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.

中文翻译：

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非厄米调谐拓扑带隙

材料的外部可控带隙特性对于按需设计具有所需特性的光电器件至关重要。在这里，研究了通过在原本无关紧要的绝缘体中引入线性增益来对无关紧要的拓扑带隙进行单参数调谐的可能性。增益被选择性地注入二聚体的一维晶格中，使得所得的非厄米哈密顿量在空间反转下对称，但在时间反转下不对称。晶格的反转对称性使得通过与体哈密顿量相关的双正交 Zak 相探测体边界对应性和拓扑不变性。分析表明，当增益参数在非厄米简并上进行调整时，会发生拓扑微不足道到非微不足道的相变和受保护边缘状态的出现。讨论了通过改变增益分布在边界和体内部的边缘状态位置的可调谐性。在 InGaAsP 半导体腔阵列的实际设计中报告了增益控制拓扑边缘状态的确认。