Pseudomagnetic fields in fully relaxed twisted bilayer and trilayer graphene

Abstract

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>θ</mml:mi> <mml:mo>&gt;</mml:mo> <mml:msup> <mml:mn>1.4</mml:mn> <mml:mrow> <mml:mo>∘</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , 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.