Magnetic-impurity Resonance States For Different Pairing Symmetries In Twisted Bilayer Graphene

In this work,we use a two-orbital model on the emergent honeycomb lattice to study the magnetic impurity resonance states in the superconducting phase of 'magic'angle twisted bilayer graphene for different pairing symmetries.In chapter 1,we introduce the research background of graphene,in chapter 2,we construct the total Hamiltonian composed with three parts,(1)the Bogoliubov-de Gennes(BdG)Hamiltonian of superconducting TwBG for four kinds of different pairing symmetries,the s-wave,extended s-wave,chiral p-wave,and d+id-wave pairings,(2)the impurity Hamiltonian with strong Coulomb interaction,and(3)the hybridization between the magnetic impurity and superconducting TwBG.In chapter 3,we give a theoretical derivation of the local density of states(LDOS),In chapter 4,we analyze the numerical results for different pairing symmetries and different filling ratios,In chapter 5,we summarize the dissertation.Here are our main results from both symmetry analysis and numerical calculations:(1)When the impurity is hybridized to the two orbitals at one site of the emergent honeycomb lattice,i.e.the impurity is located at the center of the AB or BA spot,for any pairing symmetry belongs to the irreducible representations of D3 point group,the spacial distribution of the resonance states will break both the threefold rotation symmetry around the z-axis and the twofold rotation symmetry around the y-axis.(2)When the impurity is located at the center of the emergent honeycomb lattice,i.e.at the center of the AA spot,and hybridized to the six nearest neighbors symmetrically,there are only two kinds of hybridizations which belong to the two-dimensional irreducible representations of the D3 point group.For each hybridization and pairing symmetry studied,the spacial distribution of the resonance states reveals six-fold rotation symmetry.(3)For the hybridizations given in point(2),the in-gap resonance peak at the position close to the impurity must be vanishing for the s-wave pairing,extended s-wave pairing,and any other pairing symmetry belongs to the A1 representation of D3 point group.(4)For the hybridizations given in point(2),the unique resonance peak with negative resonance energy at R=(0,0)indicates that the pairing potential may be the topological nontrivial p-wave or d+id-wave pairing.