Brueckner $G$-matrix approach to two-dimensional Fermi gases with the finite-range attractive interaction

TL;DR

This paper uses the Brueckner G-matrix approach to analyze how finite-range attractive interactions influence the ground-state properties of two-dimensional Fermi gases across the BEC-BCS crossover.

Contribution

It introduces analytical formulas for ground-state properties of 2D Fermi gases with finite-range interactions, advancing understanding of many-body effects in low-dimensional systems.

Findings

Finite-range effects significantly modify the Fermi-polaron energy.

The equation of state varies with the scattering length and effective range.

Analytical formulas provide insights into the BEC-BCS crossover in 2D systems.

Abstract

Two-dimensional spin-1/2 fermions with the finite-range interaction are theoretically studied. Characterizing the attractive interaction in terms of the scattering length and the effective range, we discuss the finite-range effects on the ground-state properties in this system. The Brueckner $G$-matrix approach is employed to analyze the finite-range effects on an attractive Fermi-polaron energy and the equation of state throughout the BEC-BCS crossover in two dimensions, which can be realized in the population-imbalanced and -balanced cases between two components, respectively. The analytical formulae for these ground states obtained in this study would be useful for understanding many-body phenomena with finite-range interactions in low-dimensional systems.