  We study a non-Hermitian Rice-Mele model without breaking time-reversal
symmetry, with the non-Hermiticity arising from imbalanced hopping rates. The
Berry connection, Berry curvature and Chern number are introduced in the
context of biorthonormal inner product. It is shown that for a bulk system,
although the Berry connection can be complex numbers, the Chern number is still
quantized, as topological invariant. For an opened chain system, the mid-gap
edge modes are obtained exactly, obeying the bulk-edge correspondence.
Furthermore, we also introduce a local current in the context of biorthonormal
inner product to measure the pumping charge generated by a cyclic adiabatic
evolution. Analytical analysis and numerical simulation of the time evolution
of the mid-gap states show that the pumping charge can be a dynamical
topological invariant in correspondence with the Chern number. It indicates
that the geometric concepts for Hermitian topological insulator can be extended
to the non-Hermitian regime.
