The ability to make electrical contact to single molecules creates opportunities to examine fundamental processes governing electron flow on the smallest possible length scales. We report experiments in which we controllably stretched individual cobalt complexes having spin S = 1, while simultaneously measuring current flow through the molecule. The molecule's spin states and magnetic anisotropy were manipulated in the absence of a magnetic field by modification of the molecular symmetry. This control enabled quantitative studies of the underscreened Kondo effect, in which conduction electrons only partially compensate the molecular spin. Our findings demonstrate a mechanism of spin control in single-molecule devices and establish that they can serve as model systems for making precision tests of correlated-electron theories.

We study electron transport through C(60) molecules in the Kondo regime using a mechanically controllable break junction. By varying the electrode spacing, we are able to change both the width and the height of the Kondo resonance, indicating modification of the Kondo temperature and the relative strength of coupling to the two electrodes. The linear conductance as a function of T/T(K) agrees with the scaling function expected for the spin-1/2 Kondo problem. We are also able to tune finite-bias Kondo features which appear at the energy of the first C(60) intracage vibrational mode.

We demonstrate a device geometry for single-molecule electronics experiments that combines both the ability to adjust the spacing between the electrodes mechanically and the ability to shift the energy levels in the molecule using a gate electrode. With the independent in-situ variations of molecular properties provided by these two experimental "knobs", we are able to achieve a much more detailed characterization of electron transport through the molecule than is possible with either technique separately. We illustrate the devices' performance using C 60 molecules.

The electronic thermal conductivity of graphene and 2D Dirac materials is of fundamental interest and can play an important role in the performance of nano-scale devices. We report the electronic thermal conductivity, K e , in suspended graphene in the nearly intrinsic regime over a temperature range of 20 to 300 K. We present a method to extract K e using two-point DC electron transport at low bias voltages, where the electron and lattice temperatures are decoupled. We find K e ranging from 0.5 to 11 W/m.K over the studied temperature range. The data are consistent with a model in which heat is carried by quasiparticles with the same mean free-path and velocity as graphene's charge carriers.

We study the Josephson-like interlayer tunneling signature of the strongly correlated T 1 quantum Hall phase in bilayer two-dimensional electron systems as a function of the layer separation, temperature, and interlayer charge imbalance. Our results offer strong evidence that a finite temperature phase transition separates the interlayer coherent phase from incoherent phases which lack strong interlayer correlations. The transition temperature is dependent on both the layer spacing and charge imbalance between the layers. DOI: 10.1103/PhysRevLett.100.096801 PACS numbers: 73.43.Jn, 71.10.Pm, 71.35.Lk Bilayer two-dimensional electron systems (2DES) at high magnetic fields can exhibit drastically different quantum collective phases depending on whether their interlayer spacing is large or small. When the spacing is large, the two layers act independently and display the familiar fractional quantum Hall and related effects. Conversely, at small interlayer separation, bilayer collective phases with no single layer analog appear [1].An especially interesting example of this occurs when the total density n T of electrons in the bilayer equals the degeneracy eB=h of a single spin-resolved Landau level created by the magnetic field B. In this situation, the total Landau level filling factor is T n T =eB=h 1. If the spacing between the two layers is small, the 2DES is a gapped quantum Hall effect (QHE) liquid [1] with several very unusual properties, including Josephson-like interlayer tunneling [2] and vanishing Hall and longitudinal resistances [3][4][5] when currents are driven in opposition (counterflow) in the two layers. For layer spacings larger than a critical value, the system properties revert to those characteristic of independent layers. Interlayer tunneling is heavily suppressed, no anomalous counterflow transport properties are observed, and, for equal density layers (i.e., with individual filling factors top bot 1=2), there is no quantized Hall effect.There now exists a large theoretical literature dealing with the strongly correlated bilayer T 1 QHE phase at small layer separation. It is widely believed that the system is well described as an easy-plane ferromagnet with the layer index (''top'' or ''bottom'') of the electrons regarded as a pseudospin quantum number (''up'' or ''down''). Exchange interactions favor a configuration in which all electrons occupy a single coherent linear combination of up and down pseudospin states. Interlayer charging effects favor equal amplitudes of the two states and thus the net pseudospin moment lies near the x-y plane. In the limit of zero tunneling, the transition to this coherent state is believed to be spontaneous. At the qualitative level, this picture accounts well for many of the most dramatic experimental observations, including the existence of the QHE [1] in weakly tunneling samples, the strong manybody enhancement of the tunneling at zero bias [2], the presence of a linearly dispersing collective mode [6], and the peculiar counterflow transport properties ...