  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.
