[Paper Review] Evolution of the Berry curvature dipole in uniaxially strained bilayer graphene

Karel Cuypers, Robin Smeyers+2 more|arXiv (Cornell University)|Jan 9, 2026

Graphene research and applications0 citations

TL;DR

The paper uses a full tight-binding model with Slater–Koster parametrization to study how uniaxial strain, parameterization, and interlayer distance affect the Berry curvature dipole and nonlinear Hall response in bilayer graphene. It shows strong parameterization dependence and highlights the limits of continuum models at higher strains.

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.

Motivation & Objective

• Investigate how uniaxial strain induces a finite Berry curvature dipole in bilayer graphene.
• Assess how different TB parameterizations affect the Berry curvature and dipole.
• Examine the impact of interlayer distance and gating on the Berry curvature dipole.
• Benchmark tight-binding results against low-energy continuum models.

Proposed method

• Build a Slater–Koster tight-binding model for AB-stacked bilayer graphene including 3 and 4 skew hoppings.
• Model uniform uniaxial strain by deforming lattice vectors and updating hoppings with distance-dependent Slater–Koster functions.
• Compute Berry curvature numerically from Bloch wave functions on a k-space grid and derive the Berry curvature dipole by integrating over energy below the Fermi level.
• Compare TB results with an effective low-energy continuum Hamiltonian and analyze differences.
• Explore effects of interlayer gating potential, interlayer distance, and higher strain magnitudes on the BCD.

Experimental results

Research questions

• RQ1 How does uniaxial strain generate a finite Berry curvature dipole in bilayer graphene?
• RQ2 How do different parameterizations (bilayer graphene vs. bulk graphite) affect the Berry curvature and BCD predictions?
• RQ3 What is the role of the 4 skew hopping term in shifting satellite Dirac cones and modifying the BCD with strain?
• RQ4 How do interlayer distance and interlayer gating influence the BCD under strain?
• RQ5 To what extent do tight-binding results agree with continuum models across strain regimes?

Key findings

• The Berry curvature dipole in bilayer graphene is highly sensitive to the TB parameterization, especially when including the 4 skew hopping.
• Including the 4 hopping shifts satellite Dirac cones upward in energy, altering their contributions to the BCD and causing sign changes at certain electron densities.
• The TB results differ qualitatively from continuum models at strains above ~1%, with larger strains yielding different trends and sign changes.
• Out-of-plane compression enhances the BCD by broadening Dirac cones, while out-of-plane expansion suppresses it.
• Interlayer gating and the magnitude of U modulate the BCD, with smaller U yielding larger BC but sharper energy localization near band edges.
• Stronger interlayer coupling from reduced interlayer distance amplifies the BCD, while increasing distance reduces it.
• The study emphasizes that realistic TB modeling is essential for reliable predictions of strain-tuned Berry curvature phenomena in bilayer graphene.