A general route to form topologically-protected surface and bulk Dirac fermions along high-symmetry lines

Abstract

The band inversions that generate the topologically non-trivial band gaps of topological insulators and the isolated Dirac touching points of three-dimensional Dirac semimetals generally arise from the crossings of electronic states derived from different orbital manifolds. Recently, the concept of single orbital-manifold band inversions occurring along high-symmetry lines has been demonstrated, stabilising multiple bulk and surface Dirac fermions. Here, we discuss the underlying ingredients necessary to achieve such phases, and discuss their existence within the family of transition metal dichalcogenides. We show how their three-dimensional band structures naturally produce only small kz projected band gaps, and demonstrate how these play a significant role in shaping the surface electronic structure of these materials. We demonstrate, through spin-and angle-resolved photoemission and density functional theory calculations, how the surface electronic structures of the group-X TMDs PtSe2 and PdTe2 are host to up to five distinct surface states, each with complex band dispersions and spin textures. Finally, we discuss how the origin of several recentlyrealised instances of topological phenomena in systems outside of the TMDs, including the iron-based superconductors, can be understood as a consequence of the same underlying mechanism driving kz-mediated band inversions in the TMDs.

Fermi-crossing Type-II Dirac fermions and topological surface states in NiTe2

“…The vicinity of TSS0 to EF in NiTe 2 makes it unique compared to other surface states and implies finite contribution of topological surface carriers to the non-trivial transport properties. All topological surface states found previously in other TMX 2 are also found in NiTe 2 [6][7][8][9][10] , but notably TSS0 is absent in PtSe 2 . To complete our studies, we map the Fermi surface of NiTe 2 using photon energy tuned to the A-point (hν = 23 eV) (Fig.…”

“…These bands cross EF and form electron pockets. This type-II Dirac fermion has been found in other TMX 2 ; however, the proximity of BDP-II to the Fermi level is unique to NiTe 2 [6][7][8][9][10]18 . In NiTe 2 , the location of BDP-II in momentum space is slightly closer to A-point than PtTe 2 (k z = ± 0.346c*) but further away from A than in PdTe 2 (k z = ± 0.40c*) 7,9,10,21 .…”

“…The p z orbital transform according to the irreducible representation (IREP) R 4 7 . The two Te sites in the unit cell imply that the p -orbitals are split into bonding (B) and antibonding (AB) levels at the Γ ( k = (0, 0, 0)) and the A ( k = (0, 0, π/c))-points of the Brillouin zone 7 , 10 . Symmetry wise, the p -bands associated with B and AB levels at Γ and A points transform as the IREPs of the double space groups ( ), 19 , 20 .…”

“…In the vicinity of these points, the electronic bands cross linearly, opening up the potential for carriers with ultrahigh-mobility, such as are found in Cd 3 As 2 5 . The class of transition metal dichalcogenides (TMDs), already well-known for hosting an array of correlated electronic phenomena, has recently been identified as a materials system which also hosts topologically-protected states [6][7][8][9][10][11] . Density functional theory (DFT) calculations for a wide range of compounds predict a set of bulk Dirac points and band inversions (associated with topological surface states, TSS), as the chalcogen orbital symmetries combined with a natural hierarchy of energy scales ensure that these states exist rather generically.…”

“…The symmetry of the states are labelled with IREPs (Γ i , A j , Δ k ) and parity (+/−). Inspired from Ref 7,10. .Figure made using Adobe Illustrator 30 .…”