Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides

Abstract

Topological metals with protected band-crossing points have been attracting great interest. Here we report novel topological band features in a family of metal diboride materials. Using firstprinciples calculations, we show that these materials are metallic, and close to Fermi level, there appears coexistence of one pair of nodal rings and one pair of triply-degenerate nodal points (TNPs). The nodal ring here is distinct from the previously studied ones in that its formation requires four entangled bands, not just two as in previous cases, hence it is termed as a four-band nodal ring (FNR). Remarkably, we show that FNR features Dirac-cone-like surface states, in contrast to the usual drumhead surface states for two-band nodal rings. Due to the presence of inversion symmetry, the TNP here is also different from those discussed previously in inversion-asymmetric systems. Especially, when spin-orbit coupling is included, the TNP here transforms into a novel Dirac point that is close to the borderline between the type-I and type-II Dirac point categories. We discuss their respective symmetry protections, and construct effective models for their characterization. The large linear energy range (> 2 eV) in these materials should facilitate the experimental detection of the signatures of these nontrivial band crossings.

Symmetry demanded topological nodal-line materials

“…Including SOC typically turns the DNLS into either a DSM or a TI. Some predicted centrosymmetric DNL materials include cubic antiperovskite materials Cu 3 NX [83,84], CaTe [92], LaX [93], Ca 3 P 2 [94], CaP 3 family [95], BaSn 2 [96,97], AlB 2 -type diborides [98][99][100], and 3D carbon allotrope materials with negligible SOC such as Mackay-Terrones crystals [54] and hyperhoneycomb lattices [101]. In addition, two-dimensional DNL materials have also been proposed in monolayer Cu 2 Si [102] and honeycomb-kagome lattice [103].…”

“…In particular, both LaSb and LaBi show extreme MR, which are possibly originated from a combination of electron-hole compensation and a special orbital texture on the electron pocket [104,105]. Their anisotropic characteristic of MR is the result of ellipsoidal electron pockets [ [98][99][100] centered at the X point [106]. However, ARPES measurements show that LaSb is topological trivial without any surface state observed [107], and LaBi with an usual surface state which has a linear conduction band and a parabolic valence band [108].…”

“…AlB 2 -type diborides [98][99][100]: Both TiB 2 and ZrB 2 crystallize in centrosymmetriclayered hexagonal structure with space group P6/mmm No. 191 (Table 2).…”

“…Take TiB 2 as an example, without SOC, six band crossings emerge around the E F , along the H-, -A, A-H, K-, M-K, and L-A directions. These band crossings give rise to four different kinds of nodal line structures, including 1) a nodal ring in the M x y plane centered around K point [100]; 2) a nodal ring in the in the M x y plane centered around A point; 3) nodal lines in three vertical mirror planes σ v1 , σ v2 , and σ v3 ; and 4) nodal line along -A starting from a triple point. All the four classes of nodal lines together compose a complex nodal net structure.…”

From Multiple Nodal Chain to Dirac/Weyl Semimetal and Topological Insulator in Ternary Hexagonal Materials

“…Such a material is known as 3D Dirac semimetal (DSM). [17][18][19][20][21][22][23][24][25][26] Around these points, the low-energy physics is described by a 4 × 4 massless Dirac Hamiltonian. In The Weyl Hamiltonian is quite robust against any perturbation.…”