Delft University of Technology Single-molecule quantum-transport phenomena in break junctions

Single-molecule junctions — devices in which a single molecule is electrically connected by two electrodes — enable the study of a broad range of quantum-transport phenomena even at room temperature. These quantum features are related to molecular orbital and spin degrees of freedom and are characterized by various energy scales that can be chemically and physically tuned: level spacings, charging energies, tunnel couplings, exchange energies, vibrational energies and Kondo correlation energies. The competition between these different energy scales leads to a rich variety of processes, which researchers are now starting to be able to control and tune experimentally. In this Technical Review, we present the status of the molecular electronics field from this quantumtransport perspective with a focus on recent experimental results obtained using break-junction devices, including scanning probe and mechanically controlled break junctions as well as electromigrated gold and graphene break junctions. [H1] Introduction Today’s electronic components comprise nanoscale building blocks with varying functionalities that act as conducting interconnects, switches or sensing elements. For almost two decades, researchers in the field of molecular electronics have aimed to condense electronic functionalities into single molecules by chemical design 1 , 2 . However, before molecular electronic components can be Nature Reviews Physics 1 (2019) 381 – 396 DOI: 10.1038/s42254-019-0055-1 fabricated, the single-molecule building blocks need to be characterized in junctions to understand their electronic behaviour. To this end, tremendous advances have been reported and reviewed; for example, single-molecule transistors, switches and diodes have been demonstrated. Nevertheless, it is still difficult to experimentally identify the physical mechanisms behind these functionalities or how single molecules arrange in an electronic junction; therefore, predictions based on existing models for molecular device functionality are often unreliable. The realization of functional molecular devices thus requires deeper understanding of the quantumtransport features and experimental elucidation of the intrinsic structure–property relationships of different molecules. In this Technical Review, we assess the recent developments in single-molecule electronics and highlight the fascinating quantum-transport properties using recent results from break-junction experiments as examples. A brief summary of the computational efforts in understanding quantum-transport phenomena using ab initio approaches is provided in the Supplementary Information. A single-molecule junction consists of a molecule connected to two electrodes — one at either end; sometimes there is a third terminal (known as the gate electrode) that can shift the electrostatic potential of the molecule independently from the potential of the electrodes. Junction fabrication involves breaking a conducting wire, and this can be achieved using one of several techniques (Fig. 1a–c). In a break junction, the conductance along the backbone of the molecule is probed. Thus, we do not consider molecules lying on a surface, for which the current flows in the perpendicular direction; these are typically studied by means of low-temperature scanning tunnelling microscopy. The nature of the anchoring determines the electronic molecule–electrode tunnel coupling, i, where i is L or R for the left and right electrode, respectively. The total tunnel coupling is given by  = L + R. Although the electrons in the electrodes have a continuous spectrum of energy states, on the isolated molecule, they occupy a discrete set of levels that, in the junction, are broadened to a width of order . This set of levels gives rise to a rich variety of transport phenomena, the accessibility of which depends on the energy scales of , kBT (where kB is Boltzmann’s constant and T is the temperature) and the energy cost to add an extra charge to the molecule. This latter contribution is known as the addition energy, Eadd = 2EC + , where the charging energy EC = e/2C; here, C is the total junction capacitance,  is the quantum level spacing (that is, the orbital contribution) and e is the elementary charge. If  is smaller than both kBT and Eadd, Coulomb blockade and incoherent transport through two-step single-electron tunnelling prevails — this is the weak coupling regime. In the opposite, strong coupling regime, coherent transport is typically observed, usually involving off-resonant transport, although for very small molecules, such as H2, resonant transport applies, resulting in conductance values close to the conductance quantum. A unique aspect of molecular junctions is the interplay between the different energy scales that determine the transport characteristics. These energy scales are the electronic coupling (~0.1– 1 meV), the temperature (which varies from 2 eV to 25 meV) and the addition energy (often >100 meV). The vibrational and spin degrees of freedom are of special interest, as these features are specific to molecular transport and are not easily accessible in transport experiments with other systems, such as inorganic quantum dots. For vibrational modes (Box 1), the relevant parameters are the mode energy (ħ = 1–300 meV, where ħ is the reduced Planck’s constant and  is the angular frequency) and the electron–phonon coupling strength. The latter parameter determines the extent to which electron flow is affected by the presence of phonons. As single molecules are floppy systems, this coupling can be much stronger than in, for example, crystals and leads to novel transport phenomena such as the Franck–Condon blockade of transport (Box 1). Chemical design offers various ways to incorporate spin degrees of freedom into a molecule. The coupling between spin and transport forms an interesting field of research called molecular spintronics. Upon the introduction of spin degrees of freedom, additional energy scales must be considered, such as the exchange energy between interacting spins, J. Spin-dependent correlations between the electrons on the molecules and the conduction electrons in the electrodes can give rise to a so-called Kondo peak in the transmission at zero bias; this peak is quantified by a Kondo temperature, TK, above which the anomaly disappears. In practice, experimental exchange energies and the Kondo temperature vary between a few tenths of a meV to several meV. If the molecule exhibits magnetic anisotropy (that is, if the spin has a preferred orientation along an easy axis and therefore acts as a miniature magnet), the axial anisotropy parameter, D, may become relevant. This parameter can be viewed as a measure for the extent to which the preferred orientation is maintained, and the transverse anisotropy parameter, E, is responsible for quantum tunnelling of the spin orientation between its up and down state. D is the largest energy scale of the two with values <<1 meV, and E is typically in the eV range. The electrodes can also be made of a superconducting material, in which case the superconducting gap,  becomes relevant. Although there are different energy scales associated with the different break-junction platforms (Fig. 1a–c) and transport mechanisms (Fig. 1d), it is important to note that there are no sharp boundaries between the different regimes. The different single-molecule junctions have distinctive properties, which are summarized in Table 1. We begin by describing the break-junction platforms used to perform single-molecule conductance measurements before discussing different aspects of quantum-transport phenomena, including the single-level model, orbital engineering beyond the single-level model, quantum interference effects, quantum thermopower and heat transport as well as single-molecule spintronics. We conclude by discussing future research directions. [H1] Single-molecule break junctions There are two main break-junction techniques: mechanical and electrical break junctions. Mechanical break junctions (Fig. 1a,b) are realized by means of scanning tunnelling microscopy (STM) to form a STM break junction (STM-BJ) or with nanolithography techniques to form mechanically controlled break junctions (MCBJs). In the STM-BJ approach, a metallic tip is usually gently pushed onto a metallic substrate on which the molecules are deposited. Upon retracting the tip from the substrate, atomically sharp contacts can form, and the conductance (G) of a molecule trapped between the substrate and tip is measured as a function of distance (d), resulting in a conductancebreaking trace. The junction lifetime is limited by the drift in the position of the tip. The STM-BJ technique is not to be confused with scanning a substrate, typically at low temperature with a defined sample-to-tip distance, to image molecules lying on the surface and perform spectroscopy on them. Breaking traces are also measured in a MCBJ experiment, although the contact geometry is different: in this case, bending of the device breaks a conducting wire, which yields an atomically sharp contact pair. Just like in STM-BJs, current–voltage (I–V) characteristics and conductance-breaking traces can be measured; however, the MCBJ approach enables a more systematic study thereof as junction lifetimes are much longer owing to superior mechanical stability (Table 1). Especially at low temperatures, the MCBJ set-up is often used to record I–V characteristics and to perform inelastictunnelling spectroscopy of vibrational modes. Both mechanical break-junction methods can be used to measure the conductance as a function of time at a fixed distance (sometimes called a blinking experiment). In such an experiment, a sudden increase in the conductance signals the trapping of a molecule between the two electrodes, but additional information about the junction configuration is difficult to obtain. Thus, one has to be cautious in interpreti