A method is presented for calculating the diamagnetic coefficient of an exciton in a semiconductor nanostructure. The diamagnetic coefficient characterizes the response of a confined exciton to a weak magnetic field, and gives information about the roles of confinement and of the Coulomb interaction in determining the optical properties. A general formulation is presented for nanostructures of arbitrary size, shape, and dimensionality. We introduce a generalized gauge transformation that allows us to express the diamagnetic coefficient in terms of two characterizations of the size of an exciton, one involving confinement and the other involving the Coulomb interaction. Calculations of the diamagnetic coefficient are given for quantum well, wire, and dot geometries.

• Received 27 August 1997

DOI:https://doi.org/10.1103/PhysRevB.57.9088