Probing Boundary Spins in the Su-Schrieffer-Heeger-Hubbard model

Abstract

Studying boundary excitations provides a powerful approach to probe correlations in topological phases. We propose that localized spins near the ends of a Su-Schrieffer-Heeger-Hubbard chain embedded in an insulating environment can be detected experimentally using scanning tunneling microscopy (STM) combined with electron spin resonance (ESR). When the STM tip is in the contact regime, the tip-end-spin coupling realizes an effective Anderson impurity problem, giving rise to a Kondo peak at low bias. Spatially resolving the Kondo resonance width as the STM tip approaches the chain ends provides an indirect yet clear signature of these localized spins. To support this proposal, we use density-matrix renormalization group (DMRG) to calculate the spin gap and spin projection of end states for chains of various lengths and interaction strengths $U$ at half-filling. In the non-interacting limit ($U=0$), we derive simple analytical expressions that reproduce the numerical results for sufficiently long chains. We also discuss how the correlated phase of the isolated chain is characterized by boundary zeros in its single-particle Green's function, and briefly comment on their localization properties in relation to the boundary spins.

Figures (7)

• Figure 1: (Color online) Scheme of an interacting spin chain on top of an insulating surface. In the contact regime, the conduction electrons in the STM tip can directly hybridize with the underlying localized spin states, effectively screening them.
• Figure 2: (Color online) Spin gap as a function of system size for $t_1=0.9$ and several values of $U$. The dashed line for $U=0$ corresponds to Eq. (\ref{['sg']}). Dataset available in Ref. dataset.
• Figure 3: (Color online) Expectation value of the spin projection for each site for a SSHC of 20 sites (panel a) and 70 sites (panel b), $S_z=1$, $t_1=0.9$ and several values of $U$. Due to inversion symmetry with respect with the middle of the chain, only the left half is shown. The complete datasets are available in Ref. dataset.
• Figure 4: (Color online) Comparison between $V_j^2$ calculated using Eq. (\ref{['vj2b']}) and $2\left|\langle S^z_j\rangle \right|$ obtained from Fig. \ref{['sz2070']}, for various values of $U/t_2$ ($t_1/t_2=0.9$ is the same for all panels). Panels (a)-(d) correspond to a chain of 20 sites, while panel (e) (note the log scale in the vertical axis) correspond to a 70-site chain and $U/t_2=8$.
• Figure 5: (Color online) LDOS at the impurity site $j$ normalized to the first site of the chain at $\omega=0$, $\rho_j(\omega)/\rho_0(0)$, vs $\omega$ obtained from Eq. (\ref{['ldos']}) for a chain of $L=20$ sites. The values of $V^2_j$ used correspond to those used in Fig. \ref{['fig:V2_vs_2Sz']}(c). Other parameters are $U=4 t_2$ and $\Gamma_0=20 t_2$ (chosen for illustrative purposes).