  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 $\mu$eV, 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.
