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We study the concomitant breaking of spatial translations and dilatations inGinzburg-Landau-like models, where the dynamics responsible for the symmetrybreaking is described by an effective Mexican hat potential for spatialgradients. We show that there are fractonic modes with either subdimensionalpropagation or no propagation altogether, namely, immobility. Such class ofeffective field theories encompasses instances of helical superfluids andmeta-fluids, where fractons can be connected to an emergent symmetry underhigher moment charges, leading in turns to the trivialization of some elasticcoefficients. The introduction of a finite charge density alters the mobilityproperties of fractons and leads to a competition between the chemicalpotential and the superfluid velocity in determining the gap of the dilaton.The mobility of fractons can also be altered at zero density upon consideringadditional higher-derivative terms.

Fractons in effective field theories for spontaneously broken translations