  Externally controllable band gap properties of a material is crucial in
designing optoelectronic devices with desirable properties on-demand. Here, a
possibility of single parameter tuning of trivial to non-trivial topological
band gap by the introduction of linear gain in an otherwise trivial insulator
is investigated. Gain is selectively injected into a one dimensional lattice of
dimers such that the resulting non-Hermitian Hamiltonian is symmetric under
space-inversion but not under time-reversal. Inversion-symmetry of the lattice
renders to probe the bulk-boundary correspondence and topological invariance by
the bi-orthogonal Zak phase associated with a bulk Hamiltonian. Topological
trivial to nontrivial phase transition and emergence of protected edge states
are analytically shown to occur when the gain parameter is tuned across a
non-Hermitian degeneracy. Tuneability of edge state location both at the
boundary and inside the bulk by altering the gain distribution is discussed.
Confirmation of gain-controlled topological edge state is reported in a
realistic design of InGaAsP semiconductor cavity array.
