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Determining the complex second-order optical susceptibility in macroscale van der Waals heterobilayers

Zeyuan Zhu, Taejun Yoo, Kanchan Shaikh, Amalya C. Johnson, Qiuyang Li, Fang Liu, Hui Deng, Yuki Kobayashi

TL;DR

This work establishes a quantitative framework for the complex second-order susceptibility $\chi^{(2)}$ in macroscale MoSe$_2$/WS$_2$ heterobilayers by employing heterodyne second-harmonic generation (SHG). The authors resolve crystal-domain phases and stacking configurations, extracting $d_{22}$ and $\phi$ for both monolayers and the heterobilayer, and they show that interlayer contributions to SHG are below $1\%$ of the total signal under their conditions, with phase information remaining robust over hundreds of microns. The methodology combines a phase-controlled SHG interferometer with mm-scale sample fabrication (gold-tape exfoliation and 1-dodecanol passivation) to map crystallographic orientations and assess interlayer coupling. These results provide a practical upper bound on interlayer effects for stacking-engineered nanophotonic devices and highlight sample inhomogeneity as the dominant source of magnitude uncertainty, guiding future design and measurement at varying wavelengths.

Abstract

We report on the experimental characterization of the second-order susceptibility in MoSe$_2$/WS$_2$ heterobilayers, including their hidden complex phases. To this end, we developed a heterodyne-detection scheme for second-harmonic generation and applied it to macroscale heterobilayer samples prepared using the gold-tape exfoliation method. The heterodyne scheme enabled us to distinguish the relative orientation of the crystal domains, and further, it allowed us to characterize the complex phases of the susceptibility relative to a reference quartz sample. By comparing the results from the monolayer regions and the heterobilayer region over several hundred microns of the sample area, we determined that the contribution of interlayer effects to second-harmonic generation is within the experimental uncertainty arising from the sample inhomogeneity. The results here provide fundamental quantitative information necessary for the precise design of nanophotonic systems based on stacking engineering.

Determining the complex second-order optical susceptibility in macroscale van der Waals heterobilayers

TL;DR

This work establishes a quantitative framework for the complex second-order susceptibility in macroscale MoSe/WS heterobilayers by employing heterodyne second-harmonic generation (SHG). The authors resolve crystal-domain phases and stacking configurations, extracting and for both monolayers and the heterobilayer, and they show that interlayer contributions to SHG are below of the total signal under their conditions, with phase information remaining robust over hundreds of microns. The methodology combines a phase-controlled SHG interferometer with mm-scale sample fabrication (gold-tape exfoliation and 1-dodecanol passivation) to map crystallographic orientations and assess interlayer coupling. These results provide a practical upper bound on interlayer effects for stacking-engineered nanophotonic devices and highlight sample inhomogeneity as the dominant source of magnitude uncertainty, guiding future design and measurement at varying wavelengths.

Abstract

We report on the experimental characterization of the second-order susceptibility in MoSe/WS heterobilayers, including their hidden complex phases. To this end, we developed a heterodyne-detection scheme for second-harmonic generation and applied it to macroscale heterobilayer samples prepared using the gold-tape exfoliation method. The heterodyne scheme enabled us to distinguish the relative orientation of the crystal domains, and further, it allowed us to characterize the complex phases of the susceptibility relative to a reference quartz sample. By comparing the results from the monolayer regions and the heterobilayer region over several hundred microns of the sample area, we determined that the contribution of interlayer effects to second-harmonic generation is within the experimental uncertainty arising from the sample inhomogeneity. The results here provide fundamental quantitative information necessary for the precise design of nanophotonic systems based on stacking engineering.

Paper Structure

This paper contains 9 sections, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Results and Discussion
  3. Sample preparation and experimental setup
  4. Crystallographic orientations in monolayers
  5. Crystallographic orientations in heterobilayers
  6. Characterization of second-order susceptibility $d_{22}$ and complex phase $\phi$ in monolayers and heterobilayers
  7. Conclusions
  8. Substrate passivation with 1-dodecanol self-assembled monolayers
  9. Gold-tape exfoliation of transition-metal dichalcogenide monolayers and heterobilayers

Figures (3)

  • Figure 1: An overview of the heterodyne second-harmonic generation experiments. (a) A schematic illustration of the optical layout. We measure interference between the second-harmonic generation from TMDs and z-cut quartz, with phase precisely controlled by a fused silica wedge pair. The TMD sample is mounted on a two-axis motorized stage for precise control. (b) An optical image of the macroscale sample with monolayer, in which MoSe$_2$ is located on the left, monolayer WS$_2$ on the right, and heterobilayers MoSe$_2$/WS$_2$ at the center. (c) Second-harmonic spectra from WS$_2$, MoSe$_2$, and MoSe$_2$/WS$_2$, normalized by the monolayer WS$_2$ second-harmonic signal. (d) Polarization-dependent second-harmonic measurement of monolayers MoSe$_2$ and WS$_2$. The result shows that the stacking angle of the two monolayers is 2.6$^{\circ}$.
  • Figure 2: Heterodyne detection of SHG signals from WS$_2$ monolayer with opposite crystal orientations. (a) A schematic illustration of the second-harmonic heterodyne detection between the monolayer WS$_2$ with parallel or antiparallel subdomains and the quartz. (b) The signal interference between the monolayer WS$_2$ and the reference quartz as a function of fused silica wedge thickness. (c) The interference signal intensities with two different subdomains ($A$ and $B$) of WS$_2$. The results reveal a relative phase shift of $\pi$ between the two antiparallel domains.
  • Figure 3: Heterodyne second-harmonic characterization of TMD heterobilayers. (a) The result of the homodyne second-harmonic detection. This approach is insensitive to the relative phase of the second-harmonic signals. (b) The result of the heterodyne second-harmonic detection. Here, relative crystal-phase information is clearly resolved. (c) The result of the heterodyne second-harmonic detection with an additional $\pi$ phase shift. By comparing the results between (b) and (c), we can unambiguously identify the parallel ($AA$ and $BB$) and antiparallel ($AB$ and $BA$) regions. (d) The four stacking orientations of heterobilayers MoSe$_2$/WS$_2$: $AA$, $BB$, $AB$, and $BA$. (e) Histogram of the second-harmonic signal intensities in heterodyne detection in (c) when $\text{PSU}=\pi$, revealing four distinct peaks corresponding to the stacking orientations in (d).