Stanene cyanide: a novel candidate of Quantum Spin Hall insulator at high temperature

Abstract

The search for quantum spin Hall (QSH) insulators with high stability, large and tunable gap and topological robustness, is critical for their realistic application at high temperature. Using first-principle calculations, we predict the cyanogen saturated stanene SnCN as novel topological insulators material, with a bulk gap as large as 203 meV, which can be engineered by applying biaxial strain and electric field. The band topology is identified by Z2 topological invariant together with helical edge states, and the mechanism is s-pxy band inversion at G point induced by spin-orbit coupling (SOC). Remarkably, these systems have robust topology against chemical impurities, based on the calculations on halogen and cyano group co-decorated stanene SnXxX'1-x (X,X' = F, Cl, Br, I and CN), which makes it an appropriate and flexible candidate material for spintronic devices.

Figure 1. Geometric and electronic structures.

(a) Top view of geometric structures of SnCN monolayer, with the lattice parameters of the unit cell. (b) Side view of geometric structures of SnCN monolayer, with the bond length, buckle distance and charge transfers between Sn atom and CN. Yellow and blue area denote the accumulation and depletion electrons respectively. (c) Phonon band dispersion relations. (d) Schematic diagram of the evolution from atomic s and orbitals of Sn in SnCN into conduction and valence bands at Γ point. The three stages (I–III) represent the orbital orders with atomic potential, crystal field and spin-orbit coupling taken into account sequentially. The green dashed line denotes the Fermi energy . (e) Energy band structure near Fermi level without (left) and with (right) SOC interaction. Parities of Bloch states are denoted by +, −. The red/green dots denote s/ dominated orbitals. The size of dot denotes the weight of projection.

Figure 2

(a) Total (left panel) and spin (right panel) edge density of states for SnCN. In the spin edge plot, yellow/green lines denote the spin up/down polarization. The red dot line shows the Fermi level. (b) Real-space band decomposed charge density distribution from the edge states. The red/blue arrow denote the electrons with up/down spin.

Figure 3

(a) Topological phase diagram of SnCN as a function of strains. The metal-NI (Normal insulator) and NI-TI (Topological insulater) transition occur at −18% and −2% of the strainless lattice constant, respectively. Red/blue half dots denote fundamental/inverted gap. Brown dots show the relative energy of structures under different strains. (b) Orbital-resolved band structure under different strains. Red/blue dots denote s/ dominated orbitals. The size of dot denotes the weight of projection. (c) The energy gap as a function of extra vertical electric field. (d) Spin texture of the highest valence band of SnCN under electric field of 0.5 V/Å. Arrows refer to the in-plane orientation of spin, and the color background denotes z component of spin. (e) Spin-resolved band structure of SnCN under electric field of 0.5 V/Å. Red/blue lines denote bands with spin up/down polarization.

Figure 4

(a) Band structures of SnX_0.5X′_0.5. (b) Evolutions of Wannier centers for SnX_0.5X′_0.5 along . The evolution lines (blue dot lines) cross the arbitrary reference line (red dash line) parallel to an odd number of times, yielding v = 1. (c) Crystal structure for SnX_0.5X′_0.5 unit cell from the side view. X and X′ represent different halogeno (F, Cl, Br and I) and cyano groups. (d) The calculated enegy gap for stanene decorated by different groups.