Multipole theory of optical spatial dispersion in crystals

Natural optical activity is the paradigmatic example of an effect originating in weak spatial inhomogeneity electromagnetic field on atomic scale. In molecules, such effects are well described by multipole theory electromagnetism, where coupling to light treated semiclassically beyond electric-dipole approximation. That has two shortcomings: it limited bounded systems, and its building blocks -the transition moments- origin dependent. this work, we recast a translationally-invariant form that remains valid for crystals. Working independent-particle approximation, introduce "intrinsic" moments independent transform covariantly under gauge transformations Bloch eigenstates. Electric-dipole transitions given interband Berry connection, while magnetic-dipole electric-quadrupole matrix generalizations intrinsic magnetic moment quantum metric. addition multipole-like terms, response crystals at first order wavevector contains band-dispersion terms have no counterpart molecular theories. The full broken down into magnetoelectric quadrupolar parts, which can be isolated static limit electric fields become decoupled. rotatory-strength sum rule found equivalent topological constraint vanishing chiral equilibrium, formalism validated numerical tight-binding calculations.