  A new two-dimensional (2D) layered material, namely, titanium trisulfide
(TiS$_3$) monolayer sheet, is predicted to possess desired electronic
properties for nanoelectronic applications. On basis of the first-principles
calculations within the framework of density functional theory and deformation
theory, we show that the TiS$_3$ 2D crystal is a direct gap semiconductor with
a band gap of 1.06 eV and high carrier mobility. More remarkably, the in-plane
electron mobility of the 2D TiS$_3$ is highly anisotropic, amounting to
$\sim$10,000 cm$^2$V$^{-1}$s$^{-1}$ in the \emph{b} direction, which is higher
than that of the MoS$_2$ monolayer. Meanwhile, the hole mobility is about two
orders of magnitude lower. We also find that bulk TiS$_3$ possesses lower
cleavage energy than graphite, indicating high possibility of exfoliation for
TiS$_3$ monolayers or multilayers. Both dynamical and thermal stability of the
TiS$_3$ monolayer is examined via phonon-spectrum calculation and
Born-Oppenheimer molecular dynamics simulation in \emph{NPT} ensemble. The
predicted novel electronic properties render the TiS$_3$ monolayer an
attractive 2D material for applications in future nanoelectronics.
