Effects of the Dirac cone tilts on coupled plasmon modes in electron systems with different dimensionalities

Abstract We study the effects of the Dirac cones tilts on coupled plasmon modes arising from the Coulomb electron–electron interaction for a system consisting of a two-dimensional (2D) system of Dirac electrons embedded in a three-dimensional (3D) Dirac semimetal. We particularly take into account the long-range Coulomb electron–electron interaction between electrons from two subsystems with the tilted Dirac cone anisotropic energy band dispersions and obtain the resulting coupled optical and acoustic plasmon modes from the dielectric functions of the subsystems for their various separations. The tilts of Dirac cones anisotropically increase the coupled plasmon mode energies and renormalize their spectral weights compared to the results for the untilted energy band dispersions. We demonstrate that the effects of tilts are more pronounced for the larger separations of the subsystems when their Coulomb coupling is weaker.