The intrinsic instabilities of the Fermi surface are a fascinating subject which has been gaining more and more attention in recent years. On the one hand, there are the Pomeranchuk instabilities [Pomeranchuk 1958]. In these instabilities, electron-electron interactions lead to a spontaneous deformation of the Fermi surface breaking the point group symmetry of a crystal without any concomitant breaking of translational symmetry. This could provide the mechanism whereby the Fermi liquid enters the “quantum nematic” state posited by Fradkin, Emery and Kivelson in the 1990’s as a “missing link” leading on to stripe phases observed in many strongly-correlated systems. On the other hand, there are the Lifshitz phase transitions where the Fermi surface changes its topology, for example between spherical and toroidal topology (a “neck-closing” transition) or by changes in the number of sheets it has [Lifshitz 1960]. Such transitions are usually regarded as non-interacting phenomena, but it has been understood for some time that similar changes may also emerge as a result of electron-electron interactions. More recently it has been shown that interaction-induced topological and symmetry-breaking transitions of the Fermi surface are in direct competition [Quintanilla and Schofield, 2006].

An interesting aspect of Lifshitz transitions is their order. In the original work by Lifshitz, they were described as “2 and 1/2” order phase transitions and purported to have relatively weak thermodynamic signatures. A few years ago we examined the effect of interactions on the two-dimensional version of the neck-closing transition and we found that they modify it in a fundamental way: the transition goes 1st order in a non-analytic fashion, so that even arbitrarily weak interactions will modify the order of the transition [Quintanilla, Carr and Betouras, 2008; Carr, Quintanilla and Betouras, 2009]. However that calculation referred to a specific realisation of such transition in a particular setup with ultra-cold dipolar atoms or molecules, and it did not go beyond mean field theory.

The present work addresses the case of the related pocket-forming transition, where a hole forms in the middle of the Fermi surface. Unlike the previous work, the calculation is fairly general and, crucially, looks at the effect of interactions beyond mean field theory. Interestingly, it is again found that the transition goes first order, though for quite different, and fairly general, reasons. Here’s the link to the preprint:

Effect of paramagnetic fluctuations on a Fermi surface topological transition in two dimensions

We study the Fermi surface topological transition of the pocket-opening type in a two dimensional Fermi liquid. We find that the paramagnetic fluctuations in an interacting Fermi liquid typically drive the transition first order at zero temperature. We first gain insight from a calculation using second order perturbation theory in the self-energy. This is valid for weak interaction and far from instabilities. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. Experimental signatures are given in the light of these results.