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Topological Crystalline Transition Metals: Strained W, Ta, Mo, and Nb

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 Added by Danny Thonig
 Publication date 2016
  fields Physics
and research's language is English




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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).



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The family of two-dimensional transition metal carbides, so called MXenes, has recently found new members with ordered double transition metals M$_2$M$$C$_2$, where M$$ and M$$ stand for transition metals. Here, using a set of first-principles calculations, we demonstrate that some of the newly added members, oxide M$_2$M$$C$_2$ (M$$= Mo, W; M$$= Ti, Zr, Hf) MXenes, are topological insulators. The nontrivial topological states of the predicted MXenes are revealed by the $Z_2$ index, which is evaluated from the parities of the occupied bands below the Fermi energy at time reversal invariant momenta, and also by the presence of the edge states. The predicted M$_2$M$$C$_2$O$_2$ MXenes show nontrivial gaps in the range of 0.041 -- 0.285 eV within the generalized gradient approximation and 0.119 -- 0.409 eV within the hybrid functional. The band gaps are induced by the spin-orbit coupling within the degenerate states with $d_{x^2-y^2}$ and $d_{xy}$ characters of M$$ and M$$, while the band inversion occurs at the $Gamma$ point among the degenerate $d_{x^2-y^2}$/$d_{xy}$ orbitals and a non-degenerate $d_{3z^2-r^2}$ orbital, which is driven by the hybridization of the neighboring orbitals. The phonon dispersion calculations find that the predicted topological insulators are structurally stable. The predicted W-based MXenes with large band gaps might be suitable candidates for many topological applications at room temperature. In addition, we study the electronic structures of thicker ordered double transition metals M$_2$M$_2$C$_3$O$_2$ (M$$= Mo, W; M$$= Ti, Zr, Hf) and find that they are nontrivial topological semimetals.
Two-dimensional topological insulators and two-dimensional materials with ferroelastic characteristics are intriguing materials and many examples have been reported both experimentally and theoretically. Here, we present the combination of both features - a two-dimensional ferroelastic topological insulator that simultaneously possesses ferroelastic and quantum spin Hall characteristics. Using first-principles calculations, we demonstrate Janus single-layer MSSe (M=Mo, W) stable two-dimensional crystals that show the long-sought ferroelastic topological insulator properties. The material features low switching barriers and strong ferroelastic signals, beneficial for applications in nonvolatile memory devices. Moreover, their topological phases harbor sizeable nontrivial band gaps, which supports the quantum spin Hall effect. The unique coexistence of excellent ferroelastic and quantum spin Hall phases in single-layer MSSe provides extraordinary platforms for realizing multi-purpose and controllable devices.
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Charge density functional plus $U$ calculations are carried out to examine the validity of molecular $J_text{eff}$=1/2 and 3/2 state in lacunar spinel GaM$_4$X$_8$ (M = Nb, Mo, Ta, and W). With LDA (spin-unpolarized local density approximation)$+U$, which has recently been suggested as the more desirable choice than LSDA (local spin density approximation)$+U$, we examine the band structure in comparison with the previous prediction based on the spin-polarized version of functional and with the prototypical $J_text{eff}$=1/2 material Sr$_2$IrO$_4$. It is found that the previously suggested $J_text{eff}$=1/2 and 3/2 band characters remain valid still in LDA$+U$ calculations while the use of charge-only density causes some minor differences. Our result provides the further support for the novel molecular $J_text{eff}$ state in this series of materials, which can hopefully motivate the future exploration toward its verification and the further search for new functionalities.
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