Quantum Valley Hall Effect without Berry Curvature.

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Quantum Phenomena

Background:

• The quantum valley Hall effect (QVHE) relies on the valley Chern number (VCN) to create 1D chiral metallic states at domain walls.
• QVHE systems have zero total Berry curvature (BC), but local BC around valleys defines VCN, requiring negligible intervalley scattering.

Purpose of the Study:

• To introduce a novel valley-dependent topological phenomenon: zero Berry curvature quantum valley Hall effect (ZBC QVHE).
• To characterize ZBC QVHE using the valley Euler number (VEN) in 2D systems with space-time inversion symmetry.
• To identify conditions for topologically protected 1D helical metallic states at domain walls.

Main Methods:

• Theoretical framework development for ZBC QVHE.
• Integration of Euler curvature for VEN calculation.
• Tight-binding model studies and first-principles calculations.

Main Results:

• Established the fundamental origin of ZBC QVHE.
• Demonstrated that 1D helical metallic states are protected at domain walls between opposite VENs under specific symmetry conditions.
• Identified stacked hexagonal bilayer lattices (h-BX) and twisted bilayer graphenes as candidate materials.

Conclusions:

• ZBC QVHE offers a new paradigm in topological physics.
• The valley Euler number provides a robust characterization for this phenomenon.
• Candidate materials show promise for realizing protected helical domain wall states.