Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains

Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains

21 Feb 2024 | Chenxiao Zhao, Gonçalo Catarina, Jin-Jiang Zhang, João C. G. Henriques, Lin Yang, Ji Ma, Xinliang Feng, Oliver Gröning, Pascal Ruffieux, Joaquín Fernández-Rossier, Roman Fasel
This study presents a realization of spin-1/2 alternating-exchange Heisenberg (AH) chains in nanographene-based systems, enabling the exploration of tunable topological phases. By using on-surface synthesis, the researchers covalently link Clar's goblets—nanographenes each hosting two antiferromagnetically coupled unpaired electrons—to form spin-1/2 AH chains with tunable antiferromagnetic couplings J₁ and J₂. Scanning tunneling microscopy (STM) is employed to control the chain lengths, parities, and exchange-coupling terminations, while inelastic tunneling spectroscopy is used to probe the magnetic response. The study confirms the gapped nature of bulk excitations, known as triplons, and extracts their dispersion relation from spatial variations in tunneling spectral amplitudes. Depending on the parity and termination of the chains, varying numbers of in-gap S=1/2 edge spins are observed, enabling the determination of the degeneracy of distinct topological ground states in the thermodynamic limit—either 1, 2, or 4. By monitoring interactions between these edge spins, the exponential decay of spin correlations is identified. The experimental findings, corroborated by theoretical calculations, present a phase-controlled many-body platform, opening promising avenues toward the development of spin-based quantum devices. The AH model is a paradigmatic example of a topological spin system, representing the spinful many-body analog of the Su-Schrieffer-Heeger (SSH) model. The model is described by the Hamiltonian: $$ \hat{\mathcal{H}}=\sum_{i}(J_{1}\hat{S}_{2i-1}\cdot\hat{S}_{2i}+J_{2}\hat{S}_{2i}\cdot\hat{S}_{2i+1}) $$ where J₁ and J₂ denote the alternating antiferromagnetic couplings, and S_i represents the vector of spin-1/2 operators at site i. The study shows that the AH chains with open boundary conditions (OBC) terminated by the weaker coupling J₁ have in-gap edge excitations that become gapless in the thermodynamic limit, leading to a fourfold degenerate ground state. In contrast, AH chains terminated by the stronger coupling J₂ have a non-degenerate ground state without edge spins, and AH chains with mixed terminations have a twofold degenerate ground state with a dangling spin localized at the J₁ terminus. The degeneracy of the ground state can be 1, 2, or 4, reflecting the underlying symmetry-protected topological order. The study also demonstrates the quantum confinement of dispersive triplons in finite-length AH chains. The one-triplon band shows a cosine-like dispersion, and the spatial and energy modulations of the triplon modes are reflected in spatially-resolved spin spectralThis study presents a realization of spin-1/2 alternating-exchange Heisenberg (AH) chains in nanographene-based systems, enabling the exploration of tunable topological phases. By using on-surface synthesis, the researchers covalently link Clar's goblets—nanographenes each hosting two antiferromagnetically coupled unpaired electrons—to form spin-1/2 AH chains with tunable antiferromagnetic couplings J₁ and J₂. Scanning tunneling microscopy (STM) is employed to control the chain lengths, parities, and exchange-coupling terminations, while inelastic tunneling spectroscopy is used to probe the magnetic response. The study confirms the gapped nature of bulk excitations, known as triplons, and extracts their dispersion relation from spatial variations in tunneling spectral amplitudes. Depending on the parity and termination of the chains, varying numbers of in-gap S=1/2 edge spins are observed, enabling the determination of the degeneracy of distinct topological ground states in the thermodynamic limit—either 1, 2, or 4. By monitoring interactions between these edge spins, the exponential decay of spin correlations is identified. The experimental findings, corroborated by theoretical calculations, present a phase-controlled many-body platform, opening promising avenues toward the development of spin-based quantum devices. The AH model is a paradigmatic example of a topological spin system, representing the spinful many-body analog of the Su-Schrieffer-Heeger (SSH) model. The model is described by the Hamiltonian: $$ \hat{\mathcal{H}}=\sum_{i}(J_{1}\hat{S}_{2i-1}\cdot\hat{S}_{2i}+J_{2}\hat{S}_{2i}\cdot\hat{S}_{2i+1}) $$ where J₁ and J₂ denote the alternating antiferromagnetic couplings, and S_i represents the vector of spin-1/2 operators at site i. The study shows that the AH chains with open boundary conditions (OBC) terminated by the weaker coupling J₁ have in-gap edge excitations that become gapless in the thermodynamic limit, leading to a fourfold degenerate ground state. In contrast, AH chains terminated by the stronger coupling J₂ have a non-degenerate ground state without edge spins, and AH chains with mixed terminations have a twofold degenerate ground state with a dangling spin localized at the J₁ terminus. The degeneracy of the ground state can be 1, 2, or 4, reflecting the underlying symmetry-protected topological order. The study also demonstrates the quantum confinement of dispersive triplons in finite-length AH chains. The one-triplon band shows a cosine-like dispersion, and the spatial and energy modulations of the triplon modes are reflected in spatially-resolved spin spectral
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