Superconductivity and special symmetry of twisted tri-layer graphene in chiral model

Superconducting properties of twisted tri-layer graphene (TTG) are studied within the scope of the chiral model based on using the unitary matrix (U in SU(2)) as an order parameter. To check the superconductor behavior of this system, the interaction with the external magnetic field (B_0) oriented along the graphene sheets is switched on and the internal magnetic intensity in the center is calculated as the function of the twisting angle. Vanishing of this function, due to the Meissner effect, being the important feature of the superconductivity, the corresponding dependence of the magic twisting angle on (B_0) is calculated. The unusual effect of re-entrant superconductivity for large values of (B_0) is discussed.