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Chinese Physics B

Quantum fluctuation effect of a two-dimensional Fermi gas with d -wave pairing

S C Wang, Tingting Shi, Wei Zhang

Published Apr 27, 2026• 0 citations
Publisher

Abstract

Abstract We investigate quantum fluctuation effects in a two-dimensional Fermi superfluid with $d_{x^2\textrm{-}y^2}$-wave pairing through an evolution from Bardeen-Cooper-Schrieffer (BCS) limit to Bose-Einstein condensate (BEC) limit. Using the Gaussian pair fluctuation (GPF) theory beyond the mean-field approximation, we derive a modified particle number equation and solve it self-consistently with the gap equation. We find that key physical properties, including the equation of state, the compressibility, and the sound velocity, are strongly renormalized by quantum fluctuations, reflecting their crucial role near the phase transition. Both mean-field and GPF theory reveal a pronounced Lifshitz transition at zero chemical potential $\mu=0$, but occurring at different interaction strengths. As the system evolves from the BCS to BEC regime, the fluctuation-induced particle number grows rapidly and saturates near the transition point, further highlighting the importance of quantum fluctuations. We also analyze the quasiparticle excitation spectrum, which exhibits a transition from a nodal BCS regime with characteristic $C_4$ symmetry to a fully gapped BEC regime, providing direct insight into the interplay between pairing symmetry, phase transition of spectrum topology, and quantum fluctuations.

DOI
10.1088/1674-1056/ae64cc

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Abstract We study the crossover from the Bardeen–Cooper–Shrieffer regime to the Bose–Einstein-condensation regime in an anisotropic trapped quantum gas of ultracold fermionic atoms. Using an effective two-dimensional Hamiltonian with renormalized interactions between atoms and dressed molecules, we extend the Gaussian pair fluctuation theory to quasi-two-dimensional systems. The equation of state, pair size and sound velocity as well as the convexity parameters of the Goldstone mode are investigated to show how Fermi superfluidity is affected by reduced dimensionality and Gaussian fluctuations at zero temperature in a wide range of crossover. We compare our results with the recent experiment of 6 L i atomic gases and find good agreements.
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