Large-Gap Quantum Spin Hall Insulators in Tin Films

The search for large-gap quantum spin Hall (QSH) insulators and effective approaches to tune QSH states is important for both fundamental and practical interests. Based on first-principles calculations we find two-dimensional tin films are QSH insulators with sizable bulk gaps of 0.3 eV, sufficiently large for practical applications at room temperature. These QSH states can be effectively tuned by chemical functionalization and by external strain. The mechanism for the QSH effect in this system is band inversion at the $\Gamma$ point, similar to the case of a HgTe quantum well. With surface doping of magnetic elements, the quantum anomalous Hall effect could also be realized.

Figure 1

(a),(b) Crystal structure for stanene (2D Sn) and decorated stanene (2D SnX) from the top (side) view [upper (lower)]. $X$ represents the chemical functional group. In a unit cell Sn ($X$) is related to ${\mathrm{Sn}}^{\prime }$ ($X^{\prime }$) by an inversion operation. (c) The calculated energy gap for stanene (labeled by “none”) and decorated stanene (labeled by “-$X$”) at their equilibrium lattice constants. Red squares and blue circles mark topological and trivial insulators, respectively.

Figure 2

Band structure for (a) stanene, (b) fluorinated stanene, and (c) stanane without (black dash-dotted lines) and with (red solid lines) spin-orbital coupling. The inset of (a) shows a zoomed in energy dispersion near the $K$ point. The Fermi level is indicated by the dashed line. Parities of the Bloch states at the $\Gamma$ point are denoted by $+$, $-$.

Figure 3

(a) Schematic diagram of the evolution from the atomic $s$ and $p_{x,y}$ orbitals of Sn into the conduction and valence bands at the $\Gamma$ point for fluorinated stanene. The stages (I) and (II) represent the effect of turning on chemical bonding and spin-orbital coupling, respectively (see text). The green dashed line denotes the Fermi energy $E_{\mathrm{F}}$. (b) The energy levels $|s^{-}⟩$ and $|p_{x,y}^{+}⟩$ of fluorinated stanene at the $\Gamma$ point under different hydrostatic strains, with a schematic representation shown in the inset. The center of the two split $|p_{x,y}^{+}⟩$ levels is defined as the energy zero.

Figure 4

Band structure of armchair-edge nanoribbons for (a) stanene, (b) fluorinated stanene, and (c) stanane. The ribbon widths are 15.2, 8.4, and 7.8 nm, respectively. $X^{\prime }=0.2\pi /L_0$, where $L_0$ is the periodicity of the nanoribbon along its length direction. Helical edge states are visualized by red lines crossing linearly at the $\Gamma$ point for stanene and fluorinated stanene. No helical edge state exists for stanane.

Figure 5

A schematic diagram showing helical edge states at the phase boundary between the topological insulator and trivial insulator, and that are embedded in an atomically thin tin sheet with different chemical functional groups (e.g., $X1=\mathrm{\text{−}}\mathrm{F}$ and $X2=\mathrm{\text{−}}\mathrm{H}$). The helical edge states can be patterned by controlling the chemical functionalization and used as dissipationless conducting “wires” for electronic circuits.