Edge states and optical transition energies in carbon nanoribbons

Graphene quantum dots for biosensing and bioimaging

Graphene Quantum Dots (GQDs) are low dimensional carbon based materials with interesting physical, chemical and biological properties that enable their applications in numerous fields. GQDs possess unique electronic structures that impart special functional attributes such as tunable optical/electrical properties in addition to heteroatom-doping and more importantly a propensity for surface functionalization for applications in biosensing and bioimaging. Herein, we review the recent advancements in the top-down and bottom-up approaches for the synthesis of GQDs. Following this, we present a detailed review of the various surface properties of GQDs and their applications in bioimaging and biosensing. GQDs have been used for fluorescence imaging for visualizing tumours and monitoring the therapeutic responses in addition to magnetic resonance imaging applications. Similarly, the photoluminescence based biosensing applications of GQDs for the detection of hydrogen peroxide, micro RNA, DNA, horse radish peroxidase, heavy metal ions, negatively charged ions, cardiac troponin, etc. are discussed in this review. Finally, we conclude the review with a discussion on future prospects.

Graphene Quantum Dots and Their Applications in Bioimaging, Biosensing, and Therapy

Graphene quantum dots (GQDs) are carbon-based, nanoscale particles that exhibit excellent chemical, physical, and biological properties that allow them to excel in a wide range of applications in nanomedicine. The unique electronic structure of GQDs confers functional attributes onto these nanomaterials such as strong and tunable photoluminescence for use in fluorescence bioimaging and biosensing, a high loading capacity of aromatic compounds for small-molecule drug delivery, and the ability to absorb incident radiation for use in the cancer-killing techniques of photothermal and photodynamic therapy. Recent advances in the development of GQDs as novel, multifunctional biomaterials are presented with a focus on their physicochemical, electronic, magnetic, and biological properties, along with a discussion of technical progress in the synthesis of GQDs. Progress toward the application of GQDs in bioimaging, biosensing, and therapy is reviewed, along with a discussion of the current limitations and future directions of this exciting material.

2N+4-rule and an atlas of bulk optical resonances of zigzag graphene nanoribbons

Development of on-chip integrated carbon-based optoelectronic nanocircuits requires fast and non-invasive structural characterization of their building blocks. Recent advances in synthesis of single wall carbon nanotubes and graphene nanoribbons allow for their use as atomically precise building blocks. However, while cataloged experimental data are available for the structural characterization of carbon nanotubes, such an atlas is absent for graphene nanoribbons. Here we theoretically investigate the optical absorption resonances of armchair carbon nanotubes and zigzag graphene nanoribbons continuously spanning the tube (ribbon) transverse sizes from 0.5(0.4) nm to 8.1(12.8) nm. We show that the linear mapping is guaranteed between the tube and ribbon bulk resonance when the number of atoms in the tube unit cell is [Formula: see text], where [Formula: see text] is the number of atoms in the ribbon unit cell. Thus, an atlas of carbon nanotubes optical transitions can be mapped to an atlas of zigzag graphene nanoribbons.

Edge magnetism of Heisenberg model on honeycomb lattice

Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials.

Ferromagnetic properties in low-doped zigzag graphene nanoribbons

The temperature-dependent edge magnetic susceptibility [Formula: see text] and the uniform magnetic susceptibility χ in zigzag graphene nanoribbons is studied within the Hubbard model on a honeycomb lattice. By using the determinant quantum Monte Carlo (DQMC) method, it is found that the ferromagnetic fluctuations at the zigzag edge dominate around half-filling, and that the fluctuations are strengthened markedly by the on-site Coulomb interaction U, which may lead to a possible high-temperature edge ferromagnetic behaviour in low-doped zigzag graphene nanoribbons.

Exploration of edge-dependent optical selection rules for graphene nanoribbons

Optical selection rules for one-dimensional graphene nanoribbons are explored based on the tight-binding model. A theoretical explanation, through analyzing the velocity matrix elements and the features of the wavefunctions, can account for the selection rules, which depend on the edge structure of the nanoribbon, i.e., armchair or zigzag edges. The selection rule of armchair nanoribbons is ΔJ = Jc - Jv = 0, and the optical transitions occur from the conduction to the valence subbands of the same index. Such a selection rule originates in the relationships between two sublattices and between the conduction and valence subbands. On the other hand, zigzag nanoribbons exhibit the selection rule |ΔJ| = odd, which results from the alternatively changing symmetry property as the subband index increases. Furthermore, an efficient theoretical prediction on transition energies is obtained by the application of selection rules, and the energies of the band-edge states become experimentally attainable via optical measurements.

Zigzag graphene nanoribbons: bandgap and midgap state modulation

We study zigzag graphene nanoribbons with periodic edge roughness and report significant band gap opening. Interestingly, such nanoribbons have a near-midgap state with a small band width. We extensively study the electronic structure and the electric-field modulation of the conduction/valence bands and the near-midgap state. We summarize the important electronic-structure features like the band gap, the band width and the effective mass. We show that by applying an external electric field in the width direction, the band width of the near-midgap state varies linearly due to the edge localization, whereas the band gap remains almost constant. Additionally, the effective mass of these states can switch polarity from negative (hole-like) to positive (carrier-like) at the Γ-point with the field modulation.

Dynamical signatures of edge-state magnetism on graphene nanoribbons

We investigate the edge-state magnetism of graphene nanoribbons using projective quantum Monte Carlo simulations and a self-consistent mean-field approximation of the Hubbard model. The static magnetic correlations are found to be short ranged. Nevertheless, the correlation length increases with the width of the ribbon such that already for ribbons of moderate widths we observe a strong trend towards mean-field-type ferromagnetic correlations at a zigzag edge. These correlations are accompanied by a dominant low-energy peak in the local spectral function and we propose that this can be used to detect edge-state magnetism by scanning tunneling microscopy. The dynamic spin structure factor at the edge of a ribbon exhibits an approximately linearly dispersing collective magnonlike mode at low energies that decays into Stoner modes beyond the energy scale where it merges into the particle-hole continuum.

Magnetism of solids resulting from spin polarization of p orbitals

Magnetism in systems that do not contain transition metal or rare earth ions was recently observed or predicted to exist in a wide variety of systems. We summarize both experimental and theoretical results obtained for ideal bulk II-V and II-IV compounds, molecular crystals containing O(2) or N(2) molecules as structural units, as well as for carbon-based materials such as graphite and graphene nanoribbons. Magnetism can be an intrinsic property of a perfect crystal, or it can be induced by non-magnetic dopants or defects. In the case of vacancies, spin polarization is local and results in their high spin states. The non-vanishing spin polarization is shown to originate in the strong spin polarization of the 2p shell of light atoms from the second row of the periodic table.