Higher-Order Weyl Semimetals

Abstract

Higher-order topology yields intriguing multidimensional topological phenomena, while Weyl semimetals have unconventional properties such as chiral anomaly. However, so far, Weyl physics remain disconnected with higher-order topology. Here, we report the theoretical discovery of higher-order Weyl points and thereby the establishment of such an important connection. We demonstrate that higher-order Weyl points can emerge in chiral materials such as chiral tetragonal crystals as the intermediate phase between the conventional Weyl semimetal and 3D higher-order topological phases. Higher-order Weyl semimetals manifest themselves uniquely by exhibiting concurrent chiral Fermi-arc surface states, topological hinge states, and the momentum-dependent fractional hinge charge, revealing a novel class of higher-order topological phases.

4+ pages, 4 figures

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• Higher-order Weyl Semimetals
• Observation of a phononic higher-order Weyl semimetal
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• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
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• Topological classification of Higher-order topological phases with nested band inversion surfaces
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• Quasicrystalline second-order topological semimetals
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Topological hinge modes in Dirac semimetals
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• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
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• Mirror real Chern insulator in two and three dimensions
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• Ideal type-II Weyl points in twisted one-dimensional dielectric photonic crystals
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Two-Dimensional Higher-Order Topological Metals
• Dipolar Weyl semimetals
• Topological van Hove singularities at phase transitions in Weyl metals
• Entanglement Signature of Hinge Arcs, Fermi Arcs, and Crystalline Symmetry Protection in Higher-Order Weyl Semimetals
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Berry-dipole Semimetals
• Crystalline-electromagnetic responses of higher order topological semimetals
• Multi higher-order Dirac and nodal line semimetals
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Topological Insulators with Hybrid-order Boundary States
• Engineering rich two-dimensional higher-order topological phases by flux and periodic driving
• Tunneling in an anisotropic cubic Dirac semi-metal
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Tunneling phase diagrams in anisotropic Multi-Weyl semimetals
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Topological semimetal with coexisting nodal points and nodal lines
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
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