Scaling of excitons in graphene nanodots

Tuning the properties of graphene quantum dots by passivation

The electronic and optical properties of graphene quantum dots (GQDs) of size less than 10 nm are different from those of graphene sheets due to quantum confinement effects. For analyzing their use in optoelectronic applications, it is very crucial to optimally tune the bandgap and engineer the controlling parameters. In the present work, a systematic investigation of the band gap of hexagonal GQDs has been carried out by examining their HOMO and LUMO energies. Passivation of dangling bonds of these GQDs has been carried out with the help of electron-withdrawing substituents in order to tune the band gap and engineer their optical properties such as absorption and emission spectra by carrying out the simulation with Density Functional Theory formalism using Gaussian 09 software. Carrying out passivation with electronegative element fluorine (F) effectively decreases the band gap of these QDs resulting in a redshift in the absorption spectra. The HOMO and LUMO topographical surfaces have been used to understand the absorption spectra. These surfaces show some σ-bond characteristics along with π-bond properties on passivating GQDs with the F-atom which further results in alteration of their energies and a corresponding decrease in their band gap. Here, the absorption is found to be dependent on the size of GQDs and the type of passivating atoms (H or F). The results thus obtained are found to be in good consonance with those reported in the literature engaging different methods. The present analysis may prove to be useful in improving the working of solar cells and other optoelectronic devices.

Scaling of energy gaps in phosphorene nanoflakes

Electronic structure of phosphorene nanoflakes which consist of hundreds of phosphorus atoms are studied in the framework of unrestricted Hartree-Fock approach. On the base of Pariser-Parr-Pople model for electron-electron interactions, a simplified Bethe-Salpeter formalism is established for the calculation of excitation states of the system. Taking into account the electron-hole interaction in various dielectric environments, the optical gap of a triangular phosphorene nanoflake is shown to increase as the screening effect becomes stronger while its graphene counterpart exhibits just the opposite dependence. After confirming an exponential dependence of the optical gap on the effective dielectric constant, the quasiparticle and optical gaps are also found to obey an exponential scaling rule against the total number of atoms in the nanoflakes, respectively. By extrapolating the dependence on the size of the system, one is able to estimate the exciton binding energy of a monolayer phosphorene sheet on a SiO₂substrate to be 0.894 eV. The result is found to agree well with the previous experimental result of 0.9 eV.

Abnormal scaling of excitons in phosphorene quantum dots

Excitonic states of a many-electron system in phosphorene quantum dots (PQDs) are investigated theoretically by using a configuration interaction approach. For a triangular PQD in various dielectric environments, its exciton is found to obey two distinct scaling rules. When there is a strong screening effect present in the nanodot, the exciton binding energy (Δex) is shown to be around -150 meV as the long-range Coulomb interactions are totally suppressed and it increases to about 100 meV when the effective dielectric constant (εr) decreases to 12.5. Over this range of εr, Δex is found to be well fitted into a quadratic form of εr-1, which scales neither linearly with εr-2 like the case of bulk three-dimensional semiconductors nor linearly with εr-1 like the case previously reported for graphene nanostructures. When εr is reduced below 10.0, however, Δex is shown to exhibit a perfect linear relationship with εr-1, which behaves just like that of a two-dimensional graphene sheet. On the other hand, with the reduced εr, the quasiparticle gap is found to decrease instead of increasing like in most of the semiconductor nanostructures. As a result, it is revealed that the relationship of Δex with the quasi-particle gap deviates largely from the linear one previously reported for graphene and many other two-dimensional materials.

Hubbard excitons in two-dimensional nanomaterials

Excitons in two-dimensional nanomaterials are studied by solving the many-electron Hamiltonian with a configuration-interaction approach. It is shown that graphene or phosphorene nanoflakes can not accommodate any excitonic bound states if the long-range Coulomb interaction is suppressed when the systems are placed in a high-k dielectric environment or on a metal substrate. Hence it is revealed that an electron-hole pair created by an optical excitation does not always form an exciton even in a confined nanostructure. The negative exciton binding energy is found to exhibit distinct dependence on the strength of short-range Coulomb interaction as the system undergoes a phase transition from non-magnetic to anti-ferromagnetic. It is further shown that the electron-hole pair may form an exciton state only when the long-range Coulomb interaction is recovered in the nanoflakes.

Abnormal blueshift of the absorption edge in graphene nanodots

In a conventional semiconductor, when the dielectric screening effect is suppressed, the exciton binding energy increases and the corresponding excitonic transition would exhibit a redshift in the spectrum. In this work, I study the optical properties of hexagonal graphene nanodots by using a configuration interaction approach and reveal that the edge of the absorption spectrum shows an abnormal blueshift as the environmental dielectric constant ϵ_r decreases. The two dominant many-body effects in the nanodot: the quasiparticle and excitonic effects are both found to scale almost linearly with ϵ_r^-1. The former is shown to have a larger proportionality constant and thus accounts for the blueshift of the absorption edge. In contrast to the long-range Coulomb interaction, the on-site Coulomb energy is found to have a negative impact on the bright excitonic states. In the presence of a strong dielectric screening effect, a strong short-range Coulomb interaction is revealed to be responsible for the disintegration of the bright exciton.

Excitonic absorption spectra in graphene nanoflakes: Tuning of exciton binding energy by dielectric environments

By solving the Bethe-Salpeter equation within the Hartree-Fock formalism, we study the excitonic absorption spectra of graphene nanoflakes embedded in various dielectric environments. With the excitonic effects fully taken into account, the exciton binding energy as a function of the dielectric constant is found to be well described by a single scaling rule in which the scaling factor is found to vary slowly with the size of the nanoflakes. Furthermore, it is revealed that the exciton binding energy scales almost linearly with the on-site interaction energy and exhibits more sensitive dependence in smaller nanoflakes. Our results are found to agree well with the recent experiment.

Dark excitons and tunable optical gap in graphene nanodots

By using a configuration interaction approach with up to the fifth excitations taken into account, we study the excitonic effect in the optical absorption in graphene nanodots.