Abstract

The quantum spin Hall insulator [1] with Z2 topology has attracted great interest last two decades. There is a widely accepted belief for Z2 topological phases that a system composed of stacking two layers, where each layer has non-trivial Z2 topology, should be topologically trivial.
However, several research reports that the Z2 topological phase survives in certain parameter regions in such stacked systems [2,3], while the reason has not yet been clarified.
In this work [4], we provide a systematic understanding that the robust Z2 topological phase in a Hermitian system with chiral symmetry originates from level repulsions in the corresponding non-Hermitian system derived from Hermitization. We demonstrate this by treating a class DIII superconductor with Z2 topology and the corresponding non-Hermitian system in AII† with Z2. point-gap topology as an example. For the latter system, in the case of stacking two layers, the four-fold degeneracy of the spectrum breaks down to two-fold degeneracy due to the level repulsion between two Kramers pairs as expected. Remarkably, Z2 point-gap topology at the energy E in point gaps emerged as the level repulsion remains non-trivial. Moreover, through Hermitization, the energy E of the non-Hermitian system takes the role of the chemical potential μ of the Hamiltonian for the DIII superconductors. Due to this correspondence, the energy region for the non-trivial Z2point-gap topology coinc ides with the range of μ where Z2 topological phase of DIII stacked superconductor is non-trivial and zero-energy states appear. Our result provides the systematic understanding of robust Z2 topology in Hermitian systems with chiral symmetry, as the level repulsion in the corresponding non-Hermitian systems. Moreover, this work provides an important example to clarify an advantage of viewing Hermitian systems from non-Hermitian perspective.
[1] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005). [2] B. Zhou and S.-Q. Shen,
Phys. Rev. B 84, 054532 (2011). [3] Y. Yoshimura, W. Onishi, K. Kobayashi, T. Ohtsuki, and
K.-I. Imura, Phys. Rev. B 94, 235414 (2016). [4] Z. Jiang, M. Sato, and H. Obuse, Phys. Rev. B
110, 245404 (2024).