Quantum Valley Hall effect without Berry curvature

Abstract

The quantum valley Hall effect (QVHE) is characterized by the valley Chern number (VCN) in a way that one-dimensional (1D) chiral metallic states are guaranteed to appear at the domain walls (DW) between two domains with opposite VCN for a given valley. Although in the case of QVHE, the total BC of the system is zero, the BC distributed locally around each valley makes the VCN well-defined as long as inter-valley scattering is negligible. Here, we propose a new type of valley-dependent topological phenomenon that occurs when the BC is strictly zero at each momentum. Such zero Berry curvature (ZBC) QVHE is characterized by the valley Euler number (VEN) which is computed by integrating the Euler curvature around a given valley in two-dimensional (2D) systems with space-time inversion symmetry. 1D helical metallic states can be topologically protected at the DW between two domains with the opposite VENs when the DW configuration preserves either the mirror symmetry with respect to the DW or the combination of the DW space-time inversion, and chiral symmetries. We establish the fundamental origin of ZBC-QVHE. Also, by combining tight-binding model study and first-principles calculations, we propose stacked hexagonal bilayer lattices including h-BX (X=As, P) and large-angle twisted bilayer graphenes as candidate systems with robust helical DW states protected by VEN.

3+6 figure,

References in corpus (29)

• Topological Insulators with Inversion Symmetry
• Valley Dependent Optoelectronics from Inversion Symmetry Breaking
• Observation of topological valley transport of sound in sonic crystals
• Topological confinement in bilayer graphene
• Colloquium: Quantum anomalous Hall effect
• Edge states in Graphene: from gapped flat band to gapless chiral modes
• Coupling the valley degree of freedom to antiferromagnetic order
• Spin-Valleytronics in Silicene: Quantum-Spin-Quantum-Anomalous Hall Insulators and Single-Valley Semimetals
• Electronic Highways in Bilayer Graphene
• Valley-Hall Kink and Edge States in Multilayer Graphene
• Topological Euler class as a dynamical observable in optical lattices
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Geometric approach to fragile topology beyond symmetry indicators
• Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• The fate of topological-insulator surface states under strong disorder
• Conventional superconductivity in quasicrystals
• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Minimal non-abelian nodal braiding in ideal metamaterials
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Controlling Valley-Polarisation in Graphene via Tailored Light Pulses
• All-Optical Ultrafast Valley Switching in Two-Dimensional Materials
• Second-order and real Chern topological insulator in twisted bilayer $\alpha$-graphyne
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry
• Real Hopf Insulator
• Bulk-edge correspondence of Stiefel-Whitney and Euler insulators through the entanglement spectrum and cutting procedure
• Quantum Valley and Sub-valley Hall Effect in the Large Angle Twisted Bilayer Graphene
• Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture

Cited by in corpus (5)

• Experimental probe of band structures of bilayer valley photonic crystals
• Valley Gapless Semiconductor: Models and Applications
• Dirac-Rashba fermions and quantum valley Hall insulators in graphene-based 2D heterostructures
• Euler band topology in superfluids and superconductors
• Hinge modes of three-dimensional Euler insulators