  The spectral and transport properties of a non-Hermitian tight-binding
lattice with unidirectional hopping are theoretically investigated in three
different geometrical settings. It is shown that, while for the
infinitely-extended (open) and for the ring lattice geometries the spectrum is
complex, lattice truncation makes the spectrum real. However, an exceptional
point of order equal to the number of lattice sites emerges. When a homogeneous
dc force is applied to the lattice, in all cases an equally-spaced real
Wannier-Stark ladder spectrum is obtained, corresponding to periodic
oscillatory dynamics in real space. Possible physical realizations of
non-Hermitian lattices with unidirectional hopping are briefly discussed.
