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.

We study correlated two-level quantum dots, coupled in effective 1-channel fashion to metallic leads; with electron interactions including on-level and inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics and electronic transport properties are considered; and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterised by a normal Fermi liquid fixed point (FP), the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of non-integral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first order level-crossing transitions at high symmetry points. A 'Friedel-Luttinger sum rule' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T = 0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase; the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.

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.

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.

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