Fully Quantized Electron Transfer Observed in a Single Redox Molecule at a Metal Interface.

Long-range electron transfer is a ubiquitous process that plays an important role in electrochemistry, biochemistry, organic electronics, and single molecule electronics. Fundamentally, quantum mechanical processes, at their core, manifest through both electron tunneling and the associated transition between quantized nuclear vibronic states (intramolecular vibrational relaxation) mediated by electron-nuclear coupling. Here, we report on measurements of long-range electron transfer at the interface between a single ferrocene molecule and a gold substrate separated by a hexadecanethiol quantum tunneling barrier. These redox measurements exhibit quantized nuclear transitions mediated by electron-nuclear coupling at 4.7 K in vacuum. By detecting the electric force associated with redox events by atomic force microscopy (AFM), with increasing AFM oscillation amplitude, the intensity of the observed  cantilever resonance frequency shift peak increases and then exhibits a series of discrete steps that are indicative of quantized nuclear transitions. The observed peak shapes agree well with a single-electron tunneling model with quantized nuclear state transitions associated with the conversion of the molecule between oxidized and reduced electronic states. This technique opens the door to simultaneously investigating quantized electron and nuclear dynamics in a diverse range of systems.

Relating Franck-Condon blockade to redox chemistry in the single-particle picture.

In this work, we explore Franck-Condon blockade in the "redox limit," where nuclear relaxation processes occur much faster than the rate of electron transfer. To this end, the quantized rate expressions for electron transfer are recast in terms of a quantized redox density of states (DOS) within a single phonon mode model. In the high temperature regime, this single-particle picture formulation of electron transfer is shown to agree well with the semi-classical rate and DOS expressions developed by Gerischer and Hopfield. Upon incorporation into a two electrode formulation, utilizing the master equation approach, the low temperature quantized conductance features of Franck-Condon blockade are reproduced. Moreover, at sufficiently large reorganization energies, it is argued that Franck-Condon blockade should also be observable in room temperature systems. In general, this work aims to further bridge descriptions of electron transfer and transport in the single-particle picture.

Quantum state readout of individual quantum dots by electrostatic force detection.

Electric charge detection by atomic force microscopy (AFM) with single-electron resolution (e-EFM) is a promising way to investigate the electronic level structure of individual quantum dots (QDs). The oscillating AFM tip modulates the energy of the QDs, causing single electrons to tunnel between QDs and an electrode. The resulting oscillating electrostatic force changes the resonant frequency and damping of the AFM cantilever, enabling electrometry with a single-electron sensitivity. Quantitative electronic level spectroscopy is possible by sweeping the bias voltage. Charge stability diagram can be obtained by scanning the AFM tip around the QD. e-EFM technique enables to investigate individual colloidal nanoparticles and self-assembled QDs without nanoscale electrodes. e-EFM is a quantum electromechanical system where the back-action of a tunneling electron is detected by AFM; it can also be considered as a mechanical analog of admittance spectroscopy with a radio frequency resonator, which is emerging as a promising tool for quantum state readout for quantum computing. In combination with the topography imaging capability of the AFM, e-EFM is a powerful tool for investigating new nanoscale material systems which can be used as quantum bits.

Revealing energy level structure of individual quantum dots by tunneling rate measured by single-electron sensitive electrostatic force spectroscopy.

We present theoretical and experimental studies of the effect of the density of states of a quantum dot (QD) on the rate of single-electron tunneling that can be directly measured by electrostatic force microscopy (e-EFM) experiments. In e-EFM, the motion of a biased atomic force microscope cantilever tip modulates the charge state of a QD in the Coulomb blockade regime. The charge dynamics of the dot, which is detected through its back-action on the capacitavely coupled cantilever, depends on the tunneling rate of the QD to a back-electrode. The density of states of the QD can therefore be measured through its effect on the energy dependence of tunneling rate. We present experimental data on individual 5 nm colloidal gold nanoparticles that exhibit a near continuous density of state at 77 K. In contrast, our analysis of already published data on self-assembled InAs QDs at 4 K clearly reveals discrete degenerate energy levels.