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Two-dimensional electron gases (2DEGs) at transition-metal oxide (TMO) interfaces, and boundary states in topological insulators, are being intensively investigated. The former system harbors superconductivity, large magneto-resistance, and ferromagnetism. In the latter, honeycomb-lattice geometry plus bulk spin-orbit interactions lead to topologically protected spin-polarized bands. 2DEGs in TMOs with a honeycomb-like structure could yield new states of matter, but they had not been experimentally realized, yet. We successfully created a 2DEG at the (111) surface of KTaO3, a strong insulator with large spin-orbit coupling. Its confined states form a network of weakly-dispersing electronic gutters with 6-fold symmetry, a topology novel to all known oxide-based 2DEGs. If those pertain to just one Ta-(111) bilayer, model calculations predict that it can be a topological metal. Our findings demonstrate that completely new electronic states, with symmetries not realized in the bulk, can be tailored in oxide surfaces, promising for TMO-based devices.
Current theoretical studies of electronic correlations in transition metal oxides typically only account for the local repulsion between d-electrons even if oxygen ligand p-states are an explicit part of the effective Hamiltonian. Interatomic interactions such as U-pd between d- and (ligand) p-electrons, as well as the local interaction between p-electrons, are neglected. Often, the relative d-p orbital splitting has to be adjusted 'ad hoc' on the basis of the experimental evidence. By applying the merger of local density approximation and dynamical mean field theory to the prototypical case of the three-band Emery dp model for the cuprates, we demonstrate that, without any 'ad hoc' adjustment of the orbital splitting, the charge transfer insulating state is stabilized by the interatomic interaction U-pd. Our study hence shows how to improve realistic material calculations that explicitly include the p-orbitals.