Charged skyrmions and topological origin of superconductivity in magic-angle graphene

Abstract

Topological solitons, a class of stable nonlinear excitations, appear in diverse domains as in the Skyrme model of nuclear forces. Here, we argue that similar excitations play an important role in a remarkable material obtained on stacking and twisting two sheets of graphene. Close to a magic twist angle, insulating behavior is observed, which gives way to superconductivity on doping. Here, we propose a unifying description of both observations. A symmetry breaking condensate leads to the ordered insulator, while topological solitons in the condensate—skyrmions—are shown to be charge 2e bosons. Condensation of skyrmions leads to a superconductor, whose physical properties we calculate. More generally, we show how topological textures can mitigate Coulomb repulsion and provide a previously unexplored route to superconductivity. Our mechanism not only clarifies why several other moiré materials do not show superconductivity but also points to unexplored platforms where robust superconductivity is anticipated.

Electrostatic interactions in twisted bilayer graphene

“…This paper does not attempt to cover in full the already extensive literature devoted to this topic. We leave out analyses beyond mean field, such as RPA calculations of the low energy excitations [15][16][17][18][19][20][21][22][23]. The main conclusions, which description a number of novel features almost unique to twisted bilayer graphene, are consistent with most studies carried out to date.…”

“…Finally, the zeroth point energy of excitations above the Hartree-Fock solutions discussed here can also favor specific combinations of wavefunctions of the type shown in Eq. ( 17) with different Chern numbers [22], see Eq. (19).…”

Resonant optical topological Hall conductivity from skyrmions

“…Skyrmions then appear as topological defects in the "ferromagnetic" phase [21], and they have been shown to support movable Majorana zero modes, providing a new, potential platform for realizing topological quantum computation [22]. Skyrmions have also been proposed to drive superconductivity in twisted bilayer graphene [23].…”

Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands

“…Indeed, the topological moiré minibands have been identified in the twisted multilayer graphene [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53], ABC-stacked-trilayer graphene/hBN heterostructure [54][55][56], and transition metal dichalcogenide (TMD) homobilayer [57]. The interplay between electronic correlation and nontrivial topology in MSL can stabilize exotic quantum states including unconventional superconductivity [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76] and fractional Chern insulator [77][78][79][80][81].…”