Inverse Isotope Effects in Single-Crystal to Single-Crystal Reactivity and the Isolation of a Rhodium Cyclooctane σ-Alkane Complex.

The sequential solid/gas single-crystal to single-crystal reaction of [Rh(Cy2P(CH2)3PCy2)(COD)][BArF 4] (COD = cyclooctadiene) with H2 or D2 was followed in situ by solid-state 31P{1H} NMR spectroscopy (SSNMR) and ex situ by solution quenching and GC-MS. This was quantified using a two-step Johnson-Mehl-Avrami-Kologoromov (JMAK) model that revealed an inverse isotope effect for the second addition of H2, that forms a σ-alkane complex [Rh(Cy2P(CH2)3PCy2)(COA)][BArF 4]. Using D2, a temporal window is determined in which a structural solution for this σ-alkane complex is possible, which reveals an η2,η2-binding mode to the Rh(I) center, as supported by periodic density functional theory (DFT) calculations. Extensive H/D exchange occurs during the addition of D2, as promoted by the solid-state microenvironment.

Quantitative mass imaging of single biological macromolecules.

The cellular processes underpinning life are orchestrated by proteins and their interactions. The associated structural and dynamic heterogeneity, despite being key to function, poses a fundamental challenge to existing analytical and structural methodologies. We used interferometric scattering microscopy to quantify the mass of single biomolecules in solution with 2% sequence mass accuracy, up to 19-kilodalton resolution, and 1-kilodalton precision. We resolved oligomeric distributions at high dynamic range, detected small-molecule binding, and mass-imaged proteins with associated lipids and sugars. These capabilities enabled us to characterize the molecular dynamics of processes as diverse as glycoprotein cross-linking, amyloidogenic protein aggregation, and actin polymerization. Interferometric scattering mass spectrometry allows spatiotemporally resolved measurement of a broad range of biomolecular interactions, one molecule at a time.

Structural principles that enable oligomeric small heat-shock protein paralogs to evolve distinct functions.

Oligomeric proteins assemble with exceptional selectivity, even in the presence of closely related proteins, to perform their cellular roles. We show that most proteins related by gene duplication of an oligomeric ancestor have evolved to avoid hetero-oligomerization and that this correlates with their acquisition of distinct functions. We report how coassembly is avoided by two oligomeric small heat-shock protein paralogs. A hierarchy of assembly, involving intermediates that are populated only fleetingly at equilibrium, ensures selective oligomerization. Conformational flexibility at noninterfacial regions in the monomers prevents coassembly, allowing interfaces to remain largely conserved. Homomeric oligomers must overcome the entropic benefit of coassembly and, accordingly, homomeric paralogs comprise fewer subunits than homomers that have no paralogs.

Mott transitions in the periodic Anderson model.

The periodic Anderson model (PAM) is studied within the framework of dynamical mean-field theory, with particular emphasis on the interaction-driven Mott transition it contains, and on resultant Mott insulators of both Mott-Hubbard and charge-transfer type. The form of the PAM phase diagram is first deduced on general grounds using two exact results, over the full range of model parameters and including metallic, Mott, Kondo and band insulator phases. The effective low-energy model which describes the PAM in the vicinity of a Mott transition is then shown to be a one-band Hubbard model, with effective hoppings that are not in general solely nearest neighbour, but decay exponentially with distance. This mapping is shown to have a range of implications for the physics of the problem, from phase boundaries to single-particle dynamics; all of which are confirmed and supplemented by NRG calculations. Finally we consider the locally degenerate, non-Fermi liquid Mott insulator, to describe which requires a two-self-energy description. This is shown to yield a number of exact results for the associated local moment, charge, and interaction-renormalised levels, together with a generalisation of Luttinger's theorem to the Mott insulator.

Mott insulators and the doping-induced Mott transition within DMFT: exact results for the one-band Hubbard model.

The paramagnetic phase of the one-band Hubbard model is studied at zero-temperature, within the framework of dynamical mean-field theory, and for general particle-hole asymmetry where a doping-induced Mott transition occurs. Our primary focus is the Mott insulator (MI) phase, and our main aim to establish what can be shown exactly about it. To handle the locally doubly-degenerate MI requires two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the standard single self-energy. Exact results are obtained for the local charge, local magnetic moment and associated spin susceptibilities, the interaction-renormalised levels, and the low-energy behaviour of the self-energy in the MI phase. The metallic phase is also considered briefly, and shown to acquire an emergent particle-hole symmetry as the Mott transition is approached. Throughout the metal, Luttinger's theorem is reflected in the vanishing of the Luttinger integral; for the generic MI by contrast this is shown to be non-vanishing, but again to have a universal magnitude. Numerical results are also obtained using NRG, for the metal/MI phase boundary, the scaling behaviour of the charge as the Mott transition is aproached from the metal, and associated universal scaling of single-particle dynamics as the low-energy Kondo scale vanishes.

Local moment formation and Kondo screening in impurity trimers.

We study theoretically a triangular cluster of three magnetic impurities, hybridizing locally with conduction electrons of a metallic host. Such a cluster is the simplest to exhibit frustration, an important generic feature of many complex molecular systems in which different interactions compete. Here, low-energy doublet states of the trimer are favored by effective exchange interactions produced by strong electronic repulsion in localized impurity orbitals. Parity symmetry protects a level crossing of such states on tuning microscopic parameters, while an avoided crossing arises in the general distorted case. Upon coupling to a metallic host, the behavior is shown to be immensely rich because collective quantum many-body effects now also compete. In particular, impurity degrees of freedom are totally screened at low temperatures in a Kondo-screened Fermi liquid phase, while degenerate ground states persist in a local moment phase. Local frustration drives the quantum phase transition between the two, which may be first order or of Kosterlitz-Thouless type, depending on symmetries. Unusual mechanisms for local moment formation and Kondo screening are found due to the orbital structure of the impurity trimer. Our results are of relevance for triple quantum dot devices. The problem is studied by a combination of analytical arguments and the numerical renormalization group.

Tunneling transport and spectroscopy in carbon nanotube quantum dots.

This paper provides a theoretical description of sequential tunneling transport and spectroscopy, in carbon nanotube quantum dots weakly tunnel coupled to metallic leads under a voltage bias. The effects of Coulomb blockade charging, spin-orbit fine structure, and orbital- and spin-Zeeman effects arising from coupling to applied magnetic fields are considered; and the dependence of the conductance upon applied gate voltage, bias voltage, and magnetic fields is determined. The work is motivated by recent experiments on ultraclean carbon nanotube dots [Kuemmeth et al., Nature (London) 452, 448 (2008)], to which comparison is made.

A local moment approach to the degenerate Anderson impurity model.

The local moment approach is extended to the orbitally degenerate (SU(2N)) Anderson impurity model (AIM). Single-particle dynamics are obtained over the full range of energy scales, focusing on particle-hole symmetry in the strongly-correlated regime where the onsite Coulomb interaction leads to many-body Kondo physics with entangled spin and orbital degrees of freedom. The approach captures many-body broadening of the Hubbard satellites and recovers the correct exponential vanishing of the Kondo scale for all N, and its universal scaling spectra are found to be in very good agreement with numerical renormalization group (NRG) results. In particular the high-frequency logarithmic decays of the scaling spectra, obtained here in closed form for arbitrary N, coincide essentially perfectly with available numerics from the NRG. A particular case of an anisotropic Coulomb interaction, in which the model represents a system of N 'capacitively coupled' SU(2) AIMs, is also discussed. Here the model is generally characterized by two low-energy scales, the crossover between which is seen directly in its dynamics.

Zero-bias conductance in carbon nanotube quantum dots.

We present numerical renormalization group calculations for the zero-bias conductance of quantum dots made from semiconducting carbon nanotubes. These explain and reproduce the thermal evolution of the conductance for different groups of orbitals, as the dot-lead tunnel coupling is varied and the system evolves from correlated Kondo behavior to more weakly correlated regimes. For integer fillings N=1, 2, 3 of an SU(4) model, we find universal scaling behavior of the conductance that is distinct from the standard SU(2) universal conductance, and concurs quantitatively with experiment. Our results also agree qualitatively with experimental differential conductance maps.

Quantum phase transition in capacitively coupled double quantum dots.

We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling, a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom, followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi-liquid "charge-ordered" phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.