  We show that a one-dimensional ordered fermionic lattice system with
power-law-decaying hopping, when connected to two baths at its two ends with
different chemical potentials at zero temperature, features two phases showing
sub-diffusive scaling of conductance with system size. These phases have no
analogues in the isolated system (i.e, in absence of the baths) where the
transport is perfectly ballistic. In the open system scenario, interestingly,
there occurs two chemical-potential-driven sub-diffusive to ballistic phase
transitions at zero temperature. We discuss how these phase transitions, to our
knowledge, are different from all the known non-equilibrium quantum phase
transitions. We provide a clear understanding of the microscopic origin of
these phases and argue that the sub-diffusive phases are robust against the
presence of arbitrary number-conserving many-body interactions in the system.
These phases showing sub-diffusive scaling of conductance with system size in a
two-terminal set-up are therefore universal properties of all ordered
one-dimensional number-conserving fermionic systems with power-law-decaying
hopping at zero temperature.
