We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.

中文翻译：

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从巴丁-库珀-施里弗到二维玻色-爱因斯坦凝聚的演变：交叉和拓扑量子相变


我们回顾了从巴丁-库珀-施里弗（BCS）到二维玻色-爱因斯坦凝聚（BEC）的演变的各个方面，这些演变现在已经与低密度系统相关，例如门控超导体Li xZrNCl、魔角扭曲三层石墨烯、FeSe、FeSe1− xS x 和超冷费米超流体。我们强调了在一能带和两能带超流体和超导体的 BCS-BEC 演化过程中化学势在确定交叉或拓扑量子相变中发挥的重要作用。我们强调，在非节点 s 波通道中配对时会发生从 BCS 到 BEC 的交叉，而在任何节点较高角动量通道（例如 d 波）中配对时会出现序参数对称性不改变的拓扑量子相变。 。最后，我们讨论了一些关于二维 BCS 到 BEC 演化的悬而未决的问题，包括序参数的模量涨落、临界温度的更严格上限，以及双带超导体和超流体中晶格效应的探索。