In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields Hc1 and Hc2. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in onedimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understanding of a broad class of quantum magnets in their gapless phase (between Hc1 and Hc2). In this phase, the low temperature divergence of the NMR relaxation demonstrates its Luttinger liquid nature as well as the novel quantum critical regime at higher temperature. The general behavior close these quantum critical points can be tied to known models of quantum magnetism.PACS. 75.10.Jm Quantized spin models -75.40.-s Critical-points effects, specific heats, short range order -76.60.-k Nuclear magnetic resonance and relaxation

On-surface covalent self-assembly of organic molecules is a very promising bottom–up approach for producing atomically controlled nanostructures. Due to their highly tuneable properties, these structures may be used as building blocks in electronic carbon-based molecular devices. Following this idea, here we report on the electronic structure of an ordered array of poly(para-phenylene) nanowires produced by surface-catalysed dehalogenative reaction. By scanning tunnelling spectroscopy we follow the quantization of unoccupied molecular states as a function of oligomer length, with Fermi level crossing observed for long chains. Angle-resolved photoelectron spectroscopy reveals a quasi-1D valence band as well as a direct gap of 1.15 eV, as the conduction band is partially filled through adsorption on the surface. Tight-binding modelling and ab initio density functional theory calculations lead to a full description of the band structure, including the gap size and charge transfer mechanisms, highlighting a strong substrate–molecule interaction that drives the system into a metallic behaviour.

We report the synthesis and first electronic characterization of an atomically thin two dimensional p-conjugated polymer. Polymerization via Ullmann coupling of a tetrabrominated tetrathienoanthracene on Ag(111) in ultra-high vacuum (UHV) produces a porous 2D polymer network that has been characterized by scanning tunnelling microscopy (STM). High-resolution X-ray photoelectron spectroscopy (HRXPS) shows that the reaction proceeds via two distinct steps: dehalogenation of the brominated precursor, which begins at room temperature (RT), and CC coupling of the resulting Agbound intermediates, which requires annealing at 300 C. The formation of the 2D conjugated network is accompanied by a shift of the occupied molecular states by 0.6 eV towards the Fermi level, as observed by UV photoelectron spectroscopy (UPS). A theoretical analysis of the electronic gap reduction in the transition from monomeric building blocks to various 1D and 2D oligomers and polymers yields important insight into the effect of topology on the electronic structure of 2D conjugated polymers.