Fate of a multiple-band Fermi liquid that is coupled with critical φ⁴ bosons

Multiple-band nature of electronic energy bands leads to novel physical effects in solids. In this paper, we clarify physical properties of a Fermi system with a pair of electron and hole Fermi surfaces (FSs), whose coupling is mediated by a critical U(1) boson field. By using a one-loop renormalization group analysis, we show that when the boson field undergoes a quantum phase transition with broken U(1) symmetry, the multiple-band Fermi system shows a non-Fermi liquid (non-FL) behaviour in its thermodynamic and magnetic properties. At a quantum critical point (QCP), Fermi velocities of the two FSs are renormalized into a same critical velocity as a boson velocity, and the fermion's density of states (DOS) shows a pseudo-gap behaviour with a logarithmic energy dependence at the QCP.