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Point defects, such as oxygen vacancies, control the physical properties of complex oxides, relevant in active areas of research from superconductivity to resistive memory to catalysis. In most oxide semiconductors, electrons that are associated with oxygen vacancies occupy the conduction band, leading to an increase in the electrical conductivity. Here we demonstrate, in contrast, that in the correlated-electron perovskite rare-earth nickelates, R NiO 3 ( R is a rare-earth element such as Sm or Nd), electrons associated with oxygen vacancies strongly localize, leading to a dramatic decrease in the electrical conductivity by several orders of magnitude. This unusual behavior is found to stem from the combination of crystal field splitting and filling-controlled Mott–Hubbard electron–electron correlations in the Ni 3 d orbitals. Furthermore, we show the distribution of oxygen vacancies in NdNiO 3 can be controlled via an electric field, leading to analog resistance switching behavior. This study demonstrates the potential of nickelates as testbeds to better understand emergent physics in oxide heterostructures as well as candidate systems in the emerging fields of artificial intelligence.

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high-dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization that effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors that are relevant for matching.