Abstract
Non-Hermitian physics, which extends the Hermitian framework for closed systems to include dissipation and gain, unveils a wealth of novel phenomena, ranging from the non-Hermitian skin effect induced by point gaps to ultra-sensitive sensors based on exceptional points. Non-Hermitian band theory has emerged as a powerful tool for exploring these effects. This talk begins with the motivation and challenges of experimentally probing non-Hermitian band structures, where both complex energy and complex momentum play crucial roles. To overcome these challenges, a non-Bloch supercell framework has been developed. It effectively flattens the imaginary components of wavevectors into engineered hoppings and incorporates twisted boundary conditions, enabling direct experimental access. Implemented in both one- and two-dimensional acoustic crystals, this approach has led to the experimental extraction of key features of non-Hermitian band structures, in agreement with real-space observations under open boundary conditions. Based on this framework, a novel type of geometric structure, the Whitney cusp, has been experimentally revealed, and its emergence is closely associated with geometry and non-Bloch exceptional points. The second part of the talk focuses on the impact of non-Hermitian factors on soliton formation and dynamics. By constructing a soliton phase diagram, two distinct soliton phases and their transitions are theoretically identified. A Wannier-function-based nonlinear Hamiltonian shows that soliton formation critically depends on how skin-mode localization and band nonreciprocity suppress or enhance wave dispersion. Both soliton phases have been demonstrated to be dynamically accessible from bulk and edge excitations.