Meta-generalized gradient approximations for quantum materials

Although meta-generalized gradient approximations (meta-GGAs) [1,2] have been available for the materials science community for years, these approximations have not been harnessed for electronic structure to the extent that their potential indicates. Some of these meta-GGAs like SCAN and r²SCAN have undoubtedly become very popular for ground state applications [3]. Meta-GGAs have the potential to bridge the gap between GGAs and hybrid density functionals. This opportunity has not been recognized and exploited far enough in materials science. Meta-GGA approximations exhibit an extra flexibility via the kinetic energy density ingredient and functions built upon this ingredient. Meta-GGAs are also implicit functionals of the electron density and explicit functionals of Kohn-Sham orbitals. Increasing spatial nonlocality was shown to be associated with the kinetic energy density ingredient [4]. Quantum materials span a broad platform for a theorist with challenges for both structure and electronic properties. The physical situations that occur in these materials go far beyond the reach of any GGA-level-only density functional. Phenomena such as charge density waves, band gaps and phase changes of topological materials require a framework with enough flexibility to capture all these physical situations. Within this talk I will present the recent evolution of some meta-GGA density functionals and highlight the relevance of their ingredients through tests and applications [5] involving quantum materials.