Pomeranchuk and topological Fermi surface instabilities from central interactions

We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle

interactions. We find that Pomeranchuk instabilities with all symmetries

except l=1 can take place if the interaction is repulsive and has

a finite range r(0) of the order of the interparticle distance. We

demonstrate this by solving the mean field equations analytically

for an explicit model interaction, as well as numerical results for

more realistic potentials. We find in addition to the Pomeranchuk

instability other, subtler phase transitions in which the Fermi surface

changes topology without rotational symmetry breaking. We argue that

such interaction-driven topological transitions may be as generic

to such systems as the Pomeranchuk instability.