Fermi surface resonance and quantum criticality in strongly interacting Fermi gases

Abstract

Fermions in a Fermi gas obey the Pauli exclusion principle restricting any two fermions from occupying the same quantum state. Strong interactions between fermions can completely change the properties of the Fermi gas. In our theoretical study we find an exotic quantum phase in strongly interacting Fermi gases subject to a certain condition imposed on the Fermi surfaces that we call the Fermi surface resonance. The phase is quantum critical in time and space and can be identified by the power-law dependence of the spectral density in frequency and momentum. The linear-response functions are singular in the static limit and at the Kohn anomalies. We analyze the quantum critical state at finite temperatures $T$ and finite size $L$ of the Fermi gas and provide a qualitative $L\ensuremath{-}T$ phase diagram. The quantum critical phase can be experimentally found in typical semiconductor heterostructures.