The detection of gravitational waves from the coalescences of binary compact stars by current interferometry experiments has opened up a new era of gravitational-wave astrophysics and cosmology. The search for a stochastic gravitational-wave background is underway by correlating signals from a pair of detectors in the detector network formed by the LIGO, Virgo, and KAGRA. In a previous work, we have developed a method based on spherical harmonic expansion to calculate the overlap reduction functions of the LIGO-Virgo-KAGRA network for a polarized stochastic gravitational-wave background. In this work, we will apply the method to calculate the overlap reduction functions of third-generation detectors such as a ground-based network linking the Einstein Telescope, the Cosmic Explorer, and the LISA-Taiji joint space mission.
