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We investigate a two-species Fermi gas in which one species is confined in atwo-dimensional plane (2D) or one-dimensional line (1D) while the other is freein the three-dimensional space (3D). We discuss the realization of such asystem with the interspecies interaction tuned to resonance. When the massratio is in the range 0.0351<m_2D/m_3D<6.35 for the 2D-3D mixture or0.00646<m_1D/m_3D<2.06 for the 1D-3D mixture, the resulting system is stableagainst the Efimov effect and has universal properties. We calculate keyquantities in the many-body phase diagram. Other possible scale-invariantsystems with short-range few-body interactions are also elucidated.

Universal Fermi gases in mixed dimensions