Magnetoroton in a two-dimensional Bose-Bose mixture

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 a weakly- and strongly-interacting regimes. In a dilute system, the latter may be achieved by adjusting inter-species attraction such as to obtain a resonance in the $p$-wave scattering channel. Resonantly enhanced $p$-wave attraction results in the self-localization of magnons and 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 three dimensions (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.