Stable Higher-Order Topological Dirac Semimetals with \(\mathbb{Z}_2\) Monopole Charge in Alternating-twisted Multilayer Graphenes and beyond

We demonstrate that a class of stable \(\mathbb{Z}_2\) monopole charge Dirac point (\(\mathbb{Z}_2\)DP) phases can robustly exist in real materials, which surmounts the understanding: that is, a \(\mathbb{Z}_2\)DP is unstable and generally considered to be only the critical point of a \(\mathbb{Z}_2...

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Bibliographic Details
Published inarXiv.org
Main Authors Qian, Shifeng, Li, Yongpan, Cheng-Cheng, Liu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.12.2023
Subjects
Bilayers
Brillouin zones
Circuits
Coupling
Critical point
Electronic materials
Graphene
Interlayers
Metamaterials
Multilayers
Phases
Symmetry
Topology
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Summary:We demonstrate that a class of stable \(\mathbb{Z}_2\) monopole charge Dirac point (\(\mathbb{Z}_2\)DP) phases can robustly exist in real materials, which surmounts the understanding: that is, a \(\mathbb{Z}_2\)DP is unstable and generally considered to be only the critical point of a \(\mathbb{Z}_2\) nodal line (\(\mathbb{Z}_2\)NL) characterized by a \(\mathbb{Z}_2\) monopole charge (the second Stiefel-Whitney number \(w_2\)) with space-time inversion symmetry but no spin-orbital coupling. For the first time, we explicitly reveal the higher-order bulk-boundary correspondence in the stable \(\mathbb{Z}_2\)DP phase. We propose the alternating-twisted multilayer graphene, which can be regarded as 3D twisted bilayer graphene (TBG), as the first example to realize such stable \(\mathbb{Z}_2\)DP phase and show that the Dirac points in the 3D TBG are essential degenerate at high symmetric points protected by crystal symmetries and carry a nontrivial \(\mathbb{Z}_2\) monopole charge (\(w_2=1\)), which results in higher-order hinge states along the entire Brillouin zone of the \(k_z\) direction. By breaking some crystal symmetries or tailoring interlayer coupling we are able to access \(\mathbb{Z}_2\)NL phases or other \(\mathbb{Z}_2\)DP phases with hinge states of adjustable length. In addition, we present other 3D materials which host \(\mathbb{Z}_2\)DPs in the electronic band structures and phonon spectra. We construct a minimal eight-band tight-binding lattice model that captures these nontrivial topological characters and furthermore tabulate all possible space groups to allow the existence of the stable \(\mathbb{Z}_2\)DP phases, which will provide direct and strong guidance for the realization of the \(\mathbb{Z}_2\) monopole semimetal phases in electronic materials, metamaterials and electrical circuits, etc.
ISSN:2331-8422