Abstract: In this work, we present an unsupervised physics-informed neural network (PINN) framework for the inverse design of one-dimensional photonic crystals, addressing the limitations of conventional methods, such as high computational cost and inability to optimize materials. A "mixture-of-physics-experts" method for nanophotonic design is proposed, which pretrains a library of PINN models for various material combinations. This allows for not only rapid structure optimization directly from target spectra, even hand-drawn ones but also efficient selection of the optimal material system for a given task, a capability traditional algorithms lack. By embedding physical governing equations as a loss constraint, our framework eliminates the need for large labeled datasets and enhances physical explainability. As a practical demonstration, we apply this framework to design a spectral-splitting optical filter for a high-bandgap/low-bandgap hybrid photovoltaic system. We compare designs from five pretrained material-specific PINN models and identify the optimal material configuration that enhances the overall PV system efficiency by 22.4% compared with a standalone GaAs solar cell and 41.9% compared with a GaInP cell. Notably, the designed filters exhibit excellent angular robustness with only 3.5% relative efficiency degradation at 45° oblique incidence and significantly reduce the operating temperature of low-bandgap cells by 12.8-14.6°C. This physics-guided, material-aware framework establishes a new paradigm for photonic device design, balancing computational efficiency, design flexibility, and practical applicability.