In the search for axion dark matter, the cavity-based haloscope offers the most sensitive approach to the theoretically interesting models in the microwave region. However, experimental searches have been limited to relatively low masses up to a few tens of
, benefiting from large detection volumes and high-quality factors for a given experimental setup. We propose a new cavity design suitable for axion searches in higher mass regions with enhanced performance. The design features a periodic arrangement of dielectric material in a conventional conducting cavity where the resonant frequency is determined by the interspace. This photonic crystal haloscope can make full use of a given volume even at high frequencies while substantially improving the cavity quality factor. An auxetic structure is considered to deploy the array for two-dimensional frequency tuning. We present the characteristics of this haloscope design and demonstrate its feasibility for high-mass axion searches.