论文标题
在非热式周期性电位下的带结构：连接几乎没有的和双凝的紧密结合模型
Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
论文作者
论文摘要
我们探索基于连续模型和紧密结合模型的周期性非热门操作员描述的一维开放系统的带结构。我们表明，假想的标量电势不会打开带隙，而是导致形成异常点，只要电势的强度超过阈值，这与封闭的系统形成了鲜明的对比，在封闭的系统中，真实电势在无限强度的强度上打开缝隙。由于自由系统中的堕落性提升，假想矢量的电势阻碍了低能带的分离。此外，我们还通过基于非热门操作员及其Hermitian结合物的Bloch波函数来构建通过双向异常的Wannier函数构建紧密结合模型。我们表明，当复杂的标量电势足够大时，双向异式的紧密结合模型很好地再现了连续模型的分散关系。
We explore band structures of one-dimensional open systems described by periodic non-Hermitian operators, based on continuum models and tight-binding models. We show that imaginary scalar potentials do not open band gaps but instead lead to the formation of exceptional points as long as the strength of the potential exceeds a threshold value, which is contrast to closed systems where real potentials open a gap with infinitesimally small strength. The imaginary vector potentials hinder the separation of low energy bands because of the lifting of degeneracy in the free system. In addition, we construct tight-binding models through bi-orthogonal Wannier functions based on Bloch wavefunctions of the non-Hermitian operator and its Hermitian conjugate. We show that the bi-orthogonal tight-binding model well reproduces the dispersion relations of the continuum model when the complex scalar potential is sufficiently large.
