Interference and interaction of charge carriers in graphene

Electron transport at low temperatures in two-dimensional electron systems is governed by two quantum corrections to the conductivity: weak localisation and electron-electron interaction in the presence of disorder. We present the first experimental observation of these quantum corrections in graphene, a single layer of carbon atoms, over a temperature range 0.02 - 200 K. Due to the peculiar properties of graphene, weak localisation is sensitive not only to inelastic, phase-breaking scattering events, but also to elastic scattering mechanisms. The latter includes scattering within and between the two valleys (intra- and inter-valley scattering, respectively). These specifics make it possible, for example, to observe a transition from weak localisation to antilocalisation. Our work reveals a number of surprising features. First of all the transition occurs not only as the carrier density is varied, but also as the temperature is tuned. The latter has never been observed in any other system studied before. Second, due to weak electron-phonon interaction in graphene, quantum interference of electrons survives at very high temperatures, up to 200 K. For comparison, in other two-dimensional (2D) systems the weak localisation effect is only seen below 50 K. The electron-electron interaction correction is also affected by elastic scattering. In a two-valley system, there are two temperature regimes of the interaction correction that depend on the strength of inter-valley scattering. In both regimes the correction has its own expression. We show that because of the intra-valley scattering, a third regime is possible in graphene, where the expression for the correction takes a new form. The study of weak localisation demonstrates that the third regime is realised in our experiments. We use the new expression to determine the Fermiliquid parameter, which turns out to be smaller than in other 2D systems due to the chirality of charge carriers. At very low temperatures (below 100 mK) we observe a saturation of the electron dephasing length. We study different mechanisms that could be responsible for the saturation and discuss in detail one of them – spin-orbit interaction. We determine the spin coherence length from studies of weak localisation and the temperature dependence of the conductivity and found good agreement between the two types of experiments. We also show the way to tune the spin coherence length by an order of magnitude by controlling the level of disorder. However, experiment shows contradictions with theory both in values of the spin coherence length and the type of spin relaxation. We speculate about another spin-related mechanism, spin flip by vacancies, which to some extent could also explain our observations. We also present electron transport in graphene irradiated by gallium ions. Depending on the dosage of irradiation the behavior of electrons changes. Namely, electron localisation can be tuned from weak to strong. At low dosages we observe the weak localisation regime, where the mentioned quantum corrections to the conductivity dominate at low temperatures. We found the electron scattering between the valleys to be enhanced, attributing it to atomically sharp defects (kicked out carbon atoms) produced by ion irradiation. We also speculate that gallium ions can be embedded in the substrate or trapped between silica and graphene. We draw this conclusion after investigation of the spin-orbit interaction in irradiated samples. At high dosages electrons become strongly localised and their transport occurs via variable-range hopping

Increasing the extraction efficiency of quantum light from 2D materials

Direct bandgap 2D semiconductor materials such as monolayers of transition metal dichalcogenides (TMDCs), show great promise in optoelectronic devices enabling exciting new technologies such as ultra-thin quantum light LED’s [1]. These structures can have incredible advantages, enabling almost seamless integration into conventional silicon structures. However, extracting light out of these structures can be a challenge, often requiring costly and time consuming processing e.g. engineered waveguides or cavities [2]. Furthermore none of these methods allow you to observe the light directly, therefore are unhelpful in certain applications, such as an optical version of a quantum unique device [3]. We have previously demonstrated that epoxy based solid immersion lenses can be used to increase light out of semiconductor nanostructures. We furthered this idea to see if they could be used to increase the light out of monolayer TMDC materials; and investigate how the epoxy-2D material interface affects the emission. Our studies revealed that a SIL can greatly enhance the photoluminescence of WSe2 by up to 6x (more than theory predicts for a SIL of this shape), without effecting the wavelength (figure 1). However we also found that the epoxy appears to reduce the emission of the MoS2, suggesting that there could be doping effects due to the epoxy. Overall this method shows great promise as a cheap, and scalable method for enhancing the efficiency of low intensity WSe2 based devices

Increasing quantum light extraction from TMDC's

Much of the recent explosion of research into 2D semiconductor materials has focused on direct bandgap materials such as monolayers of transition metal dichalcogenides (TMDCs), which show great promise in optoelectronic devices such as ultra-thin LEDs [1, 2]. Extraction of light out of these structures can be enhanced in the near field through the integration of these monolayers into waveguides, cavities, or photonic crystals [3]; however these methods are not ideal as they require costly and time consuming processing. Furthermore none of these methods allow you to observe the light directly, therefore are unhelpful in certain applications, such as quantum unique devices [4]. The research we present demonstrates a solution to this problem by encapsulating a range of two-dimensional materials in Solid Immersion Lenses (SILs), dynamically-shaped from UV cure epoxy. We show that the advantages of using SILs formed in this way are numerous, with the most prominent being they can be deterministically placed and directly tuned, to ensure the extraction efficiency is maximised. We will also present detailed photoluminescence maps showing how the reduction of laser spot size caused by focusing through a SIL can allow for very detailed mapping of WSe2 multilayer structures

Increasing the light extraction and longevity of TMDC monolayers using liquid formed micro-lenses

The recent discovery of semiconducting two-dimensional materials is predicted to lead to the introduction of a series of revolutionary optoelectronic components that are just a few atoms thick. Key remaining challenges for producing practical devices from these materials lie in improving the coupling of light into and out of single atomic layers, and in making these layers robust to the influence of their surrounding environment. We present a solution to tackle both of these problems simultaneously, by deterministically placing an epoxy based micro-lens directly onto the materials’ surface. We show that this approach enhances the photoluminescence of tungsten diselenide (WSe2) monolayers by up to 300%, and nearly doubles the imaging resolution of the system. Furthermore, this solution fully encapsulates the monolayer, preventing it from physical damage and degradation in air. The optical solution we have developed could become a key enabling technology for the mass production of ultra-thin optical devices, such as quantum light emitting diodes

Sub-bandgap voltage electroluminescence and magneto-oscillations in a WSe2 light-emitting van der Waals heterostructure

We report on experimental investigations of an electrically driven WSe2 based light-emitting van der Waals heterostructure. We observe a threshold voltage for electroluminescence significantly lower than the corresponding single particle band gap of monolayer WSe2. This observation can be interpreted by considering the Coulomb interaction and a tunneling process involving excitons, well beyond the picture of independent charge carriers. An applied magnetic field reveals pronounced magneto-oscillations in the electroluminescence of the free exciton emission intensity with a 1/B-periodicity. This effect is ascribed to a modulation of the tunneling probability resulting from the Landau quantization in the graphene electrodes. A sharp feature in the differential conductance indicates that the Fermi level is pinned and allows for an estimation of the acceptor binding energy.Comment: Accepted for publication in Nano Letter

Exfoliation of natural van der Waals heterostructures to a single unit cell thickness

Weak interlayer interactions in van der Waals crystals facilitate their mechanical exfoliation to monolayer and few-layer two-dimensional materials, which often exhibit striking physical phenomena absent in their bulk form. Here we utilize mechanical exfoliation to produce a two-dimensional form of a mineral franckeite and show that the phase segregation of chemical species into discrete layers at the sub-nanometre scale facilitates franckeite's layered structure and basal cleavage down to a single unit cell thickness. This behaviour is likely to be common in a wider family of complex minerals and could be exploited for a single-step synthesis of van der Waals heterostructures, as an alternative to artificial stacking of individual two-dimensional crystals. We demonstrate p-type electrical conductivity and remarkable electrochemical properties of the exfoliated crystals, showing promise for a range of applications, and use the density functional theory calculations of franckeite's electronic band structure to rationalize the experimental results

Interplay between spin proximity effect and charge-dependent exciton dynamics in MoSe2/CrBr3 van der Waals heterostructures

Semiconducting ferromagnet-nonmagnet interfaces in van der Waals heterostructures present a unique opportunity to investigate magnetic proximity interactions dependent upon a multitude of phenomena including valley and layer pseudospins, moiré periodicity, or exceptionally strong Coulomb binding. Here, we report a charge-state dependency of the magnetic proximity effects between MoSe2 and CrBr3 in photoluminescence, whereby the valley polarization of the MoSe2 trion state conforms closely to the local CrBr3 magnetization, while the neutral exciton state remains insensitive to the ferromagnet. We attribute this to spin-dependent interlayer charge transfer occurring on timescales between the exciton and trion radiative lifetimes. Going further, we uncover by both the magneto-optical Kerr effect and photoluminescence a domain-like spatial topography of contrasting valley polarization, which we infer to be labyrinthine or otherwise highly intricate, with features smaller than 400 nm corresponding to our optical resolution. Our findings offer a unique insight into the interplay between short-lived valley excitons and spin-dependent interlayer tunneling, while also highlighting MoSe2 as a promising candidate to optically interface with exotic spin textures in van der Waals structures.T. P. L. acknowledges financial support from the EPSRC Doctoral Prize Fellowship scheme under Grant Reference EP/R513313/1. T. P. L., K. S. N. and A. I. T. acknowledge financial support from the European Graphene Flagship Projects under grant agreements 785219 and 881603, and EPSRC grants EP/P026850/1 and EP/S030751/1. K. S. N. also acknowledges support from EU Quantum Technology Flagship Programs, European Research Council Synergy Grant Hetero2D, the Royal Society, EPSRC grants EP/N010345/1, EP/S030719/1. We gratefully acknowledge the Exeter Time-Resolved Magnetism Facility (EXTREMAG - EPSRC Grant Reference EP/R008809/1) for the time allocated to this study for low temperature, wide-field Kerr microscopy. The DFT calculations were performed on the Tirant III cluster of the Servei d‘Informàtica of the University of Valencia (project vlc82) and on Mare Nostrum cluster of the Barcelona Supercomputing Center (project FI-2019-2-0034). A.M.-S. acknowledges the Marie-CurieCOFUND program Nano TRAIN For Growth II (Grant Agreement 713640). J.F.-R. acknowledges financial support from FCT for the grant UTAP-EXPL/NTec/0046/2017, as well as Generalitat Valenciana funding Prometeo 2017/139 and MINECO-Spain (Grant no. MAT2016-78625-C2). Growth of hexagonal boron nitride crystals was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan, and the CREST (JPMJCR15F3), J.S.

Graphene hot-electron light bulb: incandescence from hBN-encapsulated graphene in air

The excellent electronic and mechanical properties of graphene allow it to sustain very large currents, enabling its incandescence through Joule heating in suspended devices. Although interesting scientifically and promising technologically, this process is unattainable in ambient environment, because graphene quickly oxidises at high temperatures. Here, we take the performance of graphene-based incandescent devices to the next level by encapsulating graphene with hexagonal boron nitride (hBN). Remarkably, we found that the hBN encapsulation provides an excellent protection for hot graphene filaments even at temperatures well above 2000 K. Unrivalled oxidation resistance of hBN combined with atomically clean graphene/hBN interface allows for a stable light emission from our devices in atmosphere for many hours of continuous operation. Furthermore, when confined in a simple photonic cavity, the thermal emission spectrum is modified by a cavity mode, shifting the emission to the visible range spectrum. We believe our results demonstrate that hBN/graphene heterostructures can be used to conveniently explore the technologically important high-temperature regime and to pave the way for future optoelectronic applications of graphene-based systems

Resonant band hybridization in alloyed transition metal dichalcogenide heterobilayers

Bandstructure engineering using alloying is widely utilised for achieving optimised performance in modern semiconductor devices. While alloying has been studied in monolayer transition metal dichalcogenides, its application in van der Waals heterostructures built from atomically thin layers is largely unexplored. Here, we fabricate heterobilayers made from monolayers of WSe$_2$ (or MoSe$_2$) and Mo$_x$W$_{1-x}$Se$_2$ alloy and observe nontrivial tuning of the resultant bandstructure as a function of concentration $x$. We monitor this evolution by measuring the energy of photoluminescence (PL) of the interlayer exciton (IX) composed of an electron and hole residing in different monolayers. In Mo$_x$W$_{1-x}$Se$_2$/WSe$_2$, we observe a strong IX energy shift of $\approx$100 meV for $x$ varied from 1 to 0.6. However, for $x<0.6$ this shift saturates and the IX PL energy asymptotically approaches that of the indirect bandgap in bilayer WSe$_2$. We theoretically interpret this observation as the strong variation of the conduction band K valley for $x>0.6$, with IX PL arising from the K-K transition, while for $x<0.6$, the bandstructure hybridization becomes prevalent leading to the dominating momentum-indirect K-Q transition. This bandstructure hybridization is accompanied with strong modification of IX PL dynamics and nonlinear exciton properties. Our work provides foundation for bandstructure engineering in van der Waals heterostructures highlighting the importance of hybridization effects and opening a way to devices with accurately tailored electronic properties.Comment: Supporting Information can be found downloading and extracting the gzipped tar source file listed under "Other formats

Moiré-modulated conductance of hexagonal boron nitride tunnel barriers

Monolayer hexagonal boron nitride (hBN) tunnel barriers investigated using conductive atomic force microscopy reveal moiré patterns in the spatial maps of their tunnel conductance consistent with the formation of a moiré superlattice between the hBN and an underlying highly ordered pyrolytic graphite (HOPG) substrate. This variation is attributed to a periodc modulation of the local density of states and occurs for both exfoliated hBN barriers and epitaxially grown layers. The epitaxial barriers also exhibit enhanced conductance at localized subnanometer regions which are attributed to exposure of the substrate to a nitrogen plasma source during the high temperature growth process. Our results show clearly a spatial periodicity of tunnel current due to the formation of a moiré superlattice and we argue that this can provide a mechanism for elastic scattering of charge carriers for similar interfaces embedded in graphene/hBN resonant tunnel diodes