Boost the topological gap in the px-py orbital materials


The 2D topological (quantum spin Hall) insulators are particularly important for their potential of being integrated for future device applications. However, the gap values of the current experimental systems (e.g. HgTe/CdTe and InAs/GaInSb) are too small at the order of a few Kelvins as constrained by the s-p band inversion mechanism. The reason is that the energy scale of their topological gap is essentially due to the small s-p hybridization rather than directly from spin-orbit coupling.

Boost the topological gap of 2D materials to the scale of atomic spin-orbit coupling

We proposed a new mechanism based on the px and py-orbital active honeycomb lattice materials [Ref. 1] , which greatly enlarges the topological gap. Different from graphene which is of pz-orbital only and hence orbital-inactive, our systems are with degenerate px and py-orbitals, and hence orbital-active. As a result, their topological gap values equal the full scale of the atomic spin-orbit coupling, and can reach the order of 1eV. Basically, the Bloch wave states at the Dirac points K and K^\prime correspond to non-bonding states, i.e., the two sublattices actually decouple at the Dirac points. In this case, the solid state gap opening is reduced to the atomic energy-level splitting problem. Hence, the atomic spin-orbit coupling can completely contribute to open the topological gaps.

The above mechanism was based on our previous study of the quantum anomalous Hall state with the orbital-active honeycomb optical lattices with ultra-cold fermions [Ref. 2] and [Ref. 3] , which also applies to solid state materials as well. In optical lattices, the $p_z$ orbital can be pushed to high energy by imposing a strong optical confinement along the $z$-direction, which leaves the $p_x$ and $p_y$-orbital bands active. The $p_x$ and $p_y$-band structure exhibits both flat bands and dispersive bands possessing Dirac cones. Due to the orbital structure, they are sensitive to topological gap opening by applying the ``shaking lattice method'' to realize an orbital Zeeman term, which generates the quantum anomalous Hall state.

Experimental realization in Bismuthene

Recently, with our collaborators, we have further elaborated this mechansim for Bismuthene The Kramers doubled version of the above mechanism leads to large gap quantum spin Hall insulators, in which the atomic spin-orbit coupling is the time-reversal invariant generalization of the orbital Zeeman term. It can be directly applied to a large class of 2D materials including the monolayer Bi-film, or, bismuthene. The recent experiments on bismuthene on the SiC substrate have shown the evidence of the gap up to 0.8eV by Claessen's group at University of Wuerzsburg, (Science 357, 287 (2017)) Recently, with our collaborators, we have further elaborated this mechanism for bismuthene [Ref. 4] .

For the heavy element of Bi, the hybridization between the 6s and 6p orbitals is not important any more in contrast to graphene in which there exists strong sp2 hybridization. Furthermore, the 6pz orbital forms the \sigma-bond with the substrate of SiC, and is passivated. Hence, the active orbital degrees of freedom become 6px and 6py subject to the strong onsite spin-orbit coupling Lz.\sigma_z, which precisely realizes our mechanism. Furthermore, there also exists an additional Rashba spin-orbit coupling due to the breaking of the inversion symmetry from the underlying substrate. The Rashba spin-orbit coupling breaks the double degeneracy at the top of the valence band at K and K^\prime point, but still maintains the double degeneracy at the conducting band.



References and talks

  • 1. Gu-Feng Zhang, Yi Li, Congjun Wu, "The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps",
    Phys. Rev. B 90, 075114 (2014) . See pdf file

  • 2. Congjun Wu, "Orbital analogue of quantum anomalous Hall effect in $p$-band systems",
    Phys. Rev. Lett. 101, 186807 (2008)     , see pdf file .

  • 3. Machi Zhang, Hsiang-hsuan Hung, Chuanwei Zhang, Congjun Wu, , "Quantum anomalous Hall states in the $p$-orbital honeycomb optical lattices ",
    Phys. Rev. A 83, 023615 (2011)     . See pdf file .

  • 4. Gang Li, Werner Hanke, Ewelina M. Hankiewicz, Felix Reis, Joerg Schaefer, Ralph Claessen, Congjun Wu , Ronny Thomale, "A new paradigm for the quantum spin Hall effect at high temperatures",
    arXiv:1807.09552     , to appear in Phys. Rev. B.

  • Talk: "Orbital active honeycomb mateirals " .


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    Last modified: Oct 16, 2018.