  With the successful synthesis of the two-dimensional (2D) gallium nitride
(GaN) in a planar honeycomb structure, the phonon transport properties of 2D
GaN have been reported. However, it remains unclear for the thermal transport
in Ga-based materials by substituting N to other elements in the same main
group, which is of more broad applications. In this paper, based on
first-principles calculations, we performed a comprehensive study on the phonon
transport properties of 2D GaX (X = N, P, and As) with planar or buckled
honeycomb structures. The thermal conductivity of GaP (1.52 Wm-1K-1) is found
unexpectedly ultra-low, which is in sharp contrast to GaN and GaAs despite
their similar honeycomb geometry structure. Based on PJTE theory, GaP and GaAs
stabilize in buckling structure, different from the planar structure of GaN.
Compared to GaN and GaAs, strong phonon-phonon scattering is found in GaP due
to the strongest phonon anharmonicity. Given electronic structures, deep
insight is gained into the phonon transport that the delocalization of
electrons in GaP is restricted due to the buckling structure. Thus, non-bonding
lone pair electrons of P atoms induce nonlinear electrostatic forces upon
thermal agitation, leading to increased phonon anharmonicity in the lattice,
thus reducing thermal conductivity. Our study offers a fundamental
understanding of phonon transport in GaX monolayers with honeycomb structure,
which will enrich future studies of nanoscale phonon transport in 2D materials
