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Imposing additional confinement in two-dimensional (2D) materials can yield further control over the associated electronic, optical, and topological properties. However, synthesis of ultra-narrow nanoribbons (NRs) remains a challenge, particularly for the transition metal dichalcogenides (TMDs), and synthesizing TMD NRs narrower than 50 nm has remained elusive. Here, we report the vapor-phase synthesis of ultra-narrow TaS2 NRs. The NRs are grown within the hollow cavity of carbon nanotubes, thereby limiting their lateral dimensions and layer number, while simultaneously stabilizing them against the environment. The NRs reach the monolayer (ML) limit and exhibit widths as low as 2.5 nm. Atomic-resolution scanning transmission electron microscopy (STEM) reveals the detailed atomic structure of the ultra-narrow NRs and we observe a hitherto unseen atomic structure supermodulation phenomenon of ordered defect arrays within the NRs. First-principles calculations based on density functional theory (DFT) show the presence of flat bands, as well as edge- and boundary-localized states, and help identify the atomic configuration of the supermodulation. Nanotube-templated synthesis represents a unique, transferable, and broadly deployable route toward ultra-narrow TMD NR growth.
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Extreme nanowires (ENs) represent the ultimate class of crystals: They are the smallest possible periodic materials. With atom-wide motifs repeated in one dimension (1D), they offer a privileged perspective into the Physics and Chemistry of low-dimensional systems. Single-walled carbon nanotubes (SWCNTs) provide ideal environments for the creation of such materials. Here we present a comprehensive study of Te ENs encapsulated inside ultra- narrow SWCNTs with diameters between 0.7 nm and 1.1 nm. We combine state-of-the-art imaging techniques and 1D-adapted ab initio structure prediction to treat both confinement and periodicity effects. The studied Te ENs adopt a variety of structures, exhibiting a true 1D realisation of a Peierls structural distortion and transition from metallic to insulating behaviour as a function of encapsulating diameter. We analyse the mechanical stability of the encapsulated ENs and show that nanoconfinement is not only a useful means to produce ENs, but may actually be necessary, in some cases, to prevent them from disintegrating. The ability to control functional properties of these ENs with confinement has numerous applications in future device technologies, and we anticipate that our study will set the basic paradigm to be adopted in the characterisation and understanding of such systems.
We investigate the low-lying excitation spectrum and ground-state properties of narrow graphene nanoribbons with zigzag edge configurations. Nanoribbons of comparable widths have been synthesized very recently [P. Ruffieux, emph{et al.} Nature textbf{531}, 489 (2016)], and their descriptions require more sophisticated methods since in this regime conventional methods, like mean-field or density-functional theory with local density approximation, fail to capture the enhanced quantum fluctuations. Using the unbiased density-matrix renormalization group algorithm we calculate the charge gaps with high accuracy for different widths and interaction strengths and compare them with mean-field results. It turns out that the gaps are much smaller in the former case due to the proper treatment of quantum fluctuations. Applying the elements of quantum information theory we also reveal the entanglement structure inside a ribbon and examine the spectrum of subsystem density matrices to understand the origin of entanglement. We examine the possibility of magnetic ordering and the effect of magnetic field. Our findings are relevant for understanding the gap values in different recent experiments and the deviations between them.
It is now possible to produce graphene nanoribbons (GNRs) with atomically defined widths. GNRs offer many opportunities for electronic devices and composites, if it is possible to establish the link between edge structure and functionalisation, and resultant GNR properties. Switching hydrogen edge termination to larger more complex functional groups such as hydroxyls or thiols induces strain at the ribbon edge. However we show that this strain is then relieved via the formation of static out-of-plane ripples. The resultant ribbons have a significantly reduced Youngs Modulus which varies as a function of ribbon width, modified band gaps, as well as heterogeneous chemical reactivity along the edge. Rather than being the exception, such static edge ripples are likely on the majority of functionalized graphene ribbon edges.
Matrix elements of electron-light interactions for armchair and zigzag graphene nanoribbons are constructed analytically using a tight-binding model. The changes in wavenumber ($Delta n$) and pseudospin are the necessary elements if we are to understand the optical selection rule. It is shown that an incident light with a specific polarization and energy, induces an indirect transition ($Delta n=pm1$), which results in a characteristic peak in absorption spectra. Such a peak provides evidence that the electron standing wave is formed by multiple reflections at both edges of a ribbon. It is also suggested that the absorption of low-energy light is sensitive to the position of the Fermi energy, direction of light polarization, and irregularities in the edge. The effect of depolarization on the absorption peak is briefly discussed.
Graphene nanoribbons are widely regarded as promising building blocks for next-generation carbon-based devices. A critical issue to their prospective applications is whether and to what degree their electronic structure can be externally controlled. Here, we combine simple model Hamiltonians with extensive first-principles calculations to investigate the response of armchair graphene nanoribbons to transverse electric fields. Such fields can be achieved either upon laterally gating the nanoribbon or incorporating ambipolar chemical co-dopants along the edges. We reveal that the field induces a semiconductor-to-semimetal transition, with the semimetallic phase featuring zero-energy Dirac fermions that propagate along the armchair edges. The transition occurs at critical fields that scale inversely with the width of the nanoribbons. These findings are universal to group-IV honeycomb lattices, including silicene and germanene nanoribbons, irrespective of the type of edge termination. Overall, our results create new opportunities to electrically engineer Dirac fermions in otherwise semiconducting graphene-like nanoribbons.
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