That's superconductivity. Recently, a theorem has been developed which unify superfluids and other states of matter and may leads to a deeper understanding of superconductivity. However, it's not known how that directly relates to gravity, yet, but symmetry breaking is present in these states of matter and is one of the consequences of the Higgs boson. In order to unite GR gravity with EM and the electroweak interaction (which by the Standard Model requires the Higgs mechanism), is to figure out the properties of the Higgs boson (again there are perhaps many (maybe 6) of them or particles like the Higgs that together work in some way that brings about mass).
That all being said, all motion has to be a result of the Higgs field including any motion in an EM field. Consider it. In order for something to move relative (in the GR sense) to anything else, even a single particle, the mass moves from one place to another. Now, one might argue that light has no mass - the photon has no mass - so how does it move if motion requires mass and interaction with the Higgs field? From the perspective of the photon, if you were somehow inside it, time doesn't pass and it doesn't move relative to anything, in a vacuum. Once it hits an electron, however, it is absorbed. The electron gains mass from the energy. But QM considers particles as they would behave only without mass and moving at the speed of light. The theory says nothing about mass, so then we don't understand motion at all, do we? The Standard Model may be extended, however, to incorporate gravity and mass (supersymmetric standard model). Thinking out loud now ....
I am convinced there is and this may point to "the other side of gravity" which we don't understand yet. It will result in new physics which will finally fold in mysteries of dark matter and dark energy, spooky action at a distance ~ all of the gravitational/mass elements we cannot collate today.
Will the Higgs field be seen as the "mother-of-gravity"? I like simple models.
I'm just convinced gravity is the target here in the long run...
Of course, I am not a physicist.