Impact of complex adatom-induced interactions on quantum spin Hall phases

Adsorbate engineering offers a seemingly simple approach to tailor spin-orbit interactions in atomically thin materials and thus to unlock the much sought-after topological insulating phases in two dimensions. However, the observation of an Anderson topological transition induced by heavy adatoms has proved extremely challenging despite substantial experimental efforts. Here, we present a multiscale approach combining advanced first-principles methods and accurate single-electron descriptions of adatom-host interactions using graphene as a prototypical system. Our study reveals a surprisingly complex structure in the interactions mediated by random adatoms, including hitherto neglected hopping processes leading to strong valley mixing. We argue that the unexpected intervalley scattering strongly impacts the ground state at low adatom coverage, which would provide a compelling explanation for the absence of a topological gap in recent experimental reports on graphene. Our conjecture is confirmed by real-space Chern number calculations and large-scale quantum transport simulations in disordered samples. This resolves an important controversy and suggests that a detectable topological gap can be achieved by increasing the spatial range of the induced spin-orbit interactions on graphene, e.g., using nanoparticles.

Figure 1

(a) Fully relativistic DFT band structure for a thallium atom on graphene. (b) The corresponding quasiparticle band structure from a fully relativistic $GW$ calculation.

Figure 2

Complex adatom-graphene interactions in realistic scenarios. (a) NNN hoppings. (b) On-site energies. (c), (d) Hopping processes opening the intervalley channel unveiled in this work. Green and red lines represent bare and adatom-induced hoppings, respectively; arrows indicate the presence of imaginary “chiral” components, making such hoppings sensitive to directions and spin projections.

Figure 3

Topological properties of nanoribbon and bulk graphene with random nonmagnetic heavy adatoms. (a) Schematic of a two-terminal device in the QSH regime; two edge states with opposite spins contribute with $G=2e^2/h$. (b) Energy dependence of the conductance for two distinct adatom-graphene models (1% coverage). Parameters: $t=2.7$ eV, $t_1^{\prime }=-2.4$ eV, and $t_2^{\prime \prime }=-0.23$ eV. (c) Conductance curve when a single vacancy is added to the adatom-decorated nanoribbon. Same parameters as in (b). The conductance of the defected nanoribbon in the absence of adatoms is also shown (dashed line). (d) Coverage dependence of the conductance showing the degradation of the quantized plateau. The behavior of fluctuations is shown in the inset. Parameters: Same as in (b) and (c) and $t_3^{\prime }=-1.0$ eV. (e) Disorder-averaged Chern number as a function of adatom coverage for realistic spin-orbit coupling ($t_2^{\prime \prime }=0.01t$) and selected values of $t_1$ and $t_3$. (f) Coverage dependence of $\overline{\mathcal{C}}$ when all the interactions are “turned on” using DFT base values: $t_1/t=-0.12–0.01i, t_2^{\prime }/t=-0.07–i0.01$, and $t_3/t=-0.17$. Fitting to $\overline{\mathcal{C}}\left(n\right)=tanh(n/n^{*})$ yields a critical adatom coverage $n^{*}\approx 0.01$. The inset shows the dependence of $\overline{\mathcal{C}}$ with $t_1^{\prime }$ indicating a fast closing of the topological gap upon increasing NN hopping correction. Twenty-four independent adatom configurations were used in (b) and (c), and 100 in (d). For simplicity, adatom-induced hoppings are fixed to their values at the band center, $t_n(\epsilon =0)$, in all calculations.