Existence of topological nontrivial surface states in strained transition metals: W, Ta, Mo, and Nb

Abstract

In a joint theoretical and experimental investigation we show that a series of transition metals with strained body-centered cubic lattice-W, Ta, Nb, and Mo-host surface states that are topologically protected by mirror symmetry. Our finding extends the class of topologically nontrivial systems by topological crystalline transition metals. The investigation is based on independent calculations of the electronic structures and of topological invariants, the results of which agree with established properties of the Dirac-type surface state in W(110). To further support our prediction, we investigate both experimentally by spin-resolved inverse photoemission and theoretically an unoccupied topologically nontrivial surface state in Ta(110).

Tilted Dirac cone on W(110) protected by mirror symmetry

“…The monolayers modify the spin-dependent surface states of the W(110) by hybridization with noble-metal s and p states [34,35]. Recent calculations of W, where artificial strain opens semimetal band gaps that allow to compute Chern numbers, find nontrivial bulk band structures in some case [36]. In that work, similar features are reported for Mo, Nb, and Ta as well.…”

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

“…Along this line, spin pumping experiments at Bi surfaces have been interpreted as evidence for either an interface-enhanced SHE (Hou et al, 2012) or the iSGE (Rojas-Sánchez et al, 2013). Angle-resolved photoemission studies, on the other hand, provide evidence that the iSGE is not a pure 2D effect in metallic thin films: the presence of magnetic exchange (Krupin et al, 2005), out-of-plane spin polarization (Takayama et al, 2011), spin-momentum locked quantum well states in the FM (Moras et al, 2015), and topologically protected surface states (Thonig et al, 2016) significantly alters the Rashba effect at metallic interfaces compared to model semiconducting heterostructures. Further, extrinsic effects such as impurity and interface scattering can induce additional spin currents that propagate through or away from the NM/FM interface and be polarized in directions different from the standard model, calling for a generalization of the mixing conductance concept (Amin and Stiles, 2016a,b;Chen and Zhang, 2015).…”

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

“…Spin pumping experiments at Bi surfaces have been interpreted as evidence for either an interface-enhanced SHE (Hou et al, 2012) or the iSGE (Rojas-Sánchez et al, 2013). Angle-resolved photoemission studies, on the other hand, provide evidence that the iSGE is not a pure 2D effect in metallic thin films: the presence of magnetic exchange (Krupin et al, 2005), outof-plane spin polarization (Takayama et al, 2011), spinmomentum locked quantum well states in the ferromagnet (Moras et al, 2015), and topologically protected surface states (Marmolejo-Tejada et al, 2017;Thonig et al, 2016) significantly alters the Rashba effect at metallic interfaces compared to model semiconducting heterostructures.…”