A Luttinger liquid is an interacting one-dimensional electronic system, quite distinct from the 'conventional' Fermi liquids formed by interacting electrons in two and three dimensions. Some of the most striking properties of Luttinger liquids are revealed in the process of electron tunnelling. For example, as a function of the applied bias voltage or temperature, the tunnelling current exhibits a non-trivial power-law suppression. (There is no such suppression in a conventional Fermi liquid.) Here, using a carbon nanotube connected to resistive leads, we create a system that emulates tunnelling in a Luttinger liquid, by controlling the interaction of the tunnelling electron with its environment. We further replace a single tunnelling barrier with a double-barrier, resonant-level structure and investigate resonant tunnelling between Luttinger liquids. At low temperatures, we observe perfect transparency of the resonant level embedded in the interacting environment, and the width of the resonance tends to zero. We argue that this behaviour results from many-body physics of interacting electrons, and signals the presence of a quantum phase transition. Given that many parameters, including the interaction strength, can be precisely controlled in our samples, this is an attractive model system for studying quantum critical phenomena in general, with wide-reaching implications for understanding quantum phase transitions in more complex systems, such as cold atoms and strongly correlated bulk materials.

For immobilized nitroxide spin-labels with a well-defined interprobe geometry, resolved dipolar splittings can be observed in continuous wave electron paramagnetic resonance (CW-EPR) spectra for interelectron distances as large as 30 A using perdeuterated probes. In this work, algorithms are developed for calculating CW-EPR spectra of immobilized, dipolar coupled nitroxides, and then used to define the limits of sensitivity to the interelectron distance as a function of geometry and microwave frequency. Secondly, the CW-EPR spectra of N epsilon-spin-labeled coenzyme NAD+ bound to microcrystalline, tetrameric glyceraldehyde-3-phosphate dehydrogenase (GAPDH) have been collected at 9.8, 34, and 94 GHz. These data have been analyzed, using a combination of simulated annealing and global analysis, to obtain a unique fit to the data. The values of the intermitroxide distance and the five angles defining the relative orientation of the two nitroxides are in reasonable agreement with a molecular model built from the known crystal structure. Finally, the effect of rigid body isotropic rotational diffusion on the CW-EPR spectra of dipolar coupled nitroxides has been investigated using an algorithm based on Brownian dynamics trajectories. These calculations demonstrate the sensitivity of CW-EPR spectra to dipolar coupling in the presence of rigid body rotational diffusion.

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A quantum phase transition is an abrupt change between two distinct ground states of a many-body system, driven by an external parameter. In the vicinity of the quantum critical point (QCP) where the transition occurs, a new phase may emerge that is determined by quantum fluctuations and is very different from either phase. In particular, a conducting system may exhibit non-Fermi-liquid behaviour. Although this scenario is well established theoretically, controllable experimental realizations are rare. Here, we experimentally investigate the nature of the QCP in a simple nanoscale system-a spin-polarized resonant level coupled to dissipative contacts. We fine-tune the system to the QCP, realized exactly on-resonance and when the coupling between the level and the two contacts is symmetric. Several anomalous transport scaling laws are demonstrated, including a striking non-Fermi-liquid scattering rate at the QCP, indicating fractionalization of the resonant level into two Majorana quasiparticles.Q uantum phase transitions (QPTs) are attracting strong interest in diverse fields of physics, ranging from quantum magnets and strongly correlated materials 1 to, more recently, cold atoms 2 , nanostructures 3,4 and particle physics 5 . The foremost remarkable property of QPTs is the possibility to create exotic quantum states of matter at the QCP, such as deviations from the standard Fermi-liquid paradigm for metals. These zero-temperature states then cause anomalous physical properties at finite temperatures 1 . Another intriguing aspect of QPTs is their behaviour under non-equilibrium conditions, such as either a sudden quench driving the system non-adiabatically through the transition 6 , or a strong perturbation provided by a large current density as typically realized in nanoelectronic devices 7 . Despite the ubiquity of QPTs in contemporary theoretical physics, obtaining clear experimental signatures has been challenging.Here, we present a thorough characterization of all facets of a QPT in a fully tunable single-molecule transistor built from a spinpolarized carbon nanotube quantum dot connected to strongly dissipative contacts 8,9 . As the electronic level of the quantum dot crosses the Fermi energy of the leads, in the standard case of good metallic contacts transport occurs through a resonance of finite width and height. In contrast, the presence of dissipation drives the conductance to zero (in the limit of vanishing temperature), unless one tunes the position of the resonant level to the Fermi energy and simultaneously makes the tunnel barriers between the dot and the two leads perfectly equal. In the latter case, the conductance saturates at the unitary limit, e 2 /h (e is the elementary charge and h is the Planck constant), and the resonance width tends to zero, as we recently demonstrated 9 . A quantum critical state is obtained, whose anomalous properties are the subject of the present study.By optimizing the dissipative environment, we find that the quantum critical properties surprisingly behave very cl...

Sonication of gallium or gallium-based liquid metals in an aqueous solution of vinyl monomers leads to rapid free radical polymerization (FRP), without the need for conventional molecular initiators. Under ambient conditions, a passivating native oxide separates these metals from solution and renders the metal effectively inert. However, sonication generates liquid metal nanoparticles (LMNPs) of ∼100 nm diameter and thereby increases the surface area of the metal. The exposed metal initiates polymerization, which proceeds via a FRP mechanism and yields high molecular weight polymers that can form physical gels. Spin trapping EPR reveals the generation of free radicals. Time-of-flight secondary ion mass spectrometry measurements confirm direct polymer bonding to gallium, verifying the formation of surface-anchored polymer grafts. The grafted polymers can modify the interfacial properties, that is, the preference of the metal particles to disperse in aqueous versus organic phases. The polymer can also be degrafted and isolated from the particles using strong acid or base. The concept of physically disrupting passivated metal surfaces offers new routes for surface-initiated polymerization and has implications for surface modification, reduction reactions, and fabrication of mechanically responsive materials.