Abstract
The topological phase transition in a Hermitian system is associated with a change in the topological invariant that characterizes the band structure of the two distinct phases. Recently, the delocalization-localization transition in a quasicrystal described by the non-Hermitian -symmetric extension of the Aubry-André-Harper (AAH) Hamiltonian has been related to a topological phase transition. Interestingly, the symmetry also breaks down at the same point. In this article, we have shown that the delocalization-localization transition and the breaking of symmetry are not connected to a topological phase transition. We have studied the non-Hermitian -symmetric AAH Hamiltonian in the presence of Rashba spin-orbit coupling. It has been demonstrated that except in some particular cases, the delocalization-localization and the topological transition points are not identical. In fact, it precedes the topological transition point whenever they do not coincide. However, the breaking of symmetry occurs simultaneously with the delocalization-localization transition. Moreover, we have discovered that the Lyapunov exponent, which is often used as a primary signature to characterize the delocalization-localization transition, does not always determine it correctly. The Lyapunov exponent rather identifies the topological transition point in quasicrystals.
- Received 2 October 2021
- Revised 21 December 2021
- Accepted 3 January 2022
DOI:https://doi.org/10.1103/PhysRevB.105.014202
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