  The environment surrounding supermassive black holes (SMBHs) in galactic
nuclei (GNs) is expected to harbour stellar-mass binary black hole (BBH)
populations. These binaries were suggested to form a hierarchical triple system
with the SMBH, and gravitational perturbations from the SMBH can enhance the
mergers of BBHs through Lidov-Kozai (LK) oscillations. Previous studies
determined the expected binary parameter distribution for this merger channel
in single GNs. Here we account for the different spatial distribution and mass
distribution models of BBHs around SMBHs and perform direct high-precision
regularized N-body simulations, including Post-Newtonian (PN) terms up to order
PN2.5, to model merging BBH populations in single GNs. We use a full
inspiral-merger-ringdown waveform model of BBHs with nonzero eccentricities and
take into account the observational selection effect to determine the parameter
distributions of LK-induced BBHs detected with a single advanced
gravitational-wave (GW) detector from all GNs in the Universe. We find that the
detected mergers' total binary mass distribution is tilted towards lower
masses, and the mass ratio distribution is roughly uniform. The redshift
distribution peaks between ~0.15-0.55, and the vast majority of binaries merge
within redshift ~1.1. The fraction of binaries entering the LIGO/Virgo/KAGRA
band with residual eccentricities >0.1 is below ~10%. We identify a negative
correlation between residual eccentricity and mass parameters and a negative
correlation between residual eccentricity and source distance. Our results for
the parameter distributions and correlations among binary parameters may make
it possible to disentangle this merger channel from other BBH merger channels
statistically.
