Stable higher-order topological Dirac semimetals with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> monopole charge in alternating-twist multilayer graphene and beyond

Abstract

We demonstrate that a class of stable ${\mathbb{Z}}_{2}$ monopole charge Dirac point (${\mathbb{Z}}_{2}\mathrm{DP}$) phases can robustly exist in real materials, which is counterintuitive: that is, a ${\mathbb{Z}}_{2}\mathrm{DP}$ is unstable and generally considered to be only the critical point of a ${\mathbb{Z}}_{2}$ nodal line (${\mathbb{Z}}_{2}\mathrm{NL}$) 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. We explicitly reveal the higher-order bulk-boundary correspondence in the stable ${\mathbb{Z}}_{2}\mathrm{DP}$ phase. We propose the alternating-twist multilayer graphene, which can be regarded as 3D twisted bilayer graphene (TBG), as the first example to realize such stable ${\mathbb{Z}}_{2}\mathrm{DP}$ phase and show that the Dirac points in the 3D TBG are essentially degenerate at high-symmetry 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 ${\mathbb{Z}}_{2}\mathrm{NL}$ phases or other ${\mathbb{Z}}_{2}\mathrm{DP}$ phases with hinge states of adjustable length. In addition, we present other 3D materials which host ${\mathbb{Z}}_{2}\mathrm{DPs}$ 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 ${\mathbb{Z}}_{2}\mathrm{DP}$ phases, which will provide direct and strong guidance for the realization of the ${\mathbb{Z}}_{2}$ monopole semimetal phases in (among others) electronic materials, metamaterials, and electrical circuits.

Topics & Concepts