  Topological semimetal may have substantial applications in electronics,
spintronics and quantum computation. Recently, ZrTe is predicted as a new type
of topological semimetal due to coexistence of Weyl fermion and massless triply
degenerate nodal points. In this work, the elastic and transport properties of
ZrTe are investigated by combining the first-principles calculations and
semiclassical Boltzmann transport theory. Calculated elastic constants prove
mechanical stability of ZrTe, and the bulk modulus, shear modulus, Young's
modulus and Possion's ratio also are calculated. It is found that spin-orbit
coupling (SOC) has slightly enhanced effects on Seebeck coefficient, which
along a(b) and c directions for pristine ZrTe at 300 K is 46.26 $\mu$V/K and
80.20 $\mu$V/K, respectively. By comparing the experimental electrical
conductivity of ZrTe (300 K) with calculated value, the scattering time is
determined for 1.59 $\times$ $10^{-14}$ s. The predicted room-temperature
electronic thermal conductivity along a(b) and c directions is 2.37 $\mathrm{W
m^{-1} K^{-1}}$ and 2.90 $\mathrm{W m^{-1} K^{-1}}$, respectively. The
room-temperature lattice thermal conductivity is predicted as 17.56 $\mathrm{W
m^{-1} K^{-1}}$ and 43.08 $\mathrm{W m^{-1} K^{-1}}$ along a(b) and c
directions, showing very strong anisotropy. Calculated results show that
isotope scattering produces observable effect on lattice thermal conductivity.
It is noted that average room-temperature lattice thermal conductivity of ZrTe
is slightly higher than that of isostructural MoP, which is due to larger
phonon lifetimes and smaller Gr$\mathrm{\ddot{u}}$neisen parameters. Finally,
the total thermal conductivity as a function of temperature is predicted for
pristine ZrTe.
