  Germanium selenide (GeSe) is a unique two-dimensional (2D) material showing
various polymorphs stable at ambient condition. Recently, a new phase with a
layered hexagonal lattice ({\gamma}-GeSe) was synthesized with ambient
stability and extraordinary electronic conductivity even higher than graphite
while its monolayer is semiconducting. In this work, via using first-principles
derived force constants and Boltzmann transport theory we explore the lattice
thermal conductivity ({\kappa}_l) of the monolayer {\gamma}-GeSe, together with
a comparison with monolayer {\alpha}-GeSe and {\beta}-GeSe. The {\kappa}_l of
{\gamma}-phase is relatively low (5.50 W/mK), comparable with those of
{\alpha}- and {\beta}- phases. The acoustic branches in {\alpha}-GeSe are well
separated from the optical branches, limiting scattering channels in the phase
space, while for \b{eta}-GeSe and {\gamma}-GeSe the acoustic branches are
resonant with the low-frequency optical branches facilitating more
phonon-phonon scattering. For {\gamma}-GeSe, the cumulative {\kappa}_l is
isotropic and phononic representative mean free path (rMFP) is the shortest
(17.07 nm) amongst the three polymorphs, indicating that the {\kappa}_l of the
{\gamma} phase is less likely to be affected by the size of the sample, while
for {\alpha}-GeSe the cumulative {\kappa}_l grows slowly with mean free path
and the rMFP is longer (up to 20.56 and 35.94 nm along zigzag and armchair
direction, respectively), showing a stronger size-dependence of {\kappa}_l. Our
work suggests that GeSe polymorphs with overall low thermal conductivity are
promising contenders for thermoelectric and thermal management applications.
