Unexpected Giant-Gap Quantum Spin Hall Insulator in Chemically Decorated Plumbene Monolayer

Abstract

Quantum spin Hall (QSH) effect of two-dimensional (2D) materials features edge states that are topologically protected from backscattering by time-reversal symmetry. However, the major obstacles to the application for QSH effect are the lack of suitable QSH insulators with a large bulk gap. Here, we predict a novel class of 2D QSH insulators in X-decorated plumbene monolayers (PbX; X = H, F, Cl, Br, I) with extraordinarily giant bulk gaps from 1.03 eV to a record value of 1.34 eV. The topological characteristic of PbX mainly originates from s-p(x,y) band inversion related to the lattice symmetry, while the effect of spin-orbital coupling (SOC) is only to open up a giant gap. Their QSH states are identified by nontrivial topological invariant Z2 = 1, as well as a single pair of topologically protected helical edge states locating inside the bulk gap. Noticeably, the QSH gaps of PbX are tunable and robust via external strain. We also propose high-dielectric-constant BN as an ideal substrate for the experimental realization of PbX, maintaining its nontrivial topology. These novel QSH insulators with giant gaps are a promising platform to enrich topological phenomena and expand potential applications at high temperature.

Figure 1

(a,b) Top and side views of the schematic structures of PbH monolayer. Black and green balls denote Pb and H atoms, respectively. Shadow area in (a) present the unit cell. (c) Phonon band dispersions, and (d) the area of Brilioun zone of PbH monolayer.

Figure 2. Band structures for PbH without SOC

(a) and with SOC (b) with zooming in the energy dispersion near the Fermi level. The red circles and blue squares represent the weights of the Pb-s and Pb-p_x,y character, respectively. (c) Parities of occupied spin-degenerate bands at the TRIM Points for PbH. Here, we show the parities of 5 occupied spin-degenerate bands for PbH. Positive and negative signs denote even and odd parities, respectively.

Figure 3. Electronic structures and its corresponding edge state of PbH.

(a) Comparison of band structures for PbH calculated by DFT (red lines) and Wannier function method (blue circles). (c) Illustration of the partial DOS projected onto p_z orbital of Pb and the total DOS of H atom. The Fermi level is set to zero. (b,d) show the Dirac edge states, and edge spin polarization, respectively. The Fermi level is set to zero. (e,f) the model and spectrum of a finite slab of PbH. The red and blue horizontal arrows represent the spin-up and -down polarized currents in opposite direction.

Figure 4

(a) The evolution of atomic s and p_x,y orbitals of PbH into band edges at Γ point is described as the crystal field splitting and SOC are switched in sequence. (b) Illustration of the effect of SOC on the inversion of bands around the Fermi level. (c) The calculated global band gap by PBE and HSE methods, and (d) the ratio of Pb-p_x,y component in the total orbital at Γ point near the Fermi level.

Figure 5. The calculated global band gap (E_g) of PbX with SOC as a function of external strain.

Figure 6

(a) Side and top views of the schematic illustration of the epitaxial growth PbH of large-gap QSH states on 2 × 2 BN substrate and (b) on substrate. Orbital-resolved band structures with SOC based on DFT calculations. (c,d) notes the energy band of PbH on 2 × 2 and BN substrate with SOC. The Fermi level is set to zero.