The drive towards the development of molecular electronics is placing increasing demands on the level of control that must be exerted on the electronic structure of materials. Proposed device architectures ultimately rely on tuning the interactions between individual electronic states, which amounts to controlling the detailed spatial structure of the electronic wavefunctions in the constituent molecules. Few experimental tools are available to probe this spatial structure directly, and the shapes of molecular wavefunctions are usually only known from theoretical investigations. Here we present scanning tunnelling spectroscopy measurements of the two-dimensional structure of individual wavefunctions in metallic single-walled carbon nanotubes; these measurements reveal spatial patterns that can be directly understood from the electronic structure of a single graphite sheet, and which represent an elegant illustration of Bloch's theorem at the level of individual wavefunctions. We also observe energy-dependent interference patterns in the wavefunctions and exploit these to directly measure the linear electronic dispersion relation of the metallic single-walled carbon nanotube.

Solid-state nanopores offer a promising method for rapidly probing the structural properties of biopolymers such as DNA and RNA. We have for the first time translocated RNA molecules through solid-state nanopores, comparing the signatures of translocating double-stranded RNA molecules and of single-stranded homopolymers poly(A), poly(U), poly(C). On the basis of their differential blockade currents, we can rapidly discriminate between both single-and double-stranded nucleic-acid molecules, as well as separate purine-based homopolymers from pyrimidinebased homopolymers. Molecule identification is facilitated through the application of high voltages (∼600 mV), which contribute to the entropic stretching of these highly flexible molecules. This striking sensitivity to relatively small differences in the underlying polymer structure greatly improves the prospects for using nanopore-based devices for DNA or RNA mapping.

Solid-state nanopores are considered a promising tool for the study of biological polymers such as DNA and RNA, due largely to their flexibility in size, potential in device integration and robustness. Here, we show that the precise shape of small nanopores (∼5 nm diameter in 20 nm SiN membranes) can be controlled by using transmission electron microscope (TEM) beams of different sizes. However, when some of these small nanopores are immersed in an aqueous solution, their resistance is observed to decrease over time. By comparing nanopores of different shapes using (scanning) TEM both before and after immersion in aqueous solution, we demonstrate that the stability of small nanopores is related to their three-dimensional geometry, which depends on the TEM beam size employed during pore fabrication. Optimal stability is obtained using a TEM beam size of approximately the same size as the intended nanopore diameter. In addition, we show that thermal oxidation can serve as a means to independently control nanopore size following TEM fabrication. These observations provide key guidelines for the fabrication of stable solid-state nanopores on the scale of nucleic acids and small proteins.

Solid-state nanopores can be employed to detect and study local structure along single molecules by voltage driven translocation through the nanopore. Their sensitivity and versatility can be augmented by combining them with a direct force probe, for example, optical tweezers. Such a tool could potentially be used to directly probe RNA secondary structure through the sequential unfolding of duplex regions. Here, we demonstrate the first application of such a system to the study of RNA by directly measuring the net force on individual double-stranded RNA (dsRNA) molecules. We have probed the force on dsRNA over a large range of nanopore sizes from 35 nm down to 3.5 nm and find that it decreases as the pore size is increased, in accordance with numerical calculations. Furthermore, we find that the force is independent of the distance between the optical trap and the nanopore surface, permitting force measurement on quite short molecules. By comparison with dsDNA molecules trapped in the same nanopores, we find that the force on dsRNA is on the order of, but slightly lower than, that on dsDNA. With these measurements, we expand the possibilities of the nanopore-optical tweezers to the study of RNA molecules with potential applications to the detection of RNA-bound proteins, the determination of RNA secondary structure, and the processing of RNA by molecular motors.

Solid-state nanopores have received increasing interest over recent years because of their potential for genomic screening and sequencing. In particular, small nanopores (2-5 nm in diameter) allow the detection of local structure along biological molecules, such as proteins bound to DNA or possibly the secondary structure of RNA molecules. In a typical experiment, individual molecules are translocated through a single nanopore, thereby causing a small deviation in the ionic conductance. A correct interpretation of these conductance changes is essential for our understanding of the process of translocation, and for further sophistication of this technique. Here, we present translocation measurements of double-stranded DNA through nanopores down to the diameter of the DNA itself (1.8-7 nm at the narrowest constriction). In contrast to previous findings on such small nanopores, we find that single molecules interacting with these pores can cause three distinct levels of conductance blockades. We attribute the smallest conductance blockades to molecules that briefly skim the nanopore entrance without translocating, the intermediate level of conductance blockade to regular head-to-tail translocations, and the largest conductance blockades to obstruction of the nanopore entrance by one or multiple (duplex) DNA strands. Our measurements are an important step toward understanding the conductance blockade of biomolecules in such small nanopores, which will be essential for future applications involving solid-state nanopores.