  Employing ab initio electronic calculations, we propose a new type of
two-dimensional (2D) topological insulator (TI), monolayer (ML) low buckled
(LB) mercury telluride (HgTe) and mercury selenide (HgSe), with tunable band
gaps. Monolayer LB HgTe undergoes a transition to a topological nontrivial
phase under the appropriate in-plane tensile strain ({\epsilon} > 2.6%) due to
the combination effects of strain and spin orbital coupling (SOC). Under the
2.6%< {\epsilon} <4.2% tensile strain, the band inversion and topological
nontrivial gap are induced by the SOC. For {\epsilon} >4.2%, the band inversion
is already realized by strain but the topological gap is induced by SOC. The
band gap of monolayer LB HgTe TI phase can be tuned over a wide range from 0 eV
to 0.20 eV as the tensile strain increases from 2.6% to 7.4%. Similarly, the
topological phase transition of monolayer LB HgSe is induced by strain and SOC
as the strain {\epsilon} >3.1%. The topological band gap can be 0.05 eV as the
strain increases to about 4.6%. The large band gap of 2D LB HgTe and HgSe
monolayers make this type of material suitable for practical applications at
room-temperature.
