The three-dimensional (3D) Dirac point, where two Weyl points overlap in momentum space, is usually unstable and hard to realize. Here we show, based on the first-principles calculations and effective model analysis, that crystalline A 3 Bi (A=Na, K, Rb) are Dirac semimetals with bulk 3D Dirac points protected by crystal symmetry. They possess non-trivial Fermi arcs on the surfaces, and can be driven into various topologically distinct phases by explicit breaking of symmetries. Giant diamagnetism, linear quantum magnetoresistance, and quantum spin-Hall effect will be expected for such compounds. PACS numbers: 71.20.-b, 73.20.-r, 73.43.-t 1 arXiv:1202.5636v2 [cond-mat.mtrl-sci]

A combination of scanning tunneling microscopy and spectroscopy and density functional theory is used to characterize excess electrons in TiO2 rutile and anatase, two prototypical materials with identical chemical composition but different crystal lattices. In rutile, excess electrons can localize at any lattice Ti atom, forming a small polaron, which can easily hop to neighboring sites. In contrast, electrons in anatase prefer a free-carrier state, and can only be trapped near oxygen vacancies or form shallow donor states bound to Nb dopants. The present study conclusively explains the differences between the two polymorphs and indicates that even small structural variations in the crystal lattice can lead to a very different behavior.

Polarons are quasiparticles that easily form in polarizable materials due to the coupling of excess electrons or holes with ionic vibrations. Polarons manifest themselves in many different ways and have a profound impact on materials properties and functionalities. As one of the most studied subject in physics, chemistry and material science, polarons have been the testing ground for the development of numerous theories, and their manifestations have been studied by many different experimental probes. This review aims to provide a map of the enormous amount of data and knowledge accumulated on polaron effects in materials, ranging from early studies and standard treatments to emerging experimental techniques and novel theoretical and computational approaches. 2/40 Theoretical account of polaron propertiesThis section provides a brief overview of the theoretical constructs and computational models developed in the last 90 years to describe, interpret and compute the properties of polarons loosely following a chronological order from the classical work of Landau to the ab initio theory of polarons (schematized in Tab. 1). Theoretical models and computational approaches YearTheoretical and Computational models Polaron properties 1933 6 Dielectric theory: charge moving in a dielectric crystal Auto-localization due to lattice deformation 1946-1948 4, 99-101 Self-consistent theory of a large polaron Enhancement of effective mass Landau-Pekar model Localization of the wave function 1950' 7-9, 102, 103 Quantum-mechanical variational theory of large polarons Effective mass, energy, mobility Fröhlich large polaron Hamiltonian (continuum approx.) Intermediate electron-phonon interaction 1955-2017 12,13,[104][105][106] All-coupling continuum polaron theory Energy, effective mass, mobility

We present density functional theory (DFT) calculations for MnO, Mn3O4, alpha-Mn2O3, and beta-MnO2, using different gradient corrected functionals, such as Perdew-Burke-Ernzerhof (PBE), PBE+U, and the two hybrid density functional Hartree-Fock methods PBEO and Heyd-Scuseria-Ernzerhof (HSE). We investigate the structural, electronic, magnetic, and thermodynamical properties of the mentioned compounds. Despite the lack of sufficient experimental information allowing for a comprehensive comparison of our results, we find overall that hybrid functionals provide a more consistent picture than standard PBE. Although PBE+U is limited due to the uncertainty of choosing the parameter U, it nevertheless provides satisfactory results in terms of magnetic properties and energies of formation. This is in line with results of PBEO and HSE calculations, but the PBE+U approach tends to overestimate the equilibrium volumes, and also it favors a half-metallic state for the more reduced oxides Mn3O4, alpha-Mn2O3, and beta-MnO2, rather than an insulating character as derived from the hybrid functional approaches. The comparison of measured valence-band spectra with the HSE density of states offers a further assessment of the capability of hybrid approaches in overcoming the deficiencies of DFT in treating these kinds of materials