  We carried out a comprehensive study of the electronic, magnetic, and
thermodynamic properties of Ni-doped ZrTe$_2$. High quality Ni$_{0.05}$ZrTe2
single crystals show the coexistence of charge density waves (CDW,
T$_{CDW}\approx287$ K) with superconductivity (T$_c\approx 4.1$ K), which we
report here for the first time. The temperature dependence of the lower
(H$_{c_1}$) and upper (H$_{c_2}$) critical magnetic fields both deviate
significantly from the behaviors expected in conventional single-gap s-wave
superconductors. However, the behaviors of the normalized superfluid density
$\rho_s(T)$ and H$_{c_2}(T)$ can be described well using a two-gap model for
the Fermi surface, in a manner consistent with multiband superconductivity.
Electrical resistivity and specific heat measurements show clear anomalies
centered near 287 K, suggestive of CDW phase transition. Additionally,
electronic structure calculations support the coexistence of electron-phonon
multiband superconductivity and CDW due to the compensated disconnected nature
of the electron- and hole-pockets at the Fermi surface, with very distinct
orbital characters, Fermi velocities, and nesting vectors, as well as the
softening of the acoustic phonon modes. Our calculations also suggest that
ZrTe$_2$ is a non-trivial topological type-II Dirac semimetal. These findings
highlight that Ni-doped ZrTe2 is uniquely important for probing the coexistence
of superconducting and CDW ground states in an electronic system with
non-trivial topology.
