Towards topological quasifreestanding stanene via substrate engineering

In search for a new generation of spintronics hardware, material candidates for room temperature quantum spin Hall effect (QSHE) have become a contemporary focus of investigation. Inspired by the original proposal for QSHE in graphene, several heterostructures have been synthesized, aiming at a hexagonal monolayer of heavier group IV elements promoting the QSHE bulk gap via increased spin-orbit coupling. So far, the monolayer/substrate coupling, which can manifest itself in strain, deformation, and hybridization, has proven to be detrimental to the aspired QSHE conditions for the monolayer. For stanene, the Sn analog of graphene, we investigate how an interposing buffer layer mediates between monolayer and substrate in order to optimize the QSHE setting. From a detailed density functional theory study, we highlight the principal mechanisms induced by such a buffer layer to accomplish quasifreestanding stanene in its QSHE phase. We complement our theoretical predictions by presenting attempts to grow a buffer layer on SiC(0001) on which stanene can be deposited.

Figure 1

(a) Brillouin zones of $\sqrt{3}\times \sqrt{3}R\left({30}^{\circ }\right)$ SiC (blue), $1\times 1$ stanene (black), and $2\times 2$ stanene (red), with relative high symmetry points. (b) Top and side views of the crystalline structure of buffered $\sqrt{3}\times \sqrt{3}R\left({30}^{\circ }\right)$ SiC and (c) $2\times 2$ stanene/$3\times 3$ buffered SiC. The bottom termination of the slab models is artificially passivated by H atoms. In the top view in panel (c) the colors of the substrate are intentionally less intense compared to panel (b) in order to emphasize the hexagonal lattice of $2\times 2$ stanene.

Figure 2

LEED image of Al $\sqrt{3}\times \sqrt{3}R\left({30}^{\circ }\right)$ on Si-terminated 4H-SiC(0001) recorded with an electron energy of 40 eV. Hexagons in red and blue highlight the Al induced $\sqrt{3}\times \sqrt{3}R\left({30}^{\circ }\right)$ and $1\times 1$ spots, respectively.

Figure 3

(a) Electronic band structures for group III buffered SiC (top row for Si-face and bottom row for C-face SiC) along the high-symmetry lines of the $\sqrt{3}\times \sqrt{3}R\left({30}^{\circ }\right)$ Brillouin zone [see Fig. 1]. The colored dots highlight the orbital contribution from the buffer atom. For Al we additionally show the dependence of the bonding-antibonding in-gap states on the Al-SiC distance $d_{\text{Buf}}$: green corresponds to $d_{\text{Buf}}=2.1\AA$, i.e., roughly the same equilibrium distance obtained for Tl, while red corresponds to an exaggeratedly small value $d_{\text{Buf}}=1.3\AA$. (b) Anticorrelation of the bonding-antibonding states gap with the distance between the group-III atom buffer layer and the SiC surface, shown for both substrate terminations (Si and C faces).

Figure 4

(a) Evolution of the stanene/Al/SiC electronic band structure at different stanene-Al buffer distances $(d=2.9\AA ,3.4\AA ,4.9\AA$, and $6.9\AA$ from left to right panels). Red dots highlight the unfolding weight from the $2\times 2$ Brillouin zone onto the primitive $1\times 1$, while the violet color code refers to the orbital contribution from the buffer atoms. (b) Behavior of the ${\mathbb{Z}}_2$ topological invariant close to the critical transition distance $d_{\text{cr}}$. (c) Zooms around the K point across the topological transition. Red and blue colors refer to orbital character from top and bottom Sn atoms, respectively. In the inset we report a three-dimensional view of the spin texture. The in-plane $S_x$ and $S_y$ components are negligible compared to the out-of-plane $S_z$ component.

Figure 5

(a) Buffer resolved density of the states and band structure of Al/SiC and P/SiC (C face hereafter in this caption), respectively. The dots in the band structure highlight the orbital weight of buffer atoms. In the inset, the charge distribution projected on the states forming the lone pair around 9 eV of binding energy for P/SiC is shown. (b) Binding energy curves for stanene on Al Si-terminated SiC (left panel) and on P C-terminated SiC (right panel) with and without different flavors of van der Waals corrected functionals (PBE [39], PBEsol [40], VDW1 [41], VDW2 [42], VDWopt [43]). The black dashed lines are guide to the eye to track the evolution of the equilibrium distance within the tested approximations. (c) band structure (with VDW1 van der Waals correction) of $2\times 2$ stanene on P/SiC with the red dots referring to freestanding stanene in the primitive $1\times 1$ structure. (d) Phonon spectra of freestanding stanene (leftmost panel) and stanene on P/SiC at the $3.9\AA$ PBE (central panel) and $2.9\AA$ VDW1 (rightmost panel) equilibrium distances. The color code refers to pure P/SiC (blue) and pure stanene (red) contributions to the phonon modes.