Temperature bandgaps and engineered thermal state access in driven nanophotonic resonators

We show that strong thermo-optic feedback in nanophotonic resonators creates forbidden steady state temperatures that are unreachable under any static excitation. This temperature bandgap opens when thermo-optic feedback gain overcomes optical and thermal dissipation, splitting an otherwise continuous thermal landscape into disconnected accessible bands. We experimentally map this temperature band structure using quasi-bound states in the continuum resonances in silicon metasurfaces. Continuous wavelength scans exploit spectrally accumulated thermal energy to access the forbidden interval, reaching up to ~88{\deg}C higher temperature than static excitation, both at the same wavelength and maximum power. A characteristic three-stage temperature rise near the band edge confirms the -1/2 critical exponent of saddle-node bifurcations and enables quantitative extraction of band-edge wavelengths. Combining external thermal bias with optical excitation drives programmable interband transitions, enabling nearly 8.5-fold amplification of temperature rise and wavelength-selective switching between thermal states separated by just 1 nm in excitation wavelength. The bandgap is fully designable through metasurface geometry and hybrid material integration, which tune optical absorption, confinement and resonance linewidth. These results establish the temperature bandgap as a designable degree of freedom in driven nanophotonic systems, opening routes toward all-optical thermal logic and programmable photothermal control of chemical and biological processes.