The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations. The discovery of graphene, the first truly 2D crystal and the recent experimental observation of ripples in freely hanging graphene makes these issues especially important. Beside the academic interest, understanding the mechanisms of stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest for its unusual Dirac spectrum and electronic properties. Here we address the nature of these height fluctuations by means of straightforward atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear due to thermal fluctuations with a size distribution peaked around 70 \AA which is compatible with experimental findings (50-100 \AA) but not with the current understanding of stability of flexible membranes. This unexpected result seems to be due to the multiplicity of chemical bonding in carbon.

Intrinsic ripples in graphene

We report a new type of phononic crystals with topologically nontrivial band gaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum (anomalous) Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern numbers of 1 and 2, indicating that these structures support single and multimode edge elastic waves immune to backscattering. These robust one-way phononic waveguides could potentially lead to the design of a novel class of surface wave devices that are widely used in electronics, telecommunication, and acoustic imaging.

Topological Phononic Crystals with One-Way Elastic Edge Waves

Carbon-based nanomaterials include fullerenes, carbon nanotubes, graphene and its derivatives, graphene oxide, nanodiamonds, and carbon-based quantum dots. Due to their unique structural dimensions and excellent mechanical, electrical, thermal, optical and chemical properties, these materials have attracted significant interest in diverse areas, including biomedical applications. Among them, there has been recent focus on the imaging of cells and tissues and the delivery of therapeutic molecules for disease treatment and tissue repair. The broad-range one-photon property of carbon based-nanomaterials together with their biocompatibility and ease of functionalization has made them candidate imaging agents for tumor diagnosis. In particular, the intrinsic two-photon fluorescence property of carbon based-nanomaterials in the long wavelength region (near-infrared II) allows deep-tissue optical imaging. This review highlights the recent development on carbon based-nanomaterials in the field of one-photon and two-photon imaging and discusses their possible and promising diagnostic and therapeutic applications for the treatment of various diseases including cancer.

Carbon-based nanomaterials as an emerging platform for theranostics

Graphene is considered as one of the most promising materials in a wide range of applications because of its outstanding electronic, optical, thermal, and mechanical properties. Given its large specific surface area, two-dimensional structure, facile decoration, and high adsorption capacity, numerous graphene-based nanomaterials with unprecedented characteristics have been designed, prepared, and applied in catalysis. In this article, we first reviewed common synthetic methods to prepare graphene-based catalysts followed by critical comments and possible solutions. We then briefly summarized the characterization techniques that were relevant to catalysis applications and their applications in energy conversion, environmental protection, and several other typical fields. Finally, we discussed the challenges and opportunities for the future development of graphene-based nanomaterials in sustainable catalysis. This review provides key information to the catalysis community to design and fabricate graphene-ba...

Graphene-Based Nanomaterials for Catalysis

The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement. Although these phases were discovered in a solid-state setting, recent innovations in systems of ultracold neutral atoms—uncharged atoms that do not naturally experience a Lorentz force—allow the synthesis of artificial magnetic, or gauge, fields. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladder-like, real-space lattice governed by the interacting Harper–Hofstadter model, which describes lattice-confined, coherently mobile particles in the presence of a magnetic field. We use a bottom-up strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a top-down approach that begins with a many-body system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.

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Microscopy of the interacting Harper-Hofstadter model in the few-body limit

Inspired by the success of graphene, various two-dimensional (2D) non-hexagonal graphene allotropes having sp2-bonded tetragonal rings in free-standing (hypothetical) form and on different substrates have been proposed recently. These systems have also been fabricated after modifying the topology of graphene by chemical processes. In this review, we would like to indicate the role of tetra-rings and the local symmetry breaking on the structural, electronic and optical properties of the graphene system. First-principles computations have demonstrated that the tetragonal graphene (TG) allotrope exhibits appreciable thermodynamic stability. The band structure of the TG nanoribbons (TGNRs) strongly depends on the size and edge geometry. This fact has been supported by the transport properties of TGNRs. The optical properties and Raman modes of this graphene allotrope have been well explored for characterisation purposes. Recently, a tight-binding model was used to unravel the metal-to-semiconductor transition under the influence of external magnetic fluxes. Even the introduction of transition metal atoms into this non-hexagonal network can control the magnetic response of the TG sheet. Furthermore, the collective effect of B-N doping and confinement effect on the structural and electronic properties of TG systems has been investigated. We also suggest future directions to be explored to make the synthesis of T graphene and its various derivatives/allotropes viable for the verification of theoretical predictions. It is observed that these doped systems act as a potential candidate for carbon monoxide gas sensing and current rectification devices. Therefore, all these experimental, numerical and analytical studies related to non-hexagonal TG systems are extremely important from a basic science point of view as well as for applications in sensing, optoelectronic and photonic devices.

A review on role of tetra-rings in graphene systems and their possible applications.

Size dependent magnetic and optical properties in diamond shaped graphene quantum dots: A DFT study

Present work reports an elegant method to address the emergence of two Dirac cones in a non-hexagonal graphene allotrope S-graphene (SG). We have availed nearest neighbour tight binding (NNTB) model to validate the existence of two Dirac cones reported from density functional theory (DFT) computations. Besides, the real space renormalization group (RSRG) scheme clearly reveals the key reason behind the emergence of two Dirac cones associated with the given topology. Furthermore, the robustness of these Dirac cones has been explored in terms of hopping parameters. As an important note, the Fermi velocity of the SG system (vF $$\simeq $$ c/80) is almost 3.75 times that of the graphene. It has been observed that the Dirac cones can be easily shifted along the symmetry lines without breaking the degeneracy. We have attained two different conditions based on the sole relations of hopping parameters and on-site energies to break the degeneracy. Further, in order to perceive the topological aspect of the system we have obtained the phase diagram and Chern number of Haldane model. This exact analytical method along with the supported DFT computation will be very effective in studying the intrinsic behaviour of the Dirac materials other than graphene.

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The topology and robustness of two Dirac cones in S-graphene: A tight binding approach.

We have critically examined the key role of acetylenic linkages (–CC–) in determining the opto-electronic responses of dynamically stable tetragonal (T) ‘-ynes’ with the help of a density functional theory method. The presence of –CC– between two tetra-rings invariably flips the electronic bands about the Fermi level. The underlying physics has been critically addressed with the help of a real space renormalization group (RSRG) scheme under a tight binding (TB) approximation. Besides, we have proposed an elegant approach to introduce and tune a band gap in the customarily metallic T graphene allotrope. The quantum dots of these systems exhibit diode like current–voltage (I–V) characteristics and can be used in negative differential resistance devices. In addition, the anisotropic optical properties evidently support the electronic states of the systems. In particular, the static dielectric constants for some of these ‘-ynes’ are enhanced compared to graphene and T graphene. The effective number of electrons participating in an interband transition shows saturation over 30 eV. Furthermore, electron energy loss spectra (EELS) peaks are consistent with the plasma frequencies of the corresponding systems. The intrinsic responses of the –CC– in these systems are extremely important for basic science and nanodevice research.

Acetylenic linkage dependent electronic and optical behaviour of morphologically distinct '-ynes'.

Tetragonal graphene (T-graphene) is a theoretically proposed dynamically stable, metallic allotrope of graphene. In this theoretical investigation, a tight binding (TB) model is used to unravel the metal to semiconductor transition of this 2D sheet under the influence of an external magnetic flux. In addition, the environment under which the sheet exposes an appreciable direct band gap of 1.41 ± 0.01 eV is examined. Similarly, the electronic band structure of the narrowest armchair T-graphene nanoribbon (NATGNR) also gets modified with different combinations of magnetic fluxes through the elementary rings. The band tuning parameters are critically identified for both systems. It is observed that the induced band gaps vary remarkably with the tuning parameters. We have also introduced an exact analytical approach to address the band structure of the NATGNR in the absence of any magnetic flux. Finally, the optical properties of the sheet and NATGNR are also critically analysed for both parallel and perpendicular polarizations with the help of density functional theory (DFT). Our study predicts that this material and its nanoribbons can be used in optoelectronic devices.

Arka Bandyopadhyay

Papers

A review on role of tetra-rings in graphene systems and their possible applications.

Size dependent magnetic and optical properties in diamond shaped graphene quantum dots: A DFT study

The topology and robustness of two Dirac cones in S-graphene: A tight binding approach.

Acetylenic linkage dependent electronic and optical behaviour of morphologically distinct '-ynes'.

Optical properties and magnetic flux-induced electronic band tuning of a T-graphene sheet and nanoribbon.