Quatonic and SpinQuatonic Superconductors: Twisted Bilayer Graphene and Cuprates

A novel superconducting transition temperature T_c=nV_BCS/4 and energy gap Δ(T)=2T_ctanh[Δ(T)/2T] are presented, based on BCS framework [the cut-off energy T_d ≤2T_c], where n is the carrier filling number in the primitive unit cell. The virtual exchange of Quaton (QT) [SpinQuaton (SQ)], (4 charges [spins] of 2 electrons and 2 holes on tetrahedron corners), induced by exciton [magnon], between the carriers involved, yields V_BCS = 2E_QT[E_SQ] (eigenenergy of QT [SQ]). For twisted bilayer graphene (TBG), E_QT=2E_x (exciton energy), E_x is μ, the chemical potential energy, defined by the carrier density for n=½, and T_c=μ/2. Using μ=-0.3meV calculated by Wu et al., Phys. Rev. Lett. 121, 257001 (2018), T_c(TBG)=1.74K in excellent agreement with 1.7K observed by Cao et al., Nature 556, 43 (2018). For cuprates, assigning the modes at 47meV (TlBCO) and 41 – 34meV (YBCO) in the neutron and Raman scatterings, as the respective SQs, for n=1/2, T_c (TlBCO)=135K and T_c (YBCO)=119 – 98K are in agreement with the experiments. The carrier specific heat jump [C_s/C_n -1] at T_c is found to be 1.823 (BCS value 1.43). The result of T_c=N(0)T_dV_BCS/2 [Nam, Phys. Lett. A193, 111 (1994), ibid(E) A197, 458 (1995)] is recovered with n=2N(0)T_d, where N(0) is the density of states/spin at the reference energy.