  Strain engineering is a very effective method to continuously tune the
electronic, topological, optical and thermoelectric properties of materials. In
this work, strain-dependent phonon transport of recently-fabricated antimonene
(Sb monolayer) under biaxial strain is investigated from a combination of
first-principles calculations and the linearized phonon Boltzmann equation. It
is found that the ZA dispersion of antimonene with strain less than -1\% gives
imaginary frequencies, which suggests that compressive strain can induce
structural instability. Experimentally, it is possible to enhance structural
stability by tensile strain. Calculated results show that lattice thermal
conductivity increases with strain changing from -1\% to 6\%, and lattice
thermal conductivity at 6\% strain is 5.6 times larger than that at -1\% strain
at room temperature. It is interesting that lattice thermal conductivity is in
inverse proportion to buckling parameter $h$ in considered strain range. Such a
strain dependence of lattice thermal conductivity is attributed to enhanced
phonon lifetimes caused by increased strain, while group velocities have a
decreased effect on lattice thermal conductivity with increasing strain. It is
found that acoustic branches dominate the lattice thermal conductivity over the
full strain range. The cumulative room-temperature lattice thermal conductivity
at -1\% strain converges to maximum with phonon mean free path (MFP) at 50 nm,
while one at 6\% strain becomes as large as 44 $\mathrm{\mu m}$, which suggests
that strain can give rise to very strong size effects on lattice thermal
conductivity in antimonene. These results may provide guidance on fabrication
techniques of antimonene, and offer perspectives on tuning lattice thermal
conductivity by size and strain for applications of thermal management and
thermoelectricity.
