Linear magneto-electron-light interaction in ultranarrow armchair graphene and boronitrene nanoribbons

doi:10.1016/j.diamond.2018.12.010

Diamond and Related Materials

Volume 92, February 2019, Pages 86-91

https://doi.org/10.1016/j.diamond.2018.12.010 Get rights and content

Highlights

•
Investigation and comparison the optical responses of ultranarrow armchair graphene and boronitrene nanoribbons in the presence of Zeeman magnetic field by using the tight-binding model and Greenï£¡s function technique.
•
Observation of increasing increasing behavior for static refractive index of both structures when the ribbon width and the magnetic field are increased, whereas the dynamical refractive index increases (oscillates) averagely with the ribbon width (magnetic field) at different light frequencies.
•
The absorption coefficient is generally increasing (oscillating) with the ribbon width (magnetic field).
•
The extinction coefficient introduces the scattering process in the presence of magnetic field.

Abstract

Using the synergy between the tight-binding model and the Green's function approach, this paper deals with the linear magneto-electron-light interaction in ultranarrow armchair graphene and boronitrene nanoribbons theoretically. In particular, we study the effect of ribbon width and the magnetic field on the refractive index, the absorption coefficient, and the extinction coefficient of abovementioned structures. Here, we reveal that there exists an increasing behavior for static refractive index of both structures when the ribbon width and the magnetic field are increased, whereas the dynamical refractive index increases (oscillates) in average with the ribbon width (magnetic field) at different light frequencies. We further show that the effect of ribbon width (magnetic field) on the absorption coefficient is generally increasing (oscillating) when the photon energy is altered. No refraction and absorption is reported at high enough photon frequencies independent of the ribbon width and the magnetic field strength. In addition, we find that the scattering process in the presence of the magnetic field manifests itself in the extinction coefficient. This information provides insights into the engineers in determining which ribbon width and magnetic field strength to use in the solar cell designs.

Introduction

Appealing counterparts of graphene have recently triggered numerous theoretical and experimental studies due to their valuable physical properties in future real applications in the optoelectronic industry [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]]. Graphene nanoribbons (GNRs) as one-dimensional (1D) counterparts of graphene exhibit a practical utilization in nano-optoelectronic devices [[13], [14], [15]] depending on the edge shape and size [[16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]], resulting in formation of different standing electronic waves of Dirac fermions. However, not only the ribbon width and the shape of edges provide successful uses of GNRs, but also the effect of external perturbations may have crucial roles in the information obtained [[27], [28], [29]]. In order to achieve a better efficiency, i.e. a higher photocurrent in optoelectronic devices as well as spintronic devices, GNRs are proper candidates, as proven in Refs. [2,3,30,31].

Similar to graphene, other hexagonal nanomaterials such as MoS₂ [32], SiC [33], BN [34] have been widely fabricated and synthesized by different methods. The hexagonal BN, so-called boronitrene is an insulator, providing different properties both qualitatively and quantitatively than graphene due to the quantum confinement effects. Thus, boronitrene nanoribbons (BNNRs) by cutting the BN sheet should also exhibit different features than GNRs. However, due to the wide band gap of boronitrene, the range of logic applications based on boronitrene is widen [[35], [36], [37]]. To have exotic optical properties of devices based on low-dimensional nanomaterials, it has been shown that host electron-light interaction can be influenced under external electronic perturbations, see Refs. [27,[38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53]].

While there are numerous works on 1D systems in the presence of electronic perturbations, to the best of our knowledge, a few studies have been focused on the magnetic effects on the electron-light interaction in 1D materials, see Refs. [[54], [55], [56], [57], [58]]. In the optical response, the magnetic field leads to fascinating features [27,28,59]. Here, we take into account the magnetic field effect on both intraband and interband parts of the optical responses such as refractive index, the absorption coefficient, and the extinction coefficient at finite temperature and fixed wave vector transfer of incident light. We use the linear response theory to find that optical properties are highly more sensitive to the magnetic perturbations in the intraband regime of the response function than the interband ones. The Green's function approach is applied to describe the quantum correlation functions through charge density-charge density interactions. Calculations are carried out in the tight-binding model. In addition to the magnetic field, the ribbon width is varied to predict a response for more realistic systems. It is obvious that the competition between π-electrons in GNRs and BNNRs and the external magnetic field provided by the Peierls phase factor yields nice information about the linear optical properties of 1D nanoribbons. We have calculated both real and imaginary parts of the dielectric function and then optical quantities.

The paper is organized as follows: Section 2 outlines briefly the semi-empirical tight-binding Hamiltonian model as well as the coupling between the magnetic field and the host electrons subjected to a photon beam $(ℏ ω, \vec{q})$ using the Green's function technique. In Section 3, we use the Green's functions obtained to the investigation of the dielectric response function. In Section 4, we present and discuss our findings. Finally, in Section 5, conclusions are summarized besides the discussion for future applications.

Section snippets

Semi-empirical tight-binding model and Green's function theory

In this section, we intend to set up the theory required in the present work in order to express the dynamics of Dirac fermions based on the tight-binding Hamiltonian model. We are interested in armchair GNRs (aGNRs) much more than the zigzag ones because the electronic phase in aGNRs can be tuned much more than zigzag ones. In general, aGNRs can be divided into two families: {n = 3p and n = 3p + 1} and n = 3p + 2 (n being the ribbon width) corresponding to the semiconductor and metallic

Dielectric response function

The main features of our study are given by the dielectric response function of the system subjected to an applied photon beam and magnetic field at a constant temperature. Let us first calculate the density-density response function within the linear response theory [66], $\begin{array}{l} ϵ (i ω_{p}, q_{x}) = & - \int_{0}^{1 / k_{B} T} d t^{'} e^{i ω_{p} t^{'}} \sum_{σ} ⟨ T_{t^{'}} [{\hat{ρ}}^{σ} (q_{x}, t^{'}) \\ \times {\hat{ρ}}^{σ} (- q_{x}, 0)] ⟩, \end{array}$ where ω_p = 2pπk_BT is the bosonic Matsubara frequency and ${\hat{ρ}}^{σ} (q_{x})$ refers to the charge density operator, defined by ${\hat{ρ}}^{σ} (q_{x}) = \frac{1}{N_{c}} \sum_{k_{x}, l} [ĉ_{A_{l}, k_{x} + q_{x}}^{†, σ} ĉ_{A_{l}, k_{x}}^{σ} + ĉ_{B_{l}, k_{x} + q_{x}}^{†, σ} ĉ_{B_{l}, k_{x}}^{σ}]$

Numerical results and discussions

We begin with some points about the optical quantities. The linear electron-light interactions are evaluated for the magnetic field perpendicular to aGNRs and aBNNRs. It is necessary to mention that the optical spectra are calculated for 1000 × 1000 unit cells with the broadening of about 30 meV. These abovementioned values are used either when the magnetic field is present. Furthermore, it has been assumed that the geometric structures of both lattices are optimized in the absence and presence

Conclusions

In this work, the linear optical responses in ultranarrow aGNRs and aBNNRs are investigated taking into account the effect of ribbon width and the Zeeman magnetic field using the linear response theory, tight-binding Hamiltonian model, and the Green's function technique. We observed different behaviors for refractive index, the absorption coefficient, and the extinction coefficient: (i) the static refractive index increases with both ribbon width and the magnetic field, while the dynamical

Acknowledgments

This research is funded by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.01-2017.361.

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Linear magneto-electron-light interaction in ultranarrow armchair graphene and boronitrene nanoribbons

Highlights

Abstract

Introduction

Section snippets

Semi-empirical tight-binding model and Green's function theory

Dielectric response function

Numerical results and discussions

Conclusions

Acknowledgments

Science

Superlattice. Microst.

Nano Lett.

Solid State Commun.

Carbon

Physica E

Diamond Relat. Mater.

Phys. E

The rise of graphene

Nat. Mater.

Photodetectors based on graphene, other two-dimensional materials and hybrid systems

Nat. Nanotechnol.

Graphene photonics, plasmonics, and broadband optoelectronic devices

ACS Nano

Broadband high photoresponse from pure monolayer graphene photodetector

Nat. Commun.

Physical Properties of Carbon Nanotubes

Electronic and magnetic properties of nanographite ribbons

Phys. Rev. B

Edge state in graphene ribbons: nanometer size effect and edge shape dependence

Phys. Rev. B

Peculiar width dependence of the electronic properties of carbon nanoribbons

Phys. Rev. B

Energy gaps in graphene nanoribbons

Phys. Rev. Lett.

Conductance quantization in mesoscopic graphene

Phys. Rev. B

Room-temperature ballistic transport in narrow graphene strips

Phys. Rev. B

Floquet-bloch states, quasienergy bands, and high-order harmonic generation for single-walled carbon nanotubes under intense laser fields

Phys. Rev. B

The electronic properties of graphene

Rev. Mod. Phys.

Electronic states of graphene nanoribbons and analytical solutions

Sci. Technol. Adv. Mater.

Controlled formation of sharp zigzag and armchair edges in graphitic nanoribbons

Science

Etching and narrowing of graphene from the edges

Nature Chem.

Giant edge state splitting at atomically precise graphene zigzag edges

Nat. Commun.

On-surface synthesis of atomically precise graphene nanoribbons

Adv. Mater.

Energy gaps of atomically precise armchair graphene sidewall nanoribbons

Phys. Rev. B

Recent progress in fabrication techniques of graphene nanoribbons

Mater. Horiz.

Electronic properties of zigzag graphene nanoribbons studied by TAO-DFT

J. Chem. Theory Comput.

On-surface synthesis and characterization of 9-atom wide armchair graphene nanoribbons

ACS Nano

Tuning the band gap of graphene nanoribbons synthesized from molecular precursors

ACS Nano

Voltage-dependent conductance of a single graphene nanoribbon

Nat. Nanotech.

Bottom-up graphene nanoribbon field-effect transistors

Appl. Phys. Lett.

Perturbation tuning of plasmon modes in semiconductor armchair nanoribbons

Phys. Rev. B

Zeeman-magnetic-field-induced magnetic phase transition in doped armchair boron-nitride nanoribbons

EPL

Graphene spintronics

Nat. Nanotechnol.