Collective modes of a two-dimensional Fermi gas at finite temperature

TL;DR

This paper investigates how temperature and interaction strength influence the breathing mode frequencies of a two-dimensional Fermi gas, revealing a significant down-shift below the scale-invariant value at strong interactions and finite temperature.

Contribution

It provides a detailed analysis of the temperature dependence of the breathing mode anomaly in a 2D Fermi gas using various many-body theories and hydrodynamic modeling.

Findings

Breathing mode frequency decreases significantly at strong interactions and finite temperature.

The anomaly in the breathing mode depends sensitively on both interaction strength and temperature.

Predicted a down-shift of the breathing mode frequency below 2ω₀ at high interaction strength and finite temperature.

Abstract

In this work we examine the breathing mode of a strongly interacting two-dimensional Fermi gas and the role of temperature on the anomalous breaking of scale invariance. By calculating the equation of state with different many-body $T$-matrix theories and the virial expansion approach, we obtain a hydrodynamic equation of the harmonically trapped Fermi gas (with trapping frequency $\omega_{0}$) through the local density approximation. By solving the hydrodynamic equation we determine the breathing mode frequencies as functions of interaction strength and temperature. We find that the breathing mode anomaly depends sensitively on both interaction strength and temperature. In particular, in the strongly interacting regime we predict a significant down-shift of the breathing mode frequency, below the scale invariant value of $2\omega_{0}$ for temperatures of order the Fermi temperature.