Evolution of the Berry curvature dipole in uniaxially strained bilayer graphene

TL;DR

The paper investigates how uniaxial strain in AB-stacked bilayer graphene induces a finite Berry curvature dipole (BCD), enabling nonlinear Hall responses that vanish in the unstrained system. It uses a Slater–Koster tight-binding model including longer-range interlayer hoppings to study strain along zigzag and armchair directions, benchmarking results against the McCann–Koshino effective Hamiltonian and highlighting continuum-model limitations at larger strains. The results reveal strong parameterization dependence of the BCD, with the skew hopping shifting satellite Dirac cones and altering sign changes as a function of electron density and interlayer gating $U$, and show that out-of-plane compression broadens Dirac cones and enhances the BCD. The study emphasizes that realistic TB modeling is essential for predicting strain-tuned Berry curvature phenomena and provides guidance for maximizing the nonlinear Hall response via combined in-plane strain and out-of-plane pressure.

Abstract

While in pristine bilayer graphene the Berry curvature dipole (BCD), a necessary ingredient for the nonlinear anomalous Hall effect, is zero, uniaxial strain can give rise to finite BCD. We investigate this by using a tight-binding (TB) approach build on the Slater-Koster parameterization to capture lattice deformation effects often missed by continuum models. We demonstrate that the BCD's evolution with strain and doping is highly sensitive to the choice in parameterization, particularly when including the longer range interlayer skew hoppings. Additionally, out-of-plane compression enhances the response by broadening the Dirac cones. These findings benchmark low-energy continuum models and highlight the necessity of realistic tight-binding models for accurately predicting strain-engineered Hall effects in bilayer graphene.

Figures (11)

• Figure 1: The tight-binding model of AB stacked bilayer graphene.
• Figure 2: The low-energy dispersion near the Dirac point sliced across the x-axis, e.g. $k_y=0$, calculated using both the TB and continuum models with the parameterizations given in Table \ref{['tab:model_param']} for bulk graphite a) without or b) with the $\gamma_4$ skew hopping and the band structure calculated with the parameterization for bilayer graphene c) without or d) with the $\gamma_4$ skew hopping. The dotted line indicates the value of the added gating potential, U = 10 meV, between the two layers.
• Figure 3: The electronic dispersion, the BC, and the first moment of the BC in the low energy region of the Dirac cone of bilayer graphene with an interlayer gating potential of U = 10 meV. The contour lines show the Fermi surface at various energies. These plots were made using the TB parameterization fitted to bulk graphite dresselhaus_intercalation_2002.
• Figure 4: The BCD as a function of the electron density calculated with the bulk graphite parametrization with U = 10 meV.
• Figure 5: The BCD as a function of the electron density calculated with the bilayer graphene parametrization with U = 10 meV.