Strain-induced nonlinear Hall effect in graphene systems

This thesis aims to study the nonlinear electrical transport response of monolayer and bilayer graphene systems under the influence of different lattice deformations (strain). Broken inversion and rotation symmetries can generate a second-order transverse current response called the nonlinear Hall effect in the presence of time-reversal symmetry. The nonlinear Hall currents are proportional to the Berry curvature dipole (BCD), a quantity proportional to an intrinsic topological quantity known as the Berry curvature. We investigate homo-strain and hetero-strain in bilayer graphene, in which the two carbon layers are deformed symmetrically and asymmetrically respectively. Our numerical results show that bilayer graphene systems give a larger BCD, up to an order of magnitude using homo-strain and up to two orders of magnitude using heterostrain, when compared to monolayer graphene for the same strain due to larger Berry curvature and density of states. Furthermore, we obtain a large BCD in bilayer graphene under hetero-strain, which breaks both the inversion and three-fold rotational symmetries. Based on an effective k · p analysis, it is necessary to consider higher-order corrections, that are linear in momentum qj and strain uij, in the velocity renormalization of the Dirac fermions to obtain a finite Berry curvature induced by hetero-strain. Larger BCD and the implication of hetero-strain make bilayer graphene a better candidate for practical applications such as detecting terahertz radiation. The result of this thesis motivates the investigation of hetero-strain in twisted bilayer graphene, a hot topic in condensed matter physics. In particular, the impact of strain-induced velocity renormalization is not explored systematically in the literature, which can be a subject of future study