Critical magnetic fields and electron pairing in magic-angle twisted bilayer graphene

The velocities of the quasiparticles that form Cooper pairs in a superconductor are revealed by the upper critical magnetic field. Here we use this property to assess superconductivity in magic-angle twisted bilayer graphene (MATBG), which has been observed over a range of moiré band-filling, twist angle, and screening environment conditions. An average Fermi velocity can be defined as $v$$^{*}_{F}$ ≡ k_BT_cℓ_c/ℏ, where T_c and ℓ_c are the critical temperature and magnetic length, respectively. An advantage of this definition is that $v$$^{*}_{F}$ can be directly extracted from the existing experimental data. Mean-field theory calculations of upper critical fields in model superconductors are consistent with the expectation that Fermi velocities defined in this way are nearly independent of the strength of pairing interaction. Moreover, for fixed strength pairing interaction, minima in $v$$^{*}_{F}$ as a function of band filling are coincident with maxima in T_c, as expected from the McMillan formula. Since no association between T_c maxima and $v$$^{*}_{F}$ minima is present in MATBG experimental data, we argue that the pairing interaction in MATBG is strongly filling-factor dependent. Furthermore, any theory of MATBG superconductivity must explain this dependence, which is apparently primarily responsible for the observed superconducting domes.