# Influence of a Non-Resonant Intense Laser and Structural Defect on the Electronic and Optical Properties of a GaAs Quantum Ring under Inversely Quadratic Potential

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model

^{2}mesh area. When considering the structural defect, the parameters were 1322 mesh vertices, 2544 triangles, 178 edge elements, 11 vertex elements, 2544, a 0.3259 quality element minimum, a 0.8158 quality element medium, a 0.01969 element area ratio, and a 7623 nm

^{2}mesh area.

## 3. Results and Discussion

^{−3}, $\hslash \phantom{\rule{0.166667em}{0ex}}\mathrm{\Gamma}=0.5$ meV, and ${\u03f5}_{r}=12.58$ [38,39].

^{2}, while in Figure 7d, the range was 25 nm

^{2}.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Inversely quadratic potential (Hellmann potential) as a function of the spatial coordinate, x, undressed (black line) and dressed by the laser (red and blue lines) with two values of the laser parameter.

**Figure 2.**Structure geometry without structural defect (

**a**) and with structural defect (

**b**). The black lines are the rectangular mesh used for this problem, where double refinement was used in the inner circular region of radius ${R}_{0}$, and the blue line corresponds to the boundary conditions established for this problem.

**Figure 3.**First seven electron energy levels confined in a GaAs quantum ring under the inversely quadratic potential, as a function of the magnetic field, without structural defects, and values of the non-resonant intense laser of ${\alpha}_{0}=0$ (

**a**), ${\alpha}_{0}=5$ nm (

**b**), and ${\alpha}_{0}=7$ nm (

**c**). The box in each figure shows the ground state wavefunction to indicate the laser’s effect on the structure.

**Figure 4.**First seven electron energy levels confined in a GaAs quantum ring under the inversely quadratic potential, as a function of the magnetic field, with a structural defect of 10° in the geometry of the structure, and values of the non-resonant intense laser of ${\alpha}_{0}=0$ (

**a**), ${\alpha}_{0}=5$ nm (

**b**), and ${\alpha}_{0}=7$ nm (

**c**). The box of each figure shows the ground state wavefunction to indicate the laser’s effect on the structure.

**Figure 5.**First seven electron energy levels confined in a GaAs quantum ring under the inversely quadratic potential, as a function of laser parameter ${\alpha}_{0}$, without a structural defect, and values of magnetic field of $B=0$ (

**a**), $B=5$ T (

**b**), and $B=10$ T (

**c**).

**Figure 6.**First seven electron energy levels confined in a GaAs quantum ring under the inversely quadratic potential, as a function of laser parameter ${\alpha}_{0}$, with structural defects, and values of magnetic field of $B=0$ (

**a**), $B=5$ T (

**b**), and $B=10$ T (

**c**).

**Figure 7.**Squared dipole moments as functions of the applied magnetic field for an electron confined in a GaAs quantum ring under the inversely quadratic potential, without structural defects and with ${\alpha}_{0}=5$ nm (

**a**,

**c**) and ${\alpha}_{0}=7$ nm (

**b**,

**d**).

**Figure 8.**Squared dipole moments as functions of the applied magnetic field for an electron confined in a GaAs quantum ring under the inversely quadratic potential, with structural defects and with ${\alpha}_{0}=5$ nm (

**a**,

**c**) and ${\alpha}_{0}=7$ nm (

**b**,

**d**).

**Figure 9.**The linear optical absorption coefficient is a function of the photon energy for the electron confined in a GaAs quantum ring under the inversely quadratic potential, without considering the structural defect in the structure’s geometry. The calculations were performed with right circular polarization (

**a**,

**b**) and left circular polarization (

**c**,

**d**).

**Figure 10.**The linear optical absorption coefficient as a function of the photon energy for the electron confined in a GaAs quantum ring under the inversely quadratic potential, considering a structural defect of 10°. The calculations were performed right circular polarization (

**a**,

**b**) and left circular polarization (

**c**,

**d**).

**Table 1.**Values of the dipole moments of the $|{M}_{12}{|}^{2}$ and $|{M}_{13}{|}^{2}$ transitions and their corresponding transition energies ${E}_{12}$ and ${E}_{13}$, for different values of the laser non-resonant parameter, without structural defects.

θ_{0} = 360° | Right Circular Polarization | ${\mathit{\alpha}}_{0}$ (nm) | Left Circular Polarization | ||||
---|---|---|---|---|---|---|---|

B (T) | B (T) | ||||||

0 | 2.1 | 8.7 | 0 | 2.1 | 8.7 | ||

$|{M}_{12}{|}^{2}$ (nm^{2}) | 115.51 | 92.28 | 117.71 | 5 | 115.51 | 136.29 | 112.98 |

$|{M}_{13}{|}^{2}$ (nm^{2}) | 42.79 | 65.36 | 32.37 | 42.79 | 15.36 | 45.96 | |

${E}_{12}$ (meV) | 0.46 | 0.05 | 0.34 | 0.46 | 0.05 | 0.34 | |

${E}_{13}$ (meV) | 5.42 | 6.28 | 5.22 | 5.42 | 6.28 | 5.22 | |

$|{M}_{12}{|}^{2}$ (nm^{2}) | 125.22 | 130.88 | 123.10 | 7 | 125.22 | 119.23 | 125.67 |

$|{M}_{13}{|}^{2}$ (nm^{2}) | 30.70 | 19.50 | 24.71 | 30.70 | 39.22 | 30.81 | |

${E}_{12}$ (meV) | 0.14 | 0.01 | 0.10 | 0.14 | 0.01 | 0.10 | |

${E}_{13}$ (meV) | 8.12 | 8.57 | 7.92 | 8.12 | 8.57 | 7.92 |

**Table 2.**Values of the dipole moments of the $|{M}_{12}{|}^{2}$ and $|{M}_{13}{|}^{2}$ transitions and their corresponding transition energies ${E}_{12}$ and ${E}_{13}$, for different values of the laser non-resonant parameter, with a structural defect.

θ_{0} = 350° | Right Circular Polarization | α_{0} (nm) | Left Circular Polarization | ||||
---|---|---|---|---|---|---|---|

B (T) | B (T) | ||||||

0 | 8 | 12 | 0 | 8 | 12 | ||

$|{M}_{12}{|}^{2}$ (nm^{2}) | 102.64 | 96.66 | 90.09 | 5 | 102.64 | 99.06 | 92.77 |

$|{M}_{13}{|}^{2}$ (nm^{2}) | 34.66 | 28.40 | 24.39 | 34.66 | 34.23 | 31.88 | |

${E}_{12}$ (meV) | 0.28 | 0.23 | 0.18 | 0.28 | 0.23 | 0.18 | |

${E}_{13}$ (meV) | 6.39 | 6.12 | 5.88 | 6.39 | 6.12 | 5.88 | |

$|{M}_{12}{|}^{2}$ (nm^{2}) | 78.78 | 67.12 | 54.23 | 7 | 78.78 | 67.67 | 54.75 |

$|{M}_{13}{|}^{2}$ (nm^{2}) | 27.05 | 19.99 | 16.35 | 27.05 | 28.25 | 26.82 | |

${E}_{12}$ (meV) | 0.09 | 0.07 | 0.06 | 0.09 | 0.07 | 0.06 | |

${E}_{13}$ (meV) | 8.83 | 8.49 | 8.14 | 8.83 | 8.49 | 8.14 |

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**MDPI and ACS Style**

León-González, J.C.; Toscano-Negrette, R.G.; Vinasco, J.A.; Morales, A.L.; Mora-Ramos, M.E.; Duque, C.A.
Influence of a Non-Resonant Intense Laser and Structural Defect on the Electronic and Optical Properties of a GaAs Quantum Ring under Inversely Quadratic Potential. *Condens. Matter* **2023**, *8*, 52.
https://doi.org/10.3390/condmat8020052

**AMA Style**

León-González JC, Toscano-Negrette RG, Vinasco JA, Morales AL, Mora-Ramos ME, Duque CA.
Influence of a Non-Resonant Intense Laser and Structural Defect on the Electronic and Optical Properties of a GaAs Quantum Ring under Inversely Quadratic Potential. *Condensed Matter*. 2023; 8(2):52.
https://doi.org/10.3390/condmat8020052

**Chicago/Turabian Style**

León-González, José C., Rafael G. Toscano-Negrette, Juan A. Vinasco, Alvaro L. Morales, Miguel E. Mora-Ramos, and Carlos A. Duque.
2023. "Influence of a Non-Resonant Intense Laser and Structural Defect on the Electronic and Optical Properties of a GaAs Quantum Ring under Inversely Quadratic Potential" *Condensed Matter* 8, no. 2: 52.
https://doi.org/10.3390/condmat8020052