Recently I started realizing, or convincing myself that a graviton-like excitation could exist in a 2D chiral p-wave superfluid.
A 2D p-wave superfluid refers to a 2 dimensional fermion system where the fermions form Cooper pairs owing to attractive potential in a channel with angular momentum 1 (times the Planck constant). By "Chiral" we mean the Cooper pairs have definite angular momenta, or roughly speaking perform counterclockwise or clockwise rotation.
It has been realized that compared to the standard textbook example - BCS s-wave superfluid - the 2D chiral p-wave have extra collective modes in the spectrum and the spectrum would be modified by turning on some attractive forces between fermions in a quadrupole channel.
The author was involved in part of the progress (https://arxiv.org/abs/1808.09953).
What I did not have is the idea that the extra modes can be thought of as a kind of emergent gravity effect. I was told by Omri Golan, who explained this idea brilliantly in this work https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.064503.
What I sort of understood and developed ever since was the "attractive force" I brought up previously. Such degree of freedom also has spin-2 and more importantly its mass can be tuned by a parameter in the model.
As such, this degree of freedom in principle participates the low-energy dynamics of the system and I have been investigating the spectrum of such a hydrodynamic type theory. We hope there is a hope of realizing this in electronic system with nematic phase transition.
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