  The combination of a superconductor (SC) and a topological insulator (TI)
nanowire was proposed as a potential candidate for realizing Majorana zero
modes (MZMs). In this study, we adopt the Schr\"odinger-Poisson formalism to
incorporate the electrostatic environment inside the nanowire and
systematically explore its topological properties. Our calculations reveal that
the proximity to the SC induces a band bending effect, leading to a non-uniform
potential across the TI nanowire. As a consequence, there is an upward shift of
the Fermi level within the conduction band. This gives rise to the coexistence
of surface and bulk states, localized in an accumulation layer adjacent to the
TI-SC interface. When magnetic flux is applied, these occupied states have
different flux-penetration areas, suppressing the superconducting gap. However,
this impact can be mitigated by increasing the radius of the nanowire. Finally,
We demonstrate that MZMs can be achieved across a wide range of parameters
centered around one applied flux quantum, $\phi_0 = h/2e$. Within this regime,
MZMs can be realized even in the presence of conduction bands, which are not
affected by the band bending effect. These findings provide valuable insights
into the practical realization of MZMs in TI nanowire-based devices, especially
in the presence of a complicated electrostatic environment.
