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# Correlated Materials Design: Prospects and Challenges

Abstract

The design of correlated materials challenges researchers to combine the maturing, high throughput framework of DFT-based materials design with the rapidly-developing first-principles theory for correlated electron systems. We review the physics of correlations, and propose strategies to capture their effects at each stage of the materials design workflow. We illustrate the workflow via examples in several materials classes, encompassing superconductors, charge ordering and Mott insulators, highlighting the interplay between theory and experiment and with a view towards finding new materials.

## Introduction

\label{sec:intro}

The ability to design new materials with desired properties is crucial to the development of new technology. The design of silicon and lithium-ion based materials are well known examples which led to the proliferation of consumer hand-held devices today. However, materials discovery has historically proceeded via trial and error, with a mixture of serendipity and intuition being the most fruitful path. For example, all major classes of superconductors–from elemental mercury in 1911, to the heavy fermions, cuprates and most recently, the iron-based superconductors–have been discovered by chance (Greene 2012).

The dream of materials design is to leverage, rather than ignore, our theories of electronic structure and combine them with our increasing computational ability to discover new materials. Beyond its technological implications, the challenge of materials design is also one of great intellectual depth. In principle, we know the fundamental equation needed to model the behavior of a material: it is the Schrödinger equation describing electrons moving in the potential of a periodic lattice, mutually interacting via the Coulomb repulsion. Solving this equation is another matter.

In practice, we can classify materials by how well we can solve their corresponding Schrödinger equation. For the class of compounds encompassing simple metals, insulators and semiconductors, termed weakly correlated materials, we have a well-developed theory of their excitation spectra called Fermi liquid theory. From a practical viewpoint, the theoretical framework of density functional theory (DFT) naturally lends itself to computational implementations for modeling properties. Materials which are not well-described by DFT are colloquially termed strongly correlated materials.

For weakly correlated materials, DFT has become the underlying workhorse of the scientific community. Extensive benchmarks of software implementations (Lejaeghere 2016) have shown that DFT reliably produces the total energy of a given configuration of atoms, enabling comparisons of stability between different chemical polymorphs. The maturity of DFT, combined with searchable repositories of experimental data (ICDD, ICSD, NIMS) data, has fostered the growth of databases of computed materials properties (Materials Project, AFLOWlib, NIMS). The field of weakly correlated systems has advanced to the point where one can successfully design materials (Fennie 2008, Gautier 2015, Fredeman 2011). A clear example that theoretical approaches are coming of age is the recent prediction of superconductivity in H$${}_{3}$$S under high pressure near 190 K (Duan 2014). Subsequently, hydrogen sulfide was observed to superconduct near 200 K, the highest temperature superconductor discovered so far (Drozdov 2015).

In contrast, materials design for strongly correlated systems is less mature, stemming from the fundamental challenge of understanding the physics of electron correlations. Correlated systems exhibit novel phenomena not observed in weakly-correlated materials: metal-insulator transitions, magnetic order and unconventional superconductivity are salient examples. While designing and optimizing materials with these properties would advance both technology and our understanding of the underlying physics, in practice we lack a tool akin to DFT capable of reliably modeling properties and scaling up to the thousands of calculations necessary.

In this article, we seek to summarize outstanding challenges in materials design as it pertains to correlated materials, and propose strategies to solve them. We begin by providing a practical definition of correlations (Sec. \ref{sec:correlations}), followed by a view of the workflow of materials design (Sec. \ref{sec:workflow}). Then we give four examples of materials design in correlated systems to illustrate the application of our ideas (Sec. \ref{sec:tlcscl3}-\ref{sec:bacoso}) and conclude with a brief outlook.