Nodal-link semimetals

In topological semimetals, the valance band and conduction band meet at zero-dimensional nodal points or one-dimensional nodal rings, which are protected by band topology and symmetries. In this Rapid Communication, we introduce “nodal-link semimetals”, which host linked nodal rings in the Brillouin zone. We put forward a general recipe based on the Hopf map for constructing models of nodal-link semimetals. The consequences of nodal ring linking in the Landau levels and Floquet properties are investigated.

Figure 1

Nodal rings of Eq. (6), and the pseudospin textures in the $k_y=k_z$ plane, for [(a),(b)] $m_0=3.2$, [(c),(d)] $m_0=3.0$, and [(e),(f)] $m_0=2.5$. The light-blue ring locates in the $k_y=k_z$ plane, while the dark-blue ring is perpendicular to it.

Figure 2

(a) Surface flat bands for $z=0$ boundary. (b) The spectra as a function of $k_x$ (fixed $k_y=0$) for an 800-site-thick slab perpendicular to the $z$ axis. (c) The $y=0$ surface states. (d) Spectra of a slab perpendicular to the $y$ axis. (e) $x=0$ surface Brillouin zone without surface states. (f) Spectra of a slab perpendicular to the $x$ axis. The black rings or lines in (a), (c), and (e) are projections of the bulk nodal link to the surface Brillouin zone. In (c), the number of bands in the two-disk-overlapping region is twice that of the nonoverlapping regions. Here, $m_0=2.5$.

Figure 3

Surface states of a slab perpendicular to the $z$ axis. Parameters are $\omega =4, m=1, e{A}_0=0.6, C=0.5$. (a) 3D view of surface bands. (b) $E\left(k_x\right)$ with $k_y=0$ fixed. The gray regions are bulk bands.