Finite-size-induced non-Hermitian phase transitions in real space

While non-Hermiticity provokes intriguing phenomena without Hermitian counterparts, e.g., the skin effect and the breakdown of bulk-boundary correspondence, attracting extensive attention both in fundamental physics and device engineering, the role of finite sizes therein remains elusive. Here, we propose a class of finite-size-induced non-Hermitian phase transitions, relying upon higher-order topological invariants associated with real-space wave functions. The phase diagrams for general non-Hermitian chiral models are further acquired to demonstrate our topological definition. Such phase transitions are elucidated qualitatively by an effective intercell coupling alteration that depends on finite sizes in respective directions. Besides, we mimic these phenomena by analogizing the circuit Laplacian in finite-size electric circuits with nonreciprocal couplings. The resultant admittance spectra agree with our theoretical predictions. Our findings shed light on the finite-size mechanism of non-Hermitian topological phase transitions and pave the way for applications in switching and sensing.