BCS-BEC quantum phase transition and collective excitations in two-dimensional Fermi gases with p- and d-wave pairings

TL;DR

This paper investigates the quantum phase transition in two-dimensional fermionic systems with p- and d-wave pairings, revealing non-smooth evolution of collective modes due to infrared divergences at the transition point.

Contribution

It demonstrates that the BCS-BEC transition for nonzero angular momentum pairings involves a quantum phase transition linked to infrared behavior, unlike the smooth crossover in s-wave systems.

Findings

Quantum phase transition occurs at zero chemical potential for p- and d-wave pairings.

Collective excitation modes exhibit nonanalytic behavior across the transition.

Infrared divergence causes non-smooth evolution of the Anderson-Bogoliubov mode.

Abstract

It is generally believed that the BCS-BEC evolution in fermionic systems with s-wave pairing is a smooth crossover. However, for nonzero orbital-angular-momentum pairing such as p- or d-wave pairing, the system undergoes a quantum phase transition at the point where the chemical potential $\mu$ vanishes. In this paper, we study the BCS-BEC quantum phase transition and the collective excitations associated with the order-parameter fluctuations in two-dimensional fermionic systems with p- and d-wave pairings. We show that the quantum phase transition in such systems can be generically traced back to the infrared behavior of the fermionic excitation at $\mu=0$: $E_{\bf k}\sim k^l$, where $l=1,2$ is the quantum number of the orbital angular momentum. The nonanalyticity of the thermodynamic quantities is due to the infrared divergence caused by the fermionic excitation at $\mu=0$. As a result, the evolution of the Anderson-Bogoliubov mode is not smooth: Its velocity is nonanalytical across the quantum phase transition.