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We study a two-dimensional Fermi gas with an attractive interaction subjected to synthetic magnetic fields assumed to be mutually antiparallel for two different spin components. By employing the mean-field approximation, we find that its phase diagram at zero temperature consists of pair superfluid and quantum spin Hall insulator phases and closely resembles that of the Bose-Hubbard model. The resulting two phases are separated by a second-order quantum phase transition classified into the universality class of either the dilute Bose gas or the XY model. We also show that the pairing gap can be enhanced significantly by the antiparallel magnetic fields as a consequence of magnetic catalysis, which may facilitate the realization of the pair superfluid in two dimensions by ultracold atom experiments.Comment: 6 pages, 2 figure

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A Disperse Red-labeled poly(methyl methacrylate) monolayer at the air/water interface has been investigated by surface second-harmonic generation (SHG) and surface potential measurements. Upon spreading, the polymer forms a domain having noncentrosymmetric C." symmetry. The local field factor determined by SHG in the gas phase indicates no change in the distance between the dye moiety. On the basis of the local field factor and the optical absorption spectra, we found that domains gather each other and the dye moiety slightly moves from the air/water interface to the water in the expanded phase. Consequently, the molecular tilt angle decreases in the expanded phase. These are observed not only by SHG but also by surface potential measurement. Thus, we can conclude that the polymer monolayer is ideally compressed at the air/water interface. The influence of the deposition of the monolayer onto a glass substrate has also been studied to clarify the cause of film-forming ability. While the monolayer deposited by the horizontal deposition changes the structure into a centrosymmetric fashion, the monolayer deposited by vertical moving-wall deposition maintains their structure at the air/water interface. This difference originates from hydrophilicity of the dye moiety contacting to either hydrophilic or hydrophobic substrates. In conclusion, the formation of the monolayer at the air/water interface is caused by dye moiety and the polar sites of PMMA.