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We present simple models to describe the in-plane and the out-of-planelattice relaxation in twisted bilayer and symmetrically twisted trilayergraphene. Analytical results and series expansions show that for twist angles{\theta} > 1 $^{\circ}$, the in-plane atomic displacements lead topseudomagnetic fields weakly dependent on {\theta}. In symmetrically twistedtrilayer graphene, the central layer in-plane relaxation is greatly enhanced.The joint effect of the relaxation-induced pseudoscalar potentials and theassociated energy difference between interlayer dimer and non-dimer pairsresulted in a significant electron-hole asymmetry both in twisted bilayer andtrilayer graphene.

Pseudomagnetic fields in fully relaxed twisted bilayer and trilayer graphene