We extend our theory of slow magnons in a two-component Bose-Einstein condensate to the case of two spatial dimensions (2D). We provide a detailed discussion of polaronic corrections to the magnon branch of the elementary excitation spectrum in weakly and strongly interacting regimes. In a dilute system, the latter may be achieved by adjusting interspecies attraction so as to obtain a resonance in the
p-wave scattering channel. Resonantly enhanced
p-wave attraction results in the self-localization of magnons and the formation of a magnetoroton. The nature of a ground state beyond the magnetoroton instability remains to be explored. We suggest a dilute
p-wave crystal of alternating polarization as a possible candidate. In contrast to 3D, the required strength of the attractive potential in the
s-wave channel here corresponds to tight binding, and we suggest a potential realization of our model with excitons in 2D semiconductors.
We report in this Letter the results of our investigation of 2D Bose gases beyond the dilute limit emphasizing the role played by three-body scattering events. We demonstrate that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of 2D Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied here are universal, fully characterized by the effective 2D scattering length a(2D) (or the size of the 2D bound states) and are, in comparison to the 3D case, independent of three-body ultraviolet physics. We find, within our approach, the ratios of the contribution to the chemical potential due to three-body interactions to the one due to two-body to be 0.27 near the maximum of the chemical potential and 0.73 in the vicinity of the onset instability.