Current-induced molecular dissociation: Topological insulators as robust reaction platforms

TL;DR

The study addresses how current-driven dissociation of a diatomic molecule depends on the substrate being a trivial graphene or a Kane–Mele topological insulator. It uses a tight-binding two-terminal model and non-equilibrium Green's function (NEGF) methods to compute the stationary density matrix and the non-equilibrium force on the molecular bond, highlighting the role of frontier orbital occupancies (bonding vs antibonding) within the bias window. A key finding is that edge-state localization in the topological substrate preserves molecular occupancies and yields a larger non-equilibrium force $F^{ne}$ compared to extended bulk graphene, with robustness to ribbon width and vacancy disorder. The results suggest topological edge states as robust, efficient platforms for current-driven catalysis, with implications for designing topocatalytic devices on 2D and 3D TI surfaces.

Abstract

The growing interest in topological materials with symmetry-protected surface states as catalytic platforms has sparked the emerging field of topocatalysis. As robust transport is one of the key features of topological insulators, here we explore current-induced molecular dissociation in a transport setup. Using the non-equilibrium Green's function formalism, we compare how the occupancies of bonding and antibonding levels, as well as the associated electronic forces in a diatomic molecule, are affected when the molecule is coupled to either a metallic (graphene) or a topological (Kane-Mele) substrate. We find a greater dissociative capability in the topological substrate than in graphene, a difference mainly attributed to the localized nature of the edge states. The inclusion of vacancy disorder within the substrate further enhances this disparity in the dissociative force. Our findings highlight the role of topological protection in molecular dissociation under non-equilibrium conditions, pointing to new opportunities for robust catalysis in topological materials.

Figures (9)

• Figure 1: (a) Scheme of the catalysis model, based on the interaction between the adsorbate (red circles) and the adsorbent, composed of an armchair graphene nanoribbon with passivated vacancies. The contacts extend on both sides of the sample and are represented by yellow regions. The shaded region around the adsorbate indicates the extent of the coupling with the adsorbent. Inset: Zoom of the molecule-substrate interaction region; with $\gamma_0$ the carbon-carbon hopping, $\gamma_\mathrm{d}$ the intramolecular coupling, and $\gamma(\ell)$ the hopping term between the atoms of the molecule and the carbon atoms of the substrate. (b) Honeycomb lattice with armchair edge termination. The shaded region denotes the unit cell, containing $2N$ carbon atoms.
• Figure 2: Molecular destabilization under non-equilibrium conditions. (a) Density of states (DOS), using the logarithmic scale $\log(1+\mathcal{N}_q)$, projected on the substrate region around the molecule ($q=\mathrm{s}$, blue) and on the molecule itself ($q=\mathrm{d}$, red) for graphene (G, left panels) and Kane-Mele (KM, right panels) substrates. (b) Occupation probabilities of the bonding (solid lines) and antibonding (dotted lines) levels as functions of the bias voltage for graphene (G, blue lines) and Kane-Mele model (KM, red lines) substrates. (c) Corresponding non-equilibrium intramolecular force, according to Eq. \ref{['eq:fce-d']}. We use a relaxation energy $\eta = 10^{-5} \gamma_0$, an equilibrium chemical potential $\mu_0 = 0$, and $k_\mathrm{B} T = 10^{-3} \, \gamma_0$.
• Figure 3: (a) Molecular occupancy and (b) non-equilibrium intramolecular force as functions of bias voltage for varying ribbon widths, under the condition $N=3\ell+2$. Red curves represent the Kane-Mele substrate, while blue curves indicate graphene. Note, in particular, that all red curves are superimposed. The used parameters coincide with those of Fig. \ref{['fig:rho_fza']}.
• Figure 4: (a)-(d) Averaged matrix element of the occupation kernel $[\bm{\mathcal{K}}^\rho_\mathrm{L}]_{m,m}$, indicating bonding (a,b), and antibonding (c,d) level's occupation from the left contact, for disordered graphene (a,c) and Kane-Mele (b,d) models. (e) Normalized energy integrals of the previous matrix elements. Here, blue and red lines indicate graphene and Kane-Mele cases, respectively. We use open and filled points to distinguish between bonding and antibonding occupancies. (f) Normalized non-equilibrium intramolecular force, calculated from Eq. \ref{['eq:fce-d']}, for the shown data of panel e. The parameters used coincide with those of Fig. \ref{['fig:rho_fza']}, with a central region of 31 unit cells (along the transport direction) each having a width of $W=\sqrt{3}(N-1)a/2$, where $N=3 \times 25+2$.
• Figure 5: Bonding (red) and antibonding (blue) occupancies under (a) equilibrium and (b) non-equilibrium conditions. The used parameters are: $E_\mathrm{d} = 0$, $\Gamma = k_\mathrm{B} T = 10^{-3} \, \gamma_0$, $\gamma_\mathrm{d} = 0.3 \, \gamma_0$, and $\eta = 0$, with $\gamma_0$ a reference energy. The schemes denote the contacts chemical potentials and the molecule's energy levels.