Abstract

Recently, the theory of topological Lifshitz transition has become the focus of much attention in complex materials such as high-Tc superconductors, heavy fermions compounds etc. In this talk, after reviewing the basic concepts, I will present two cases of topological Lifshitz transitions involving (i)dipolar fermions in optical lattices and (ii) itinerant electrons close to a ferromagnetic quantum critical point but in the disordered side.

In the first case, we consider an experimentally realizable two dimensional model of non-interacting chains of spinless fermions weakly coupled via a small inter-chain hopping with a repulsive inter-chain interaction. The phase diagram of this model has a surprising feature: an abrupt change in the Fermi surface as the interaction is increased. We study in detail this meta-nematic transition, and show that the well-known continuous Lifshitz transition is the critical endpoint of this first order quantum phase transition. Furthermore, in the vicinity of the endpoint, the order parameter has a non-perturbative BCS -like form. In the second case, the motivation for the work is provided by recent experiments on the material NaxCoO2. We particularly examine the role of paramagnetic fluctuations in the development of an additional Fermi surface.