We study collective excitations of a trapped Fermi gas at finite temperature using the Bogoliubov–de Gennes mean-field theory in conjunction with the generalized random-phase approximation. The collective excitations are analyzed through the density response of a monopole excitation. We show the appearance of several modes at the normal-fluid–superfluid phase-transition temperature: Higgs mode–like pairing amplitude modulations, analogues of the second sound in the trapped gas, and an edge mode that is also the strongest mode in the response.
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