Electronic structure and elastic properties of TiB2 and ZrB2

Topological Dirac nodal-net fermions in AlB2 -type TiB2 and ZrB2

“…In this work, based on first-principles calculations, we theoretically study a new type of nodal structure, namely nodal net, in two AlB 2 -type diborides TiB 2 and ZrB 2 , which present a unique combination of properties such as high bond strengths, high melting points, high thermal conductivities, low electrical resistance and low work functions and can be easily synthesized in the laboratory [47][48][49][50]. To better understand this complex nodal net structure, we find it including four classes nodal line structures: A, nodal ring in k z = 0 plane surrounding K point; B, nodal line in three vertical mirror planes σ v1 , σ v2 and σ v3 (see definition on p. 273 of [51]); C, nodal line along Γ − A starting from a triple point; and D, a single isolated nodal ring at k z =0.5 plane surrounding A point.…”

Symmetry demanded topological nodal-line materials

“…Both compounds have been successfully synthesized in laboratory and have brought much interests owing to the unique combination of properties such as high melting point, high bonding strength, high thermal, and electrical conductivity [109,110]. Some electronic properties of the AlB 2 diborides are embedded in their band structures, such as a nodal net structure including triple point, nexus, and nodal link [98,99]. 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.…”

“…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].…”

“…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).…”

“…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].…”