Quantum Geometric Moment Encodes Stacking Order of Moiré Matter.

Area of Science:

• Condensed matter physics
• Materials science
• Quantum geometry

Background:

• Moiré materials with flat bands are crucial for engineering band topology and correlation effects.
• Electronic bands in symmetry-broken moiré materials exhibit Berry curvature hotspots.
• Stacking order influences Berry curvature distribution, but experimental studies are lacking.

Purpose of the Study:

• To experimentally investigate the impact of stacking order on quantum geometric quantities in moiré materials.
• To explore the relationship between stacking order, Berry curvature, and the nonlinear Hall effect.
• To demonstrate electronic detection of stacking-induced quantum geometry.

Main Methods:

• Utilized 1.4° twisted double bilayer graphene (TDBG) with distinct AB-AB and AB-BA stacking orders.
• Formed an inversion-broken moiré superlattice with electrically tunable flat bands.
• Measured the nonlinear Hall (NLH) effect to probe Berry curvature dipole (BCD).

Main Results:

• Valley Chern numbers depended on the stacking order in TDBG.
• The BCD showed antisymmetric behavior in AB-AB TDBG, flipping sign with electric field polarity.
• The BCD exhibited symmetric behavior in AB-BA TDBG, maintaining sign regardless of electric field polarity.

Conclusions:

• The nonlinear Hall effect can electronically distinguish stacking-induced quantum geometry in moiré materials.
• Stacking order significantly impacts Berry curvature distribution and its response to electric fields.
• This work opens pathways for quantum geometry engineering and detection in moiré systems.