Antiferromagnetically ordered Mott insulator and d+id superconductivity in twisted bilayer graphene: a quantum Monte Carlo study

Abstract

Using exact quantum Monte Carlo method, we examine the recent novel electronic states seen in magic-angle graphene superlattices. From the Hubbard model on a double-layer honeycomb lattice with a rotation angle θ = 1.08 • , we reveal that an antiferromagnetically ordered Mott insulator emerges beyond a critical Uc at half filling, and with a small doping, the pairing with d+id symmetry dominates over other pairings at low temperature. The effective d + id pairing interaction strongly increase as the on-site Coulomb interaction increases, indicating that the superconductivity is driven by electron-electron correlation. Our non-biased numerical results demonstrate that the twisted bilayer graphene share the similar superconducting mechanism of high temperature superconductors, which is a new and ideal platform for further investigating the strongly correlated phenomena. arXiv:1804.06096v2 [cond-mat.supr-con]

Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene

“…This mechanism is similar to the bond-centered charge density waves considered in the context of the cuprates [49][50][51]. The usual antiferromagnetic state on the honeycomb lattice [22,26] has two sublattices, and the spin density is centered on the sites; in contrast, the state we considered had vanishing spin density on the sites of the honeycomb lattice.…”

“…The symmetry of the triangular antiferromagnet is such that all on-site spin moments on the honeycomb lattice vanish, and so such a state will not be observable in studies [22,26] which only examine on-site moments.…”

Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach

“…Several effective low-energy models based on MSL have been proposed to describe the flat bands at the magic angles [9][10][11][12][13][14][15][16][17][18]. Based on these effective models, a variety of pairing symmetries, including spin singlet d + id wave [19][20][21][22], spin singlet but valley triplet d + id wave [23], spin triplet but orbital singlet d+id wave [9,24], in- * yingsu@lanl.gov † szl@lanl.gov tertwined spin singlet (triplet) superconductivity with charge (spin) density-wave orders [25], nematic and orbital triplet spin singlet superconducting state [15], and extended s wave [26], have been proposed. It is argued that intervalley electron pairing with either chiral (d + id mixed with p − ip) or helical form factor is the dominant instability driven by the intervalley fluctuations [17].…”

Flatbands and Perfect Metal in Trilayer Moiré Graphene

“…Flat bands present a reduced kinetic energy, thereby artificially boosting electron correlations [9]. The recent discovery of correlated insulating phases at half-filling and possibly unconventional superconductivity [10][11][12][13] have unveiled bilayer moiré graphene as a tunable device for exploring novel correlated states, at zero or finite magnetic field, spurring intense theoretical work in this direction [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. On the other hand, moiré bands were also investigated for their topological properties [34][35][36][37][38][39][40] and topological phase transitions were identified close to the magic angles [37,41].…”