Symmetry, interaction and topological effects, as well as environmental screening, dominate many of the quantum properties of reduced-dimensional systems and nanostructures. These effects often lead to manifestation of counter-intuitive concepts and phenomena that may not be so prominent or have not been seen in bulk materials. In this talk, I present some fascinating physical phenomena discovered in recent studies of atomically thin two-dimensional (2D) materials. A number of highly interesting and unexpected behaviors have been found – e.g., strongly bound excitons (electron-hole pairs) with unusual energy level structures and new topology-dictated optical selection rules, massless excitons, tunable magnetism and plasmonic properties, electron supercollimation, novel topological phases, etc. – adding to the promise of these 2D materials for exploration of new science and valuable applications.
Discovery of useful or interesting new materials and molecules by computation requires an efficient, accurate, and reliable theoretical method, and the preferred method is still Kohn-Sham density functional theory. In this theory, the exact ground-state energy and electron density (and thus the nuclear positions) can be found by solving self-consistent one-electron equations. The exchange-correlation energy as a functional of the electron density must in practice be approximated. I will discuss a systematic and proven way to improve the approximations, making them more accurate and reliable at a modest increase of computational cost. Then I will show how this approach has led to SCAN , a strongly-constrained and appropriately normed functional that, without being fitted to any bonded system, makes accurate predictions for diversely-bonded materials and molecules .
 W. Kohn and L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133 (1965).
 J. Sun, A. Ruzsinszky, and J.P. Perdew, Strongly Constrained and Appropriately Normed Semi-local Density Functional, Phys. Rev. Lett. 115, 036402 (2015).
 J. Sun, et al., Accurate First-Principles Structures and Energies of Diversely-Bonded Systems from an Efficient Density Functional, Nat. Chem. 8, 831 (2016).