Topological Kirchhoff Law and Bulk-Edge Correspondence for Valley-Chern and Spin-Valley-Chern Numbers

Abstract

The valley-Chern and spin-valley-Chern numbers are the key concepts in valleytronics. They are topological numbers in the Dirac theory but not in the tight-binding model. We analyze the bulk-edge correspondence between the two phases which have the same Chern and spin-Chern numbers but different valley-Chern and spin-valley-Chern numbers. The edge state between them is topologically trivial in the tight-binding model but is shown to be as robust as the topological edge. We construct Y-junctions made of topological edges. They satisfy the topological Kirchhoff law, where the topological charges are conserved at the junction. We may interpret a Y-junction as a scattering process of particles which have four topological numbers. It would be a milestone of future topological electronics.

5 pages, 4 figures

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• Pseudospin-valley coupled edge states in a photonic topological insulator
• Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides
• Reprogrammable plasmonic topological insulators with ultrafast control
• Scattering-Free Optical Edge States between Heterogeneous Photonic Topological Insulators
• Tutorial: Computing topological invariants in two-dimensional photonic crystals
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• Designing multi-directional energy-splitters and topological valley supernetworks
• van der Waals Heterostructures of Germanene, Stanene and Silicene with Hexagonal Boron Nitride and Their Topological Domain Walls
• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• Valleytronics on the Surface of Topological Crystalline Insulator: Elliptic Dichroism and Valley-Selective Optical Pumping
• Valley Hall phases in Kagome lattices
• Symmetry Protected Topological Charge in Symmetry Broken Phase: Spin-Chern, Spin-Valley-Chern and Mirror-Chern Numbers
• Multifrequency and multimode topological waveguides in a Stampfli-triangle photonic crystal with large valley Chern numbers
• Detecting the Néel vector of altermagnet by attaching a topological insulator and crystalline valley-edge insulator
• Floquet Valley-Polarized Quantum Anomalous Hall State in Nonmagnetic Heterobilayers
• Zero-line modes at stacking faulted domain walls in multilayer graphene
• On-chip ultra-compact hexagonal boron nitride topological ring-resonator in visible region
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• Robustness of Helical Hinge States of Weak Second-Order Topological Insulators
• Phase transitions and scale invariance in topological Anderson insulators
• Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents
• Optimizing Topological Switching in Confined 2D-Xene Nanoribbons via Finite-Size Effects
• Large magnetoresistance dips and perfect spin-valley filter induced by topological phase transitions in silicene
• Nearly pure spin-valley sideband tunneling in silicene: effect of interplay of time periodic potential barrier and spin-valley-dependent Dirac mass
• Robust propagating in-gap modes due to spin-orbit domain walls in graphene
• Photonic emulation of two-dimensional materials with antiferromagnetic order
• Quantum anomalous Hall conductivity in altermagnets under applied magnetic field
• Invisible flat bands on a topological chiral edge