Doping mobile carriers into ordinary semiconductors such as Si, GaAs, and ZnO was the enabling step in the electronic and optoelectronic revolutions. The recent emergence of a class of Quantum Materials, where uniquely quantum interactions between the components produce specific behaviors such as topological insulation, unusual magnetism, superconductivity, spin-orbit-induced and magnetically-induced spin splitting, polaron formation, and transparency of electrical conductors, pointed attention to a range of doping-related phenomena associated with chemical classes that differ from the traditional semiconductors. These include wide-gap oxides, compounds containing open-shell d electrons, and compounds made of heavy elements yet having significant band gaps. The atomistic electronic structure theory of doping that has been developed over the past two decades in the sub-field of semiconductor physics has recently been extended and applied to quantum materials. The present review focuses on explaining the main concepts needed for a basic understanding of the doping phenomenology and indeed peculiarities in quantum materials from the perspective of condensed matter theory, with the hope of forging bridges to the chemists that have enabled the synthesis of some of the most interesting compounds in this field.
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