Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

Abstract

We reveal an edge spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrainedpath quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.Triplet superconductivity (SC) has been a focus of modern condensed matter physics because of its possible connection to topological quantum information and computation [1][2][3][4][5][6][7][8][9][10] . It has been proposed that a gapless Majorana bound state would localize at the end of the one-dimensional spinless p-wave superconductor 1 , which could be used to practically realize topological quantum computation 11,12 . To realize such a Majorana bound state in real material, the superconducting proximity effect was proposed [13][14][15] , and experimental evidence of its existence was recently reported 16 . Here, we explore the possibility of intrinsic triplet SC, which is generated by an electronic correlation.In this paper, we reveal a possible edge-spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons with appropriate interactions. Graphene, a single layer of carbon, has generated immense interest ever since its experimental discovery 17,18 . Recently, experimental advances in doping methods have made it possible to change the type of carriers (electrons or holes) 19,20 , opening the doors for exotic phases, such as SC and magnetism induced by repulsive interactions. For instance, it was shown by the two-stage renormalization-group calculation that unconventional SC is induced by weak repulsive interactions in honeycomb Hubbard models that are away from half-filling 21 , and that a topological d + id SC is induced in a heavily doped system [22][23][24][25][26][27][28] . At graphene edges the density of states may be peaked due to the presence of edge-localized states close to the Fermi level 29 . Especially at extended zigzag edges this leads to a phenomenon called edge magnetism, for which various theories 30-32 predict ferromagnetic (FM) intraedge and antiferromagnetic (AFM) interedge correlations. The proposed magnetism is similar to the flat-band ferromagnetism appearing in the orbital-active optical honeycomb lattice 33 , where the band flatness dramatically amplifies the interaction effect, driving the ferromagnetic transition even wit...

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