  We investigate the tunneling conductance of superconductor-insulator-normal
metal (SIN) and superconductor-insulator-superconductor (SIS) heterostructures
with one superconducting side of the junction that is electrically driven and
can exhibit $\pi$-pairing through a modification of the surface inversion
asymmetric couplings. In SIN tunneling we find that the variation of the
electrically driven interactions generally brings an increase of
quasi-particles in the gap due to orbitally polarized depaired states,
irrespective of the inter-band phase rearrangement. The peak of SIN conductance
at the gap edge varies with a trend that depends both on the strength of the
surface interactions as well as on the character of the gate-induced
superconducting state. While this shift can be also associated with thermal
effects in the SIN configuration, for the SIS geometry at low temperature the
electric field does not yield the characteristic matching peak at voltages
related with the difference between the gaps of the superconducting electrodes.
This observation sets out a distinctive mark for spectroscopically
distinguishing the thermal population effects from the quantum gate-driven
signatures. In SIS the electrostatic gating yields a variety of features with
asymmetric peaks and broadening of the conductance spectral weight. These
findings indicate general qualitative trends for both SIN and SIS tunneling
spectroscopy which could serve to evaluate the impact of gate-control on
superconductors and the occurrence of non-centrosymmetric orbital antiphase
pairing.
