Casimir effect in magnetic dual chiral density waves

We theoretically investigate the Casimir effect originating from Dirac fields in finite-density matter under a magnetic field. In particular, we focus on quark fields in the magnetic dual chiral density wave phase as a possible inhomogeneous ground state of interacting Dirac-fermion systems. In this system, the distance dependence of Casimir energy shows a complex oscillatory behavior by the interplay between the chemical potential, magnetic field, and inhomogeneous ground state. By decomposing the total Casimir energy into contributions of each Landau level, we elucidate what types of Casimir effects are realized from each Landau level: The lowest or some types of higher Landau levels lead to different behaviors of Casimir energies. Furthermore, we point out characteristic behaviors due to level splitting between different fermion flavors, i.e., up and down quarks. These findings provide new insights into Dirac-fermion (or quark) matter with a finite thickness.