Casimir effect at finite density

The Casimir effect is known as an attractive force induced by photon fields sandwiched by parallel conducting plates and appears even at zero temperature. It is well known that thermal fluctuations contribute to the Casimir energy, whereas the contribution from finite-density environments is not established. Here, we discuss the typical behaviors of the Casimir effect at finite density. We develop how to define the Casimir energy at finite density and its typical property. Our findings will be applied to fermion systems in quark matter and Dirac/Weyl semimetals.