The effect of twisted light on the ring-shaped molecules: The manipulation of the photoinduced current and the magnetic moment by transferring spin and orbital angular momentum of high frequency light
Graphical abstract
Introduction
Quantum control of an electron motion [1], [2] and the presence of local induced magnetic field [3] in a quantum structure or nanosize cluster has received great attention due to the possibility of the manipulation of physical properties by using dynamics of the electrons in a material [4]. As an example of external effect, the magnetic field is able to induce a net electron circulation in quantum systems [5], [6]. Especially, the study of Haddon et al. [7] shows the possibility of ring currents being induced by the magnetic field on and molecules. The persistent current in different materials can be induced by external magnetic field [8]. However, a more effective way to induce ring current is the electromagnetic field applied to the quantum systems [9], [10], [11], [12]. Ring current in a quantum system can be induced by the light carrying SAM [13], [14]. SAM carrying or circularly polarized light beam can lead to a net circulation of the electrons in the system [15], [16], [17].
The light is able to carry OAM as well as SAM [18], [19]. An optical vortex or so called twisted light can be produced by computer-generated holograms [20]. This kind of beam can be used as optical tweezers [21]. The possibility of transferring OAM of optical vortex into the electron in atoms [22], [23], graphene [24] and semiconductor clusters [25], [26] have been investigated.
For the application of OAM or SAM carrying light, the most suitable geometry of the structure is ring shape and circular symmetry. An electron moving freely in the ring-shaped molecule can have net circulation in the case of OAM or SAM transfer by the laser beam. The electronic structure and ring currents of some molecules and particularly ring-shaped molecules have been intensively studied [27], [28], [29], [30], [31], [32], [33], [34], [35]. The benzene is the most well-known and most fundamental molecule among ring-shaped molecules [36].
The main aim of this study is the theoretical investigation of the ring current and magnetic moment (induced by OAM or SAM transfering) analyzing the angular band structure of ring-shaped benzene molecules which is introduced in this study. Furthermore, we focus on the ring current that resulted from high-frequency transitions while previous studies investigated the ring currents induced by HOMO-LUMO transitions. We also introduce the ring currents induced by the transfer of OAM of the twisted light into the nanoscale ring shaped molecules. By SAM carrying light, the free electrons in the system can be caused to jump into the excited states, and angular momentum of the light can be transferred to the electron. When electrons are excited into a specific state which has a net magnetic quantum number, electrons have a net circulation leading to the net ring current. This induced ring current results in an explicit magnetic moment. The magnitude and direction of the current and magnetic field can be changed by applying the variation of the frequency of the light. Previous studies on ring-shaped molecules have focused on the HOMO-LUMO transitions and related induced current [28], [29], [30], [31], [32], [33], [34], [35]. In our study, we calculate the induced current caused by HOMO-LUMO transitions for comparison with the literature. But we mainly aim to obtain the current induced by the light in high frequency. The significant and attractive part of the result is the possibility of the manipulation of the current direction by the variation of the frequency of the circularly polarized light and twisted light. For benzene molecule, the amount of change in the frequency is not so small and required transition energy is out of the UV-vis range. However, the increase in the radius of the molecules can reduce the transition energy and the direction of the light can be changed just by small variation in the frequency.
Another aim of the study is the investigation of the possibility of tuning the magnitude and direction of the current by changing the OAM of the light. The twisted light due to the non-homogeneous spatial distribution and carrying orbital angular momentum can contribute to the manipulation of the current in a molecule. We will introduce the induced current in a benzene molecule by a highly focused twisted light and we will reveal the possibility of tuning the direction of current by circular polarized light and twisted light.
In this study, we will first introduce a numerical technique to reveal the electronic structure of the molecule. Than we mention the laser beam structure. After that, we will introduce the calculation technique for obtaining induced electric and magnetic field. Finally, we will discuss the results for the benzene molecule.
Section snippets
The electronic structure of the benzene molecule and the structure of Laguerre Gaussian Beam
The benzene molecule has an electronic structure which is calculated by performing Gaussian 09. For optimized structure of the benzene molecule, we have used the density functional theory (DFT) with hybrid B3PW91 functional in conjunction with the 6-31(d)G basis set to obtain electronic structure. The total wavefunction for each state is formed by combining basis sets and using numerical technique.
Twisted light carrying OAM has the vector potential with a radial dependence which is
Photoinduced current by SAM and OAM transfer of photon
The current density can be written as [23], [22]where is a time dependent wavefunction as it reads inwhere has been calculated by using DFT calculations in Cartesian coordinates. Because of the moderate intensity of the laser beam, the first order perturbation theory can be used for the calculation of expansion coefficient . where
Benzene under circularly polarized light
As a traditional method, an induced current in a ring can be represented by a magnetic moment with a perpendicular direction to the ring plane. A measurement on a magnetic moment of a system is the best way to determine the ring current. However, information about the current density in a system can also allow us to analyze the contribution of the local regions in the system. In our calculations, the current density has been obtained for different frequencies of the circularly polarized light
Conclusions
In this work, the angular electronic band structure of the ring shaped benzene molecule was introduced to reveal the relationship between the light induced ring currents and the high frequency dependent electronic transitions. For chemists, information on the light induced current density leads to understanding the electron motion in aromatic molecules in the case of exposing to the electromagnetic field. Furthermore, the studies on photo-induced current density in aromatic molecules are quite
Acknowledgment
This work was supported by TUBITAK through Project No. 112T991.
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