  Understanding the complex evolution of protoplanetary disks (PPDs) and their
dispersal via energetic stellar radiation are prominent challenges in
astrophysics. It has recently been established that specifically the X-ray
luminosity from the central protostar can significantly heat the surface of the
disk, causing powerful photoevaporative winds that eject a considerable
fraction of the disc's mass. Recent work in the field has moreover shown the
importance of global PPD simulations that simultaneously take into account
non-ideal magnetohydrodynamic (MHD) effects and detailed thermochemistry.
  Our motivation with the current paper lies in combining these two aspects and
figure out how they interact. Focus is put on the Hall Effect (HE) and the
impact it has on the overall field topology and mass loss/accretion rates.
Utilizing a novel X-ray temperature parametrisation, we perform 2D-axisymmetric
MHD simulations with the NIRVANA fluid code, covering all non-ideal effects. We
find that, in the aligned orientation, the HE causes prominent inward
displacement of the poloidal field lines that can increase the accretion rate
through a laminar Maxwell stress. We find that outflows are mainly driven by
photoevaporation -- unless the magnetic field strength is considerable (i.e.,
$\beta_p\leq 10^{3}$) or the X-ray luminosity low enough (i.e., $\log{L_X}\leq
29.3$). Inferred mass loss rate are in the range of the expected values
$10^{-8}$ to $10^{-7}M_{\odot}yr^{-1}$. For comparison, we have also performed
pure hydrodynamic (HD) runs and compared them with the equivalent MHD runs.
Here we have found that the magnetic field does indeed contribute to the mass
loss rate, albeit only discernibly so for low enough $L_X$ (i.e.,
$\log{L_X}\leq 30.8$). For values higher than that, the wind mass loss
predicted from the MHD set converges to the ones predicted from pure HD.
