Effects of Defects in Superconducting Phase of Twisted Bilayer Graphene

In this work the effects of defects in the superconducting phases of the twisted bilayer graphene (TBG) are investigated. A will-accepted low energy effective model and a non-magnetic impurity potential to mimic defects are employed. Different superconducting pairing symmetries, including $s$-wave, $(d+id)$-wave and $(p+ip)$-wave pairing, are considered. In single impurity case, the local density of states (DOS) are calculated for the pairing symmetries above. For different pairing symmetries the number and property of bound states induced by defects are different. In multi-impurity case, the phase diagrams are calculated in terms of effective gap and the strength and density of impurities. In unconventional superconducting phases, namely $(p+ip)$-wave and $(d+id)$-wave phases, superconductivity will be destroyed by impurities with strong strength or concentration. These results can in principle be detected in scanning tunnelling microscopy (STM) experiments, and therefore the pairing symmetry, at least whether the superconductivity is conventional or unconventional, may be determined.