  A unique co-existence of extremely large magnetoresistance (XMR) and
topological characteristics in non-magnetic rare-earth monopnictides
stimulating intensive research on these materials. Yttrium monobismuthide (YBi)
has been reported to exhibit XMR up to 105% but its Topological properties
still need clarification. Here we use the hybrid density functional theory to
probe the structural, electronic and topological properties of YBi in detail.
We observe that YBi is topologically trivial semimetal at ambient pressure
which is in accordance with reported experimental results. The topological
phase transitions i.e., trivial to non-trivial are obtained with volumetric
pressure of 6.5 GPa and 3% of epitaxial strain. This topological phase
transitions are well within the structural phase transition of YBi (24.5 GPa).
The topological non-trivial state is characterized by band inversions among Y-d
band and Bi-p band near {\Gamma}- and X-point in the Brillouin zone. This is
further verified with the help of surface band structure along (001) plane. The
Z2 topological invariants are calculated with the help of product of parities
and evolution of Wannier charge centers. The occurrence of non-trivial phase in
YBi with a relatively small epitaxial strain, which a thin film geometry can
naturally has, might make it an ideal candidate to probe inter-relationship
between XMR and non-trivial topology.
