Weyl fermions as emergent quasiparticles can arise in Weyl semimetals (WSMs) in which the energy bands are nondegenerate, resulting from inversion or time-reversal symmetry breaking. Nevertheless, experimental evidence for magnetically induced WSMs is scarce. Here, using photoemission spectroscopy, we observe that the degeneracy of Bloch bands is already lifted in the paramagnetic phase of EuCd₂As₂. We attribute this effect to the itinerant electrons experiencing quasi-static and quasi–long-range ferromagnetic fluctuations. Moreover, the spin-nondegenerate band structure harbors a pair of ideal Weyl nodes near the Fermi level. Hence, we show that long-range magnetic order and the spontaneous breaking of time-reversal symmetry are not essential requirements for WSM states in centrosymmetric systems and that WSM states can emerge in a wider range of condensed matter systems than previously thought.

Polaron formation plays a major role in determining the structural, electrical, and chemical properties of ionic crystals. Using a combination of first-principles calculations, scanning tunneling microscopy, and atomic force microscopy, we analyze the interaction of polarons with CO molecules adsorbed on the reduced rutile ${\mathrm{TiO}}_2(110)$ surface. Adsorbed CO shows attractive coupling with polarons in the surface layer, and repulsive interaction with polarons in the subsurface layer. As a result, CO adsorption depends on the reduction state of the sample. For slightly reduced surfaces, many adsorption configurations with comparable adsorption energies exist and polarons reside in the subsurface layer. At strongly reduced surfaces, two adsorption configurations dominate: either inside an oxygen vacancy, or at surface ${\mathrm{Ti}}_{5c}$ sites, coupled with a surface polaron. Similar conclusions are predicted for ${\mathrm{TiO}}_2(110)$ surfaces containing near-surface Ti interstitials. These results show that polarons are of primary importance for understanding the performance of polar semiconductors and transition metal oxides in catalysis and energy-related applications.

Compensating a polar surface: An ionic crystal surface can be electrostatically unstable, and the surface must reconstruct in some way to avoid this “polar catastrophe.” Setvin et al. used scanning probe microscopies and density functional theory to study the changes in the polar surface of the perovskite KTaO ₃ . They observed several structural reconstructions as the surface cleaved in vacuum was heated to higher temperatures. These ranged from surface distortions to the formation of oxygen vacancies to the development of KO and TaO ₂ stripes. Hydroxylation after exposure to water vapor also stabilized the surface. Science , this issue p. 572

Charge trapping and the formation of polarons is a pervasive phenomenon in transition-metal oxide compounds, in particular at the surface, affecting fundamental physical properties and functionalities of the hosting materials. Here we investigate via first-principles techniques the formation and dynamics of small polarons on the reduced surface of titanium dioxide, an archetypal system for polarons, for a wide range of oxygen vacancy concentrations. We report how the essential features of polarons can be adequately accounted for in terms of a few quantities: the local structural and chemical environment, the attractive interaction between negatively charged polarons and positively charged oxygen vacancies, and the spin-dependent polaron-polaron Coulomb repulsion. We combined molecular-dynamics simulations on realistic samples derived from experimental observations with simplified static models, aiming to disentangle the various variables at play. We find that depending on the specific trapping site, different types of polarons can be formed, with distinct orbital symmetries and a different degree of localization and structural distortion. The energetically most stable polaron site is the subsurface Ti atom below the undercoordinated surface Ti atom, due to a small energy cost to distort the lattice and a suitable electrostatic potential. Polaron-polaron repulsion and polaron-vacancy attraction determine the spatial distribution of polarons as well as the energy of the polaronic in-gap state. In the range of experimentally reachable oxygen vacancy concentrations, the calculated data are in excellent agreement with observations, thus validating the overall interpretation.

Significance: Molecular O 2 on semiconducting metal oxides, its adsorption, response to thermal treatment, UV irradiation, and electron/hole injection is at the heart of a wide range of technologies. These processes were studied molecule by molecule on the prototypical model oxide T i O 2 (110), using noncontact AFM. We show that the nonintrusive nature of the nc-AFM and its exceptional spatial resolution due to the functionalization of the tip with a terminal O atom allow identifying oxygen adsorption geometries which were not previously determined by other techniques. In combination with density functional theory calculations, we explain the charge states of the various adsorbed oxygen species, their dynamics upon annealing and UV irradiation, and the role of electron exchange with the T i O 2 substrate.