Non-Hermitian tuned topological band gap

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.