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Upper bounds on the superfluid stiffness and superconducting $T_c$: Applications to twisted-bilayer graphene and ultra-cold Fermi gases
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abstract
Understanding the material parameters that control the superconducting transition temperature $T_c$ is a problem of fundamental importance. In many novel superconductors, phase fluctuations determine $T_c$, rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multi-band systems, valid in any dimension. This in turn leads to an upper bound on $T_c$ in two dimensions (2D), which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry. Our bound is particularly useful for the strongly correlated regime of low-density and narrow-band systems, where mean field theory fails. For a simple parabolic band in 2D with Fermi energy $E_F$, we find that $k_BT_c \leq E_F/8$, an exact result that has direct implications for the 2D BCS-BEC crossover in ultra-cold Fermi gases. Applying our multi-band bound to magic-angle twisted bilayer graphene (MA-TBG), we find that band structure results constrain the maximum $T_c$ to be close to the experimentally observed value. Finally, we discuss the question of deriving rigorous upper bounds on $T_c$ in 3D.
Forward citations
Cited by 4 Pith papers
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Exact models of chiral flat-band superconductors
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A microscopic calculation shows that the quantum anomalous Hall ferromagnet in twisted bilayer graphene is stable against spin and valley magnons, and that valley wave fluctuations limit the ordering temperature.
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High-$T_\textrm{C}$ Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moir$\'{e}$ Superlattices
Using a fitted universal constant from earlier work, the authors calculate twisted-bilayer-graphene transition temperatures of 1.94 K and 3.02 K and claim agreement with mean-field fits to published resistance data.
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Quantum Geometry in Quantum Materials
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