Effect of Defects in Superconducting Phase of Twisted Bilayer Graphene

In this work we study the effect of impurity in the superconducting phases of the twisted bilayer graphene (TBG) by analysing bound states induced by the impurity. As a comparison with the superconducting phase, we first consider the impurity effect in the TBG without superconductivity in the scheme of a low energy effective theory. For superconductivity, our basis is a four-band model2 with different superconducting pairing symmetries. Then we construct the effective impurity Hamiltonian and compute the local density of state (DOS). We find that for different kind of pairing symmetries the numbers of bound states are different. These results can in principle be detected in scanning tunnelling microscopy (STM) experiments, and therefore the pairing symmetry may be determined. Finally we consider the multi-impurity effect and compute phase diagrams in terms of effective gap and the strength and density of impurities. We find that in (p + ip)-wave and (d + id)-wave phases superconductivity will be destroyed by impurities with strong strength or concentration