# Ab Initio Simulation of Attosecond Transient Absorption Spectroscopy in Two-Dimensional Materials

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Electron Dynamics Simulation for Periodic Systems

#### 2.2. Optical Property from Linear Response Calculation

#### 2.3. Transient Optical Properties with Pump–Probe Simulations

## 3. Attosecond Transient Absorption of Monolayer h-BN

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ATAS | Attosecond transient absorption spectroscopy |

2D | Two-dimensional |

h-BN | Hexagonal boron nitride |

TMDs | Transition metal dichalcogenides |

TDDFT | Time-dependent density functional theory |

IR | Infrared |

ALDA | Adiabatic local density approximation |

DFT | Density functional theory |

FWHM | Full width at half maximum |

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**Figure 1.**(

**a**) atomic configuration of monolayer h-BN; (

**b**) current density in time domain after the impulsive distortion at $t=0$; (

**c**) real-part of surface conductivity, $\Re \left[\sigma \left(\omega \right)\right]$, of h-BN, calculated by TDDFT with ALDA.

**Figure 2.**(

**a**) real part of the transient conductivity of monolayer h-BN under the IR pump pulse for the x-direction in Figure 1a; (

**b**) the time-profile of the applied pump electric field. The result is computed by TDDFT with ALDA.

**Figure 3.**Red lines show vertical transition energies from the highest valence band to conduction bands in monolayer h-BN around (

**a**) the M point and (

**b**) the $\Gamma $ point. The transition energies are computed by the difference of the Kohn–Sham eigenenergies of the highest valence band and conduction bands, ${\u03f5}_{c\overrightarrow{k}}-{\u03f5}_{v\overrightarrow{k}}$, corresponding to excitations in the independent particle approximation. Blue lines show the parabolic fits of specific bands.

**Figure 4.**Transient surface conductivities of parabolic two-band models under the femtosecond IR pulse. The panels (

**a**) and (

**b**) show the result of the parabolic band shown as the blue-dashed line in Figure 3a, b, respectively.

**Figure 5.**(

**a**) transient surface conductivities of the combined two-band models at M and $\Gamma $ points. This result is nothing but the summation of Figure 4a,b; (

**b**) the time-profile of the applied pump electric field.

**Figure 6.**(

**a**) real part of the transient conductivity of monolayer h-BN under the IR pump pulse for the y-direction in Figure 1a; (

**b**) the time-profile of the applied pump electric field. The result is computed by TDDFT with ALDA.

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**MDPI and ACS Style**

Sato, S.A.; Hübener, H.; De Giovannini, U.; Rubio, A. Ab Initio Simulation of Attosecond Transient Absorption Spectroscopy in Two-Dimensional Materials. *Appl. Sci.* **2018**, *8*, 1777.
https://doi.org/10.3390/app8101777

**AMA Style**

Sato SA, Hübener H, De Giovannini U, Rubio A. Ab Initio Simulation of Attosecond Transient Absorption Spectroscopy in Two-Dimensional Materials. *Applied Sciences*. 2018; 8(10):1777.
https://doi.org/10.3390/app8101777

**Chicago/Turabian Style**

Sato, Shunsuke A., Hannes Hübener, Umberto De Giovannini, and Angel Rubio. 2018. "Ab Initio Simulation of Attosecond Transient Absorption Spectroscopy in Two-Dimensional Materials" *Applied Sciences* 8, no. 10: 1777.
https://doi.org/10.3390/app8101777