I will describe the effect of interactions on a system with a single quadratic band touching point. I will focus on the situation in which the Fermi energy is exactly at the touching point and can be thought of as being at a Lifshitz transition. The interactions will be treated perturbatively within the renormalization group (RG) scheme. At the one-loop level a repulsive interaction will be shown to be marginally relevant and an attractive interaction marginally irrelevant, in contrast to what is encountered in a regular Fermi liquid. The results obtained from the RG calculation will be corroborated by a study of a microscopic model whose ground state and Green’s functions can be obtained exactly. I will show that away from the transition the system displays an instability towards forming an excitonic condensate.
Reference: J. Shah and S. Mukerjee, Phys. Rev. B 103, 195118 (2021)
Zoom link: https://us06web.zoom.us/j/82990966036?pwd=ZGJBY05rK3hNb0RrTW5ZdXNTMDF3QT09
Meeting ID: 829 9096 6036