Dissipation effects in the Su-Schrieffer-Heeger model coupled to a metallic environment

Abstract

We theoretically study the electronic and lattice properties of a trans-polyacetylene (tPA) molecule deposited on top of a metallic substrate at equilibrium. We describe the system using a modified Su-Schrieffer-Heeger (SSH) model generalized to incorporate the effects of a metallic environment, represented by independent one-dimensional semi-infinite chains coupled to each site of the SSH chain (i.e., ``local bath approximation"). We focus on the zero-temperature case and obtain the physical properties of an $N$-site tPA chain deposited on a metallic surface by minimizing its total ground-state energy (i.e., electronic plus lattice degrees of freedom) as a function of the $N$ lattice-site positions. Interestingly, in the case of a homogeneous metallic substrate, where all coupling parameters are assumed identical, the SSH chain undergoes a zero-temperature insulator-to-metal transition as the coupling parameter $γ_0$ reaches a critical value where the Peierls dimerization is fully suppressed and the system becomes metallic. In addition, our model can be generalized to describe inhomogeneous situations where the substrate contains metallic and insulating regions, as usually occurs in realistic experiments containing accidentally oxidized decoupling layers. In this case, our results predict the occurrence of local nucleation of the metalized or the Peierls-dimerized phase within the same tPA molecule, depending on whether the surface directly beneath the molecule is metallic or insulating, respectively. We finally discuss the relevance of our findings for both the correct interpretation of existing tPA/Cu(110) experiments, as well as for their possible utility in the design of novel organic nanoelectronic devices.

Figures (6)

• Figure 1: (Color online) (a) Schematic representation of a tPA molecule deposited on a hybrid surface composed of a metallic region (e.g., Cu(110)) and an insulating region (e.g., CuO). (b) Representation of the dissipative SSH model, where each site of the chain is coupled to a local reservoir (i.e., a semi-infinite vertical chain) via the coupling parameter $V_n$.
• Figure 2: (Color online) Total energy of the system at $T=0$ as a function of the dimerization parameter $u$ for different values of the broadening $\gamma_0$. Beyond a critical value of $\gamma_0$ the Peierls-dimerized state (with $u_0 \neq 0$) is destabilized and the undistorted, metallic state with $u_0=0$ is favoured.
• Figure 3: (Color online) Dimerization parameter $u_0$ vs the coupling parameter $\gamma_0$ for a tPA chain deposited ontop of a uniform metallic substrate. The value of the Peierls distortion $u_0$ is monotonically reduced as $\gamma_0$ increases, and beyond a critical value $\gamma_{0, \text{cr}}\approx 0.46 \Delta_0$, the system becomes metallic.
• Figure 4: (Color online) Profile of the smooth ($S_n$) and staggered ($\bar{R}_n$) components of the lattice distortion $y_n$ [see Eq. (\ref{['eq:yn']})] for two different values of the coupling $\gamma=0.03 \Delta_0$ and $\gamma=1.5 \Delta_0$ (blue and red symbols, respectively), applied at sites $n \in [50,150]$ (i.e., the central segment). In the weak-coupling case $\gamma=0.03 \Delta_0$, both $S_n$ and $\bar{R}_n$ remain essentially unchanged compared to the isolated SSH model. In contrast, in the strong-coupling case $\gamma=1.5 \Delta_0$, both quantities differ significantly from their isolated-case values. In particular, the Peierls dimerization characteristic of the isolated SSH model is destabilized in the coupled region, and the molecule becomes locally metallic.
• Figure 5: (Color online) Local density of states (LDOS) $\rho_{n}(\omega)$ computed at four representative positions along a chain with inhomogeneous coupling $V_n$. Panel (a) shows the LDOS at $n=20$ (insulating region), panel (b) at $n=49$ (interface on the insulating side), panel (c) at $n=50$ (interface on the metallic side), and panel (d) at $n=100$ (metallic region).