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

Abstract

Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in AlB2-type TiB2 and ZrB2 when spin-orbit coupling (SOC) is ignored. Taking TiB2 as an example, there are several topological excitations in this nodal-net structure including triple point, nexus, and nodal link, which are protected by coexistence of spatial-inversion symmetry and time reversal symmetry. This nodal-net state is remarkably different from that of IrF4, which requires sublattice chiral symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points are identified as having emerged on the Bterminated and Ti-terminated (001) surfaces of TiB2 respectively, which are analogous to those of monolayer and bilayer graphene. arXiv:1705.00511v2 [cond-mat.mtrl-sci]

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).…”

“…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.…”

Transition from a nodal-loop phase to a nodal-chain phase in a periodically modulated optical lattice

“…Several theoretical calculated materials have been proposed to realize nodal line semimetals, which have separated nodal-loop Fermi surfaces and host 'drumhead' surface states [18]. More recently, theoretical calculations unveil the existence of the nodal chain semimetals in the material of iridum tetrafluoride (IrF 4 ) [19], in AlB 2 -type TiB 2 and ZrB 2 [20] and also W-C-type HfC [21], with the nodal chain composed of several connected nodal rings. Experimental observation of nodal chains in a metallic-mesh photonic crystal has been reported very recently [22].…”