[Paper Review] Zero-magnetic-field Hall effects in artificially corrugated bilayer graphene

Sheng-Chin Ho, Ching‐Hao Chang+6 more|arXiv (Cornell University)|Oct 16, 2019

Graphene research and applications57 references4 citations

TL;DR

This study demonstrates a nonlinear anomalous Hall effect and a novel linear-response Hall effect in bilayer graphene artificially corrugated via lithographically patterned strain on hexagonal boron nitride. The engineered pseudo-magnetic fields and Berry curvature dipole—without breaking time-reversal symmetry—enable a topological Hall response driven by spatially separated antiferromagnetic pseudo-magnetic fields and interlayer coupling modulation.

ABSTRACT

The ability to engineer the electronic band structure and, more strikingly, to access new exotic phase of matter has been the cornerstone of the advance of science and technology. Twisting van der Waals materials to form moiré superlattice is a powerful paradigm and can drive graphene from a normal metallic state into an insulating, superconducting, or ferromagnetic states. Here, we present a new route to create non-trivial band structure and consequently an exotic phase of matter via lithographically patterned strain (lattice deformation). This method is used to realize an artificially corrugated bilayer graphene wherein the real-space and momentum-space pseudo-magnetic fields (Berry curvatures) coexist and have nontrivial properties, namely, the Berry curvature dipole. This new class of condensed-matter systems enables us to observe the so-called nonlinear anomalous Hall effect and a new type of Hall effect without breaking the time-reversal symmetry. Such artificial material system and our approach to unconventional electronic states may open an avenue of geometrical and/or topological quantum phenomena as well as that of band engineering in van der Waals crystals.

Motivation & Objective

• To engineer a nontrivial band structure in bilayer graphene using lithographically patterned strain to break inversion symmetry.
• To realize coexisting real-space pseudo-magnetic fields and momentum-space Berry curvature dipole in a mesoscopic system.
• To demonstrate a nonlinear anomalous Hall effect and a new type of linear Hall effect without time-reversal symmetry breaking.
• To establish a platform for exploring geometric and topological quantum phenomena in van der Waals heterostructures via strain engineering.
• To validate the role of interlayer coupling modulation and spatially separated pseudo-magnetic field pairs in generating nontrivial Hall responses.

Proposed method

• Fabricated bilayer graphene on an artificially corrugated hexagonal boron nitride substrate with 100 nm periodicity to induce localized lattice strain.
• Engineered spatially separated antiferromagnetic pseudo-magnetic fields (B_S) via step-like corrugations, ensuring nonzero first-order moment.
• Utilized effective model based on classical linear response theory and Einstein relation to compute Hall conductivity σ_xy.
• Solved Newton's equation of motion for electrons under effective fields B_eff(x) and E_eff(x), incorporating valley-dependent velocity in bilayer graphene.
• Calculated velocity correlation functions with 2×10⁶ phase-space sampling to ensure 0.001% accuracy in conductivity tensor estimation.
• Derived analytical expression for nonlinear Hall current j_y^{2ω} in AC regime, linking it to Berry curvature dipole D_x via D_x ≈ (2ħ²/e³τ) × (j_y^{2ω}/(ε_x^ω)²).

Experimental results

Research questions

• RQ1 Can a nontrivial Hall effect be realized in bilayer graphene without breaking time-reversal symmetry?
• RQ2 How does spatially separated pseudo-magnetic field pairs influence the emergence of Berry curvature dipole and Hall response?
• RQ3 What is the role of interlayer coupling modulation in generating nonlinear and linear Hall effects under strain?
• RQ4 Can a mesoscopic system with engineered strain support measurable nonlinear Hall effects detectable via transport measurements?
• RQ5 To what extent does the anisotropic transport in corrugated bilayer graphene affect the Hall conductivity and its frequency dependence?

Key findings

• A nonlinear anomalous Hall effect was observed in corrugated bilayer graphene, with the Hall current scaling as j_y^{2ω} ∝ D_x (ε_x^ω)^2, confirming the presence of a Berry curvature dipole.
• The linear Hall conductivity σ_xy was found to be nonzero and increased almost linearly with Fermi energy, consistent with theoretical predictions.
• The Hall response persisted even in systems with a single corrugation flank or short mean free path (50 nm), indicating robustness against disorder.
• The effective model confirmed that the Hall effect arises from the interplay between effective electric and pseudo-magnetic fields, not from symmetry breaking.
• The calculated Berry curvature dipole D_x was extracted from experimental nonlinear Hall voltage and current, validating the theoretical framework.
• The system exhibits anisotropic transport, requiring correction for ρ_x and ρ_y in conductivity calculations, with Hall response dominating over longitudinal response.