................................................................................ 34 4.1.1. Potential energy surface.............................................................................................................................................. 34 4.1.2. Methods to explore structures ................................................................................................................................... 34 4.2. Convex hull and phase diagrams............................................................................................................................................... 39 4.3. Artificial intelligence and machine learning............................................................................................................................. 41 4.4. First-principles calculations........................................................................................................................................................ 41 5. Trends in hydrides under pressure .......................................................................................................................................................
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