Flat bands with Berry curvature in multilayer graphene

Abstract

We demonstrate that flat bands with local Berry curvature arise naturally in chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The degree of flatness can be tuned by varying the number of graphene layers N . For N = 7 the bands become nearly flat, with a small bandwidth ∼ 3.6 meV. The two nearly flat bands coming from the K and K valleys cross along lines in the reduced zone. Weak intervalley tunneling turns the bandcrossing into an avoided crossing, producing two nearly flat bands with global Chern number zero, but with local Berry curvature. The flatness of the bands suggests that many body effects will dominate the physics, while the local Berry curvature of the bands endows the system with a nontrivial quantum geometry. The quantum geometry effects manifest themselves through the quantum distance (Fubini-Study) metric, rather than the more conventional Chern number. Multilayer graphene on BN thus provides a platform for investigating the effect of interactions in a system with a non-trivial quantum distance metric, without the complication of non-zero Chern numbers. We note in passing that flat bands with non-zero Chern number can also be realized by making use of magnetic adatoms, and explicitly breaking time reversal symmetry.

Theory of Floquet band formation and local pseudospin textures in pump-probe photoemission of graphene

“…A similar texture is also obtained for Bernal stacked bilayer graphene 29 in a perpendicular electric field 30 . In this analogy, we stress that the doubled winding in bilayer graphene persists even when the energy gap induced by the electric field goes to zero.…”

“…Also the effective perpendicular electric field generated by the circularly polarized light pulse in our work points in opposite directions at K and K 0 , in contrast to the static electric field applied in ref. 30, which corresponds to the Haldane mass term. In any case, the observation of state S 2 suggests the possibility to dynamically engineer effective models with higher pseudospin winding numbers, similarly to higherorder spin-orbital textures in topological insulators 31 .…”

Direct probing of the stacking order and electronic spectrum of rhombohedral trilayer graphene with scanning tunneling microscopy

“…The tunneling spectrum gives direct access to the local DOS of the surface. Therefore, these low-energy tunneling peaks are attributed to the signatures of the flat bands around the charge neutrality point of the r-TLG [15][16][17].…”

Observation of Topological Bloch-State Defects and Their Merging Transition

“…As our method does not couple to the spin degree of freedom, it could be used to detect spin-dependent Dirac points or non-Abelian gauge fields [27,28] by combining it with Stern-Gerlach separation. Our method is also suited to detect higher winding numbers of the pseudospin textures, which are predicted for driven graphene [29] and bilayer graphene [30,31]. Finally, using two driving frequencies, an extension to lattices with a three-atomic basis such as the Lieb lattice [32] or generally to multiband systems is conceivable.…”