Molecular electronic devices currently serve as a platform for studying a variety of physical phenomena only accessible at the nanometer scale. One such phenomenon is the highly correlated electronic state responsible for the Kondo effect, manifested here as a "Kondo resonance" in the conductance. Because the Kondo effect results from strong electron-electron interactions, it is not captured by the usual quantum chemistry approaches traditionally applied to understand chemical electron transfer. In this review we will discuss the origins and phenomenology of Kondo resonances observed in single molecule devices, focusing primarily on the spin- Kondo state arising from a single unpaired electron. We explore the rich physical system of a single-molecule device, which offers a unique spectroscopic tool for investigating the interplay of emergent Kondo behavior and such properties as molecular orbital transitions and vibrational modes. We will additionally address more exotic systems, such as higher spin states in the Kondo regime, and we will review recent experimental advances in the ability to manipulate and exert control over these nanoscale devices.

Scaling laws and universality are often associated with systems exhibiting emergent phenomena possessing a characteristic energy scale. We report nonequilibrium transport measurements on two different types of single-molecule transistor (SMT) devices in the Kondo regime. The conductance at low bias and temperature adheres to a scaling function characterized by two parameters. This result, analogous to that reported recently in semiconductor dots with Kondo temperatures two orders of magnitude lower, demonstrates the universality of this scaling form. We compare the extracted values of the scaling coefficients to previous experimental and theoretical results.

Abstract. Electromigrated nanoscale junctions have proven very useful for studying electronic transport at the single-molecule scale. However, confirming that conduction is through precisely the molecule of interest and not some contaminant or metal nanoparticle has remained a persistent challenge, typically requiring a statistical analysis of many devices. We review how transport mechanisms in both purely electronic and optical measurements can be used to infer information about the nanoscale junction configuration. The electronic response to optical excitation is particularly revealing. We briefly discuss surfaceenhanced Raman spectroscopy on such junctions, and present new results showing that currents due to optical rectification can provide a means of estimating the local electric field at the junction due to illumination.

Resistively detected nuclear magnetic resonance (NMR) is observed inside the ringlike structure, with a quantized Hall conductance of 6e(2)/h, in the phase diagram of a two-subband electron system. The NMR signal persists up to 470 mK and is absent in other states with the same quantized Hall conductance. The nuclear spin-lattice relaxation time T1, is found to decrease rapidly towards the ring center. A strong dynamic nuclear polarization by the biasing current has also been observed only inside the ring. These observations are consistent with the assertion of the ringlike region being a ferromagnetic state that is accompanied by collective spin excitations.

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