Low dimensional materials offer very interesting material and physical properties due to reduced dimensionality. At present, 2D materials are the focus of attention. However, 1D systems often show far more exotic features, such as Tomanaga-Luttinger liquid or Peierls distortion not presented in 3D and 2D materials. However,  the study of these 1D systems is strongly limited by our possibilities of their preparation and characterization on atomic scale. Nevertheless, recent progress of UHV on-surface chemistry [1] paved the way for the synthesis of molecular chains with atomic precision. Moreover, scanning probe microscopy represents the unique tool, which enables to characterize their structural and electronic structure with the unprecedented spatial resolution [2].

In this talk, we will briefly discuss several examples of 1D molecular system featuring interesting quantum properties such topological quantum phase and concerted proton tunneling.

In the first part, we will introduce a novel strategy to synthesize [3] a new class of intrinsically quasi-metallic 1D p-conjugated polymers featuring topologically non-trivial quantum states. Furthermore, we unveiled the fundamental relation between quantum topology, p-conjugation and metallicity of polymers [4]. Thus, we will make a connection between two distinct worlds of topological band theory (condensed matter physics) and p-conjugation polymer science (chemistry). We identified and visualized a quantum phase transition between two topologically distinct phases in a π-conjugated polymer. We will demonstrate that pseudo Jahn-Teller effect as the driving mechanism responsible for the quantum phase transition. Finally, we present theoretical simulations revealing coherent fluctuation of polymers of the critical length at finite temperature between two distinct quantum phases. Such calculations provide an “a smoking gun” evidence of possible presence of the quantum criticality phenomena in the π-conjugated polymer found near the phase transition.

In second part, we will demonstrate unusual mechanical and electronic properties of hydrogen bonded chains formed on a metallic surface driven by nuclear quantum effects within the chain [6]. We will show, that the concerted proton tunneling not only enhances the mechanical stability of the chain, but it also gives rise to new in-band gap electronics states localized at the ends of the chain.  This study demonstrates the new class of nuclear quantum effects, which concerted character strongly modifies physical and material properties of the system.

[1] S. Clair, D. de Otyeza, Chem. Rev. 119, 4717 (2019).
[2] P. Jelinek, J. Phys. Cond. Matt. 29 343002 (2017).
[3] A. Grande-Sanchez et al. Angew. Chem. Int. Ed. 131 6631 (2019).
[4] B. Cierra et al. Nature Nanotechnology 15 437 (2020).
[5] H. Gonzalez-Herrero et al, Adv. Mat. 33, 2104495 (2021).[6] A. Cahlik et al, ACS Nano 15 10357 (2021).