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Evolution of Fermion Pairing from Three to Two Dimensions
Interacting fermions in coupled two-dimensional (2D) layers present unique physical phenomena and are central to the description of unconventional superconductivity in high-transition-temperature cuprates and layered organic conductors. Reduced dimensionality enhances the effect of fluctuations, while interlayer coupling can stabilize superconductivity and even amplify the transition temperature. A fermionic superfluid loaded into a periodic potential should form stacks of two-dimensional superfluids with tunable interlayer coupling, a key ingredient of the model proposed by Anderson to explain high transition temperatures observed in the cuprates. For deep potentials in the regime of uncoupled 2D layers, increasing the temperature of the gas is expected to destroy superfluidity through the Berezinskii-Kosterlitz-Thouless mechanism, while more exotic multi-plane vortex loop excitations are predicted for a 3D-anisotropic BCS superfluid near the critical point.