We propose a general framework, termed the imaginary gauge phase imprint (IGPI), which enables engineering arbitrarily configurable wavefunctions with exact solutions and self-organization dynamics in any-dimensional non-Hermitian lattices under imaginary gauge fields. Using this method, we uncover a novel phase with exact critical wavefunctions, dubbed the skin critical phase (SCP), which is marked by unconventional localization, topological-skin, and dynamical characteristics. Furthermore, we validate the IGPI by imprinting and visualizing complex fractal states with Sierpinski-carpet and Koch-snowflake profiles, as well as exotic super-moire and 3D-moire states in regular lattices. Our work not only offers fresh insights into non-Hermitian critical and fractal physics, but also provides a rigorous paradigm for controlling and visualizing wavefunction patterns using the IGPI in engineered non-Hermitian systems.
We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct Berry connection forms. Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases. Most critically, we find a quantitative relation
Δϕd=Δϕg, which quantifies how cumulative minute energy differences (
Δϕd) manifest as geometric phase shifts (
Δϕg) uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for topological quantum computing and non-Hermitian photonics.
Dynamical quantum phase transitions in non-Hermitian systems pose fundamental challenges due to the intrinsic biorthogonality of their eigenstates. In this work, we extend a biorthogonal framework to investigate dynamical quantum phase transitions in non-Hermitian topological superconductors. Taking the non-Hermitian Kitaev chain as a prototypical model, we construct an associated-state formalism and reformulate the Loschmidt rate function, dynamical topological order parameter, and dynamical Fisher zeros. Within this framework, we find that the critical times at which dynamical quantum phase transitions occur differ from those based on the conventional self-normal approaches. We further analyze momentum-resolved subsystems at critical momenta and demonstrate the robustness of the biorthogonal framework. Our work highlights the essential role of biorthogonality in nonequilibrium dynamics and establishes a consistent theoretical framework for dynamical quantum phase transitions in non-Hermitian topological superconductors.