Pseudomagnetic fields in fully relaxed twisted bilayer and trilayer graphene

We present simple models to describe the in-plane and the out-of-plane lattice relaxation in twisted bilayer and symmetrically twisted trilayer graphene. Analytical results and series expansions show that for twist angles θ > 1.4 ∘ , the in-plane atomic displacements lead to pseudomagnetic fields weakly dependent on θ . In symmetrically twisted trilayer graphene, the central layer in-plane relaxation is greatly enhanced. The joint effect of the relaxation-induced pseudoscalar potentials and the associated energy difference between interlayer dimer and non-dimer pairs resulted in a significant electron–hole asymmetry both in twisted bilayer and trilayer graphene.