David Cobden

Luttinger-liquid behaviour in carbon nanotubes

Electron transport in conductors is usually well described by Fermi-liquid theory, which assumes that the energy states of the electrons near the Fermi level EF are not qualitatively altered by Coulomb interactions. In one-dimensional systems, however, even weak Coulomb interactions cause strong perturbations. The resulting system, known as a Luttinger liquid, is predicted to be distinctly different from its two- and three-dimensional counterparts. For example, tunnelling into a Luttinger liquid at energies near the Fermi level is predicted to be strongly suppressed, unlike in two- and three-dimensional metals. Experiments on one-dimensional semiconductor wires, have been interpreted by using Luttinger-liquid theory, but an unequivocal verification of the theoretical predictions has not yet been obtained. Similarly, the edge excitations seen in fractional quantum Hall conductors are consistent with Luttinger-liquid behaviour, , but recent experiments failed to confirm the predicted relationship between the electrical properties of the bulk state and those of the edge states. Electrically conducting single-walled carbon nanotubes (SWNTs) represent quantum wires that may exhibit Luttinger-liquid behaviour, . Here we present measurements of the conductance of bundles (‘ropes’) of SWNTs as a function of temperature and voltage that agree with predictions for tunnelling into a Luttinger liquid. In particular, we find that the conductance and differential conductance scale as power laws with respect to temperature and bias voltage, respectively, and that the functional forms and the exponents are in good agreement with theoretical predictions.

Electrically tunable excitonic light-emitting diodes based on monolayer WSe2 p–n junctions

The development of light-emitting diodes with improved efficiency, spectral properties, compactness and integrability is important for lighting, display, optical interconnect, logic and sensor applications. Monolayer transition-metal dichalcogenides have recently emerged as interesting candidates for optoelectronic applications due to their unique optical properties. Electroluminescence has already been observed from monolayer MoS2 devices. However, the electroluminescence efficiency was low and the linewidth broad due both to the poor optical quality of the MoS2 and to ineffective contacts. Here, we report electroluminescence from lateral p-n junctions in monolayer WSe2 induced electrostatically using a thin boron nitride support as a dielectric layer with multiple metal gates beneath. This structure allows effective injection of electrons and holes, and, combined with the high optical quality of WSe2, yields bright electroluminescence with 1,000 times smaller injection current and 10 times smaller linewidth than in MoS2 (refs 17,18). Furthermore, by increasing the injection bias we can tune the electroluminescence between regimes of impurity-bound, charged and neutral excitons. This system has the required ingredients for new types of optoelectronic device, such as spin- and valley-polarized light-emitting diodes, on-chip lasers and two-dimensional electro-optic modulators.

Lateral heterojunctions within monolayer MoSe2–WSe2 semiconductors

Heterojunctions between three-dimensional (3D) semiconductors with different bandgaps are the basis of modern light-emitting diodes, diode lasers and high-speed transistors. Creating analogous heterojunctions between different 2D semiconductors would enable band engineering within the 2D plane and open up new realms in materials science, device physics and engineering. Here we demonstrate that seamless high-quality in-plane heterojunctions can be grown between the 2D monolayer semiconductors MoSe2 and WSe2. The junctions, grown by lateral heteroepitaxy using physical vapour transport, are visible in an optical microscope and show enhanced photoluminescence. Atomically resolved transmission electron microscopy reveals that their structure is an undistorted honeycomb lattice in which substitution of one transition metal by another occurs across the interface. The growth of such lateral junctions will allow new device functionalities, such as in-plane transistors and diodes, to be integrated within a single atomically thin layer.

Kondo physics in carbon nanotubes

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically contacted single-walled carbon nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far greater tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron numbers (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.

Disorder, Pseudospins, and Backscattering in Carbon Nanotubes

We address the effects of disorder on the conducting properties of metal and semiconducting carbon nanotubes. Experimentally, the mean free path is found to be much larger in metallic tubes than in doped semiconducting tubes. We show that this result can be understood theoretically if the disorder potential is long ranged. The effects of a pseudospin index that describes the internal sublattice structure of the states lead to a suppression of scattering in metallic tubes, but not in semiconducting tubes. This conclusion is supported by tight-binding calculations.

Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2

Electric fields can break the structural inversion symmetry in bilayer 2D materials, providing a way of tuning the magnetic moment and Berry curvature. This effect can be probed directly in bilayer MoS2 using optical measurements.

Vapor–Solid Growth of High Optical Quality MoS2 Monolayers with Near-Unity Valley Polarization

Monolayers of transition metal dichalcogenides (TMDCs) are atomically thin direct-gap semiconductors with potential applications in nanoelectronics, optoelectronics, and electrochemical sensing. Recent theoretical and experimental efforts suggest that they are ideal systems for exploiting the valley degrees of freedom of Bloch electrons. For example, Dirac valley polarization has been demonstrated in mechanically exfoliated monolayer MoS2 samples by polarization-resolved photoluminescence, although polarization has rarely been seen at room temperature. Here we report a new method for synthesizing high optical quality monolayer MoS2 single crystals up to 25 μm in size on a variety of standard insulating substrates (SiO2, sapphire, and glass) using a catalyst-free vapor-solid growth mechanism. The technique is simple and reliable, and the optical quality of the crystals is extremely high, as demonstrated by the fact that the valley polarization approaches unity at 30 K and persists at 35% even at room temperature, suggesting a virtual absence of defects. This will allow greatly improved optoelectronic TMDC monolayer devices to be fabricated and studied routinely.

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit

Since the discovery of graphene, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent additions include semiconductors with spin–valley coupling, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semimetals with edge transport. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered; such a crystal would be useful in many technologies from sensing to data storage. Theoretically, magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temperatures by the Mermin–Wagner theorem. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 kelvin is only slightly lower than that of the bulk crystal, 61 kelvin, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, whereas in trilayer CrI3 the interlayer ferromagnetism observed in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering to produce interface phenomena.

New aspects of the metal-insulator transition in single-domain vanadium dioxide nanobeams

Many strongly correlated electronic materials have a domain structure that greatly influences the bulk properties and obscures the fundamental properties of the homogeneous material. Nanoscale samples, on the other hand, can be smaller than the characteristic domain size, thus making it possible to explore these fundamental properties in detail. Here, we report new aspects of the metal-insulator transition, studied in single-domain vanadium dioxide nanobeams. We have observed supercooling of the metallic phase by 50 degrees C, an activation energy in the insulating phase that is consistent with the optical gap, and a connection between the metal-insulator transition and the equilibrium carrier density in the insulating phase. Our devices also provide a nanomechanical method for determining the transition temperature, enable measurements on individual metal-insulator interphase walls to be made, and allow general investigations of phase transitions in quasi-one-dimensional geometries.

Measurement of a solid-state triple point at the metal-insulator transition in VO2

First-order phase transitions in solids are notoriously challenging to study. The combination of change in unit cell shape, long range of elastic distortion and flow of latent heat leads to large energy barriers resulting in domain structure, hysteresis and cracking. The situation is worse near a triple point, where more than two phases are involved. The well-known metal–insulator transition in vanadium dioxide, a popular candidate for ultrafast optical and electrical switching applications, is a case in point. Even though VO2 is one of the simplest strongly correlated materials, experimental difficulties posed by the first-order nature of the metal–insulator transition as well as the involvement of at least two competing insulating phases have led to persistent controversy about its nature. Here we show that studying single-crystal VO2 nanobeams in a purpose-built nanomechanical strain apparatus allows investigation of this prototypical phase transition with unprecedented control and precision. Our results include the striking finding that the triple point of the metallic phase and two insulating phases is at the transition temperature, Ttr = Tc, which we determine to be 65.0 ± 0.1 °C. The findings have profound implications for the mechanism of the metal–insulator transition in VO2, but they also demonstrate the importance of this approach for mastering phase transitions in many other strongly correlated materials, such as manganites and iron-based superconductors.