Spin and Charge Control of Topological End States in Chiral Graphene Nanoribbons on a 2D Ferromagnet

TL;DR

This work addresses the challenge of preserving and controlling spinful symmetry-protected topological end states (SPTES) in chiral graphene nanoribbons when supported on metals. By synthesizing $(3,2,8)$-chGNRs on the 2D ferromagnet GdAu$_2$, the authors achieve charge neutrality and observe two end-$S=\tfrac{1}{2}$ moments, evidenced by dual Kondo resonances; moiré-induced work-function gradients and a strong exchange field $B_\mathrm{eff}$ enable reversible switching among neutral singlet, neutral triplet, and singly anionic doublet states. An effective Hubbard dimer model incorporating $t$, $U_\mathrm{eff}$, $\mu_i$, and $B_\mathrm{eff}$ unifies electrostatic gating, electron correlations, hybridization, and exchange, yielding a phase diagram with critical lines $\Delta\mu_\mathrm{L}^\mathrm{c}$ and $B_\mathrm{eff}^\mathrm{c}$ that depend on ribbon length $L$. The results establish GdAu$_2$ as a platform for local spin-state control of π-radicls on metals, with implications for spectroscopic spintronics and the design of state-selective functionalities in graphene-based nanostructures; the approach suggests that other rare-earth surface alloys could stabilize additional charge states such as $+1$ and $-2$.

Abstract

Tailor-made graphene nanostructures can exhibit symmetry-protected topological boundary states that host localized spin-$1/2$ moments. However, one frequently observes charge transfer on coinage metal substrates, which results in spinless closed-shell configurations. Using low temperature scanning tunneling spectroscopy, we demonstrate here that pristine topologically nontrivial chiral graphene nanoribbons synthesized directly on the ferromagnet $\textrm{GdAu}_2$ can either maintain a charge-neutral diradical singlet or triplet configuration, or exist in a singly anionic doublet state. As an underlying mechanism, we identify a moiré-modulated work function and exchange field, as corroborated by Kelvin-probe force microscopy and spin-flip spectroscopy. The joint electrostatic and magnetic interactions allow reversibly switching between the three spin multiplicities by atomic manipulation. We introduce an effective Hubbard dimer model that unifies the effects of local electrostatic gating, electron-electron-correlation, hybridization and exchange field to outline the phase diagram of accessible spin states. Our results establish a platform for the local control of $π$-radicals adsorbed on metallic substrates.

Figures (4)

• Figure 1: Probing $\left(3,2,8\right)$-chGNRs on $\textrm{GdAu}_2$. (a) The chemical structure, and a scheme of the competing interactions between topological end states and the ferromagnetic surface. (b)*STM scan of *chGNR (0.4, 1, 15x15). (c, d) Differential conductance spectra of two 7-*chGNR on different adsorption sites. Insets shows tip positions where spectra were recorded. Outset shows high resolution spectra of the split Kondo feature in a narrow energy range. The former is found in a fully neutral charge state, with two screened radical moments. The latter exists in a singly anionic doublet configuration. Spectra without Kondo resonances have been scaled and offset for better comparison.
• Figure 2: Controlling the spin multiplicity of a 7chGNR on $\textrm{GdAu}_2$. By lateral manipulation of the same molecule into four different positions, we observe the excess charge leaving terminus T2 (b) and re-entering T1 (d). The intermediate neutral case is realized in (c) with large a large exchange field. In the last position (e), $B_\mathrm{eff}$ is smaller than the Kondo coupling on either termini and the zero-bias resonance is restored. Fits of the inelastic tunneling theory (b-d) and Frota lineshapes (e) are shown in gray. Traces have been offset and scaled for clarity.
• Figure 3: Visualizing the localized charging effect. (a)*KPFM of bare $\textrm{GdAu}_2$ reveals a decreased local work function in the triangular moiré minima by tens of (junction resistance 140MΩ, oscillation amplitude 50±, 5x5). (b) The shown *chGNR exhibits a doubly occupied orbital on terminus T1, laying within a moiré minimum (0.5, 1, 9x4.5). (c) The left *SPTES shows a localized increase in *LCPD, consistent with a single excess electron residing in T1 (865, 50±, 9x4.5).
• Figure 4: Predicting the *chGNR spin multiplicity from the Hubbard dimer model. (a) Sites L and R, representing SPTES under an exchange field $B_\mathrm{eff}$, experience Coulomb repulsions $U_\mathrm{eff}$ and are coupled by a hopping amplitude $t$, both obtained from tight-binding theory of $\left(3,2,8\right)$-chGNRs. Each site is additionally gated by $\mu_\mathrm{L}$ and $\mu_\mathrm{R}$, respectively. The many-body eigenstates $\ket{N,m_s}$ evolve with the local potential $\Delta\mu_\mathrm{L}=\mu_\mathrm{L}-U_\textrm{eff}$ and $B_\mathrm{eff}$. (b) Ground-state transition from two-particle states towards the charged doublet $\ket{3,\pm1/2}$ with $\Delta\mu_\mathrm{L}$. (c) Spin level scheme of the singlet-triplet transition at a critical value of $B_\mathrm{eff}$. Only one component of $\ket{2,0}$ is shown. (d) The chGNR phase diagram at $\mu_\mathrm{R}=U_\textrm{eff}/2$, here for $L=3$, exhibits two critical points in $\Delta\mu_\mathrm{L}$ and $B_\textrm{eff}$. Color denotes the total spin projection $\langle S_z \rangle$ in units of $\hbar$. (e)$\Delta\mu_\mathrm{L}^\mathrm{c}$ and $B_\mathrm{eff}^\mathrm{c}$ as a function of length. The intramolecular exchange $J=\abs{g\mu_\mathrm{B}B_\textrm{eff}^\mathrm{c}}\approx 4t^2/U_\textrm{eff}$ falls rapidly, while the critical gating potential approaches $U_\textrm{eff}/2$.