# Uniaxial Strain Dependence on Angle-Resolved Optical Second Harmonic Generation from a Few Layers of Indium Selenide

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Growth of InSe Single Crystals and Their Characterizations

^{−4}Pa. The ampoules were placed in a horizontal furnace at 550 °C for two days to obtain a partially mixed crystal. Later, the mixed crystals were used to grow the pure InSe single crystal with the help of a vertical Bridgman setup. The furnace during the Bridgman process was maintained at a high temperature of about 850 °C. The mixed crystal in the ampoule was hung and heat treated at 850 °C for 24 h; once the mixed crystal melted entirely in the ampoule, the ampoules were lowered through a temperature gradient of 1 °C at a rate of 0.1 mm/h to obtain a large-sized single crystal. Using this procedure, we obtained over 5 cm long and 1 cm in diameter InSe single crystals in bulk.

#### 2.2. Sample Preparation and Strain Engineering

#### 2.3. SHG Measurements

#### 2.4. Theoretical Calculations

^{−9}Ha, which guaranteed that the difference between the band energies in the last two consecutive SCF steps was smaller than the criterion.

## 3. Results and Discussion

## 4. Conclusions

## Supplementary Materials

**a**) [010] and (

**b**) [001]. Figure S2. (

**a**) AFM image around the edge of the InSe flake. (

**b**) The 4 line profiles as labelled in (

**a**). Figure S3. Schematic of the strain device. Figure S4. Schematic diagram of curved substrate under uniaxial strain. Figure S5. Schematic of the experimental setup. Figure S6. (

**a**) The SHG spectrum with peak wavelength at 394 nm. (

**b**) The power dependent SHG intensity. The slope of the linear fitting curve is around 2 in the log–log scale, indicating a quadratic relationship between the incident power and the SHG intensity. Figure S7. Calculated SHG susceptibility components of γ-InSe under strain of (

**a**) −2% and (

**b**) 0%. Figure S8. Strain dependence on the (

**a**) real part, (

**b**) imaginary part, and (

**c**) phase of calculated ${d}_{11}$, ${d}_{12}$, and ${d}_{26}$ at 1.55 eV. Figure S9. R-squared values of the strain-dependent experimental data by using the model from the first–principles methods (

**a**–

**d**) without parameters and (

**e**–

**h**) with one parameter to linearly modify the strain.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Images of SHG with polarization parallel to the incident light polarization for rotational angles (

**a**–

**f**) from $-20\xb0$ to $30\xb0$.

**Figure 2.**Normalized angle-resolved SHG patterns for SHG polarization parallel (blue squares) and perpendicular (orange dots) to the incident light polarization. The blue and orange solid lines are ${\mathrm{cos}}^{2}3\theta $ and ${\mathrm{sin}}^{2}3\theta $ curves, respectively.

**Figure 3.**Angle-resolved SHG of InSe under different strain levels. The dots depict the experimental data and are fitted with ${\mathrm{cos}}^{2}3\theta $, which is shown in solid lines to make it easier to see.

**Figure 4.**(

**a**) Calculated nonzero $\left|{\chi}^{\left(2\right)}\right|$ components at photon energy 1.55 eV at different uniaxial strain levels. (

**b**) Angle-resolved ${I}_{\parallel}^{\left(2\omega \right)}$ pattern under 0% and −20% strain derived from the calculated ${\chi}^{\left(2\right)}$ at 1.55 eV.

**Figure 5.**(

**a**) The experimental results in dots and the calculated curves in solid lines from the model based on the first-principles methods without a correction parameter. (

**b**) The calculated curves with a correction parameter to linearly modify the strain term.

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**MDPI and ACS Style**

Li, Z.-Y.; Cheng, H.-Y.; Kung, S.-H.; Yao, H.-C.; Inbaraj, C.R.P.; Sankar, R.; Ou, M.-N.; Chen, Y.-F.; Lee, C.-C.; Lin, K.-H.
Uniaxial Strain Dependence on Angle-Resolved Optical Second Harmonic Generation from a Few Layers of Indium Selenide. *Nanomaterials* **2023**, *13*, 750.
https://doi.org/10.3390/nano13040750

**AMA Style**

Li Z-Y, Cheng H-Y, Kung S-H, Yao H-C, Inbaraj CRP, Sankar R, Ou M-N, Chen Y-F, Lee C-C, Lin K-H.
Uniaxial Strain Dependence on Angle-Resolved Optical Second Harmonic Generation from a Few Layers of Indium Selenide. *Nanomaterials*. 2023; 13(4):750.
https://doi.org/10.3390/nano13040750

**Chicago/Turabian Style**

Li, Zi-Yi, Hao-Yu Cheng, Sheng-Hsun Kung, Hsuan-Chun Yao, Christy Roshini Paul Inbaraj, Raman Sankar, Min-Nan Ou, Yang-Fang Chen, Chi-Cheng Lee, and Kung-Hsuan Lin.
2023. "Uniaxial Strain Dependence on Angle-Resolved Optical Second Harmonic Generation from a Few Layers of Indium Selenide" *Nanomaterials* 13, no. 4: 750.
https://doi.org/10.3390/nano13040750