S. M. Rafi-Ul-Islam, Zhuo Bin Siu, Md. Saddam Hossain Razo, Haydar Sahin, Mansoor B. A. Jalil
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From knots to exceptional points: Emergence of topological features in non-Hermitian systems with long-range coupling
We present a study of complex energy braiding in a one-dimensional non-Hermitian system with -order long-range asymmetrical coupling. Our work highlights the emergence of novel topological phenomena in such systems beyond the conventional nearest-neighbor interaction. The modified SSH model displays distinct knot and link combinations in the complex energy-momentum space under periodic boundary conditions, which can be controlled by varying the coupling strengths. A topological invariant, namely the braiding index, is introduced to characterize the different complex energy braiding profiles, which depends on the zeros and poles of the characteristic polynomials. Furthermore, we demonstrate that the non-Hermitian skin effect can be localized at one or both ends, signifying conventional or bipolar localization, depending on the sign of the braiding index. Phase transitions between different braiding phases with the same (opposite) sign of the topological invariant occur at Type-1 (Type-2) exceptional points, with Type-1 (Type-2) phase transitions accompanied by single (multiple) exceptional points. We propose an experimental setup to realize the various braiding schemes based on the RLC circuit framework, which provides an accessible avenue for implementation without recourse to high-dimensional momentum space required in most other platforms.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
PRB covers the full range of condensed matter, materials physics, and related subfields, including:
-Structure and phase transitions
-Ferroelectrics and multiferroics
-Disordered systems and alloys
-Magnetism
-Superconductivity
-Electronic structure, photonics, and metamaterials
-Semiconductors and mesoscopic systems
-Surfaces, nanoscience, and two-dimensional materials
-Topological states of matter