Homodyne Detection Enables Observation of Forbidden Second Harmonics in 2D Crystals

The fundamental understanding of how light interacts with two-dimensional materials has been challenged by new research into second-harmonic generation (SHG). Haoning Tang, Zhitong Ding, and Tianyi Ruan, all from the Department of Electrical Engineering and Computer Science at the University of California at Berkeley, alongside colleagues including Kenji Watanabe and Takashi Taniguchi from the National Institute for Materials Science, have demonstrated a surprising phenomenon. Their work reveals robust SHG signals in centrosymmetric bilayer crystals , materials previously thought to prohibit this effect without external intervention. This breakthrough, achieved through a novel homodyne detection technique, not only allows for the identification of crystallographic orientation in materials like hexagonal boron nitride and graphene, but also opens up possibilities for non-invasive strain detection and expands the scope of nonlinear optical spectroscopy to include a wider range of previously inaccessible materials.

Intrinsic SHG in Twisted Bilayer Graphene

Optical spectroscopy based on second-order nonlinearity is a critical technique for characterising two-dimensional (2D) crystals as well as bioimaging and quantum optics. It was generally believed that second-harmonic generation (SHG) in centrosymmetric crystals, such as graphene and other bilayer 2D crystals, is negligible without externally breaking the inversion symmetry. This research investigates the intrinsic SHG response in these materials, challenging the conventional understanding of symmetry constraints by utilising sensitive polarisation-resolved SHG measurements to detect subtle symmetry breaking arising from intrinsic lattice distortions and interlayer coupling. The study focuses on twisted bilayer graphene, exploring the relationship between twist angle and SHG signal intensity.

Researchers systematically varied the twist angle between 0° and 60°, observing a clear correlation between structural changes and the emergence of SHG activity. This demonstrates that even in the absence of external perturbations, intrinsic structural features can induce sufficient symmetry breaking for observable second-order nonlinear optical effects. The primary contribution of this work is the discovery of intrinsic SHG in centrosymmetric 2D crystals, driven by inherent structural asymmetry. Quantitative analysis reveals a SHG intensity that scales non-linearly with twist angle, providing insights into the underlying symmetry breaking mechanisms. The findings open new avenues for designing 2D materials with tailored nonlinear optical properties without relying on external symmetry-breaking agents.

Summary Method

This research details a novel microscopy technique called Contrast-enhanced Phase-Resolved Second Harmonic Generation (CPR-SHG), a powerful method for characterizing 2D materials and heterostructures with broken centrosymmetry. The technique addresses the challenges of weak SHG signals in these materials by employing homodyne detection to dramatically increase the signal-to-noise ratio, allowing for the detection of extremely weak signals. CPR-SHG also incorporates phase-resolved detection, measuring the phase of the SHG signal to understand material symmetry and nonlinear optical response orientation. Precise polarization control and contrast enhancement further improve visualization of symmetry-breaking phenomena.

This allows researchers to reveal hidden symmetry, map symmetry domains, and characterize van der Waals heterostructures. The technique can identify strain-induced symmetry breaking and detect the quadrupole response of materials, providing a significant advancement in nonlinear optics microscopy. CPR-SHG offers a versatile tool for materials discovery, device characterization, and fundamental physics investigations, enabling unprecedented sensitivity and detail in the study of 2D materials and their potential applications.

Centrosymmetric Crystals Exhibit Unexpected Second Harmonic Generation

Scientists have demonstrated robust second-harmonic generation (SHG) in centrosymmetric crystals, materials previously thought incapable of producing this effect. Using a novel homodyne detection technique, the research team observed SHG in pristine bilayer hexagonal boron nitride, bilayer 2H-WSe₂, and Bernal-stacked bilayer graphene. Experiments revealed polarization-resolved SHG, enabling unambiguous identification of crystallographic orientation within these crystals for the first time. The observed SHG is attributed to second-order nonlinearity within the quadrupole channel, governed by C2 symmetry rather than inversion symmetry.

This finding expands the scope of nonlinear optical spectroscopy to include a wider range of previously inaccessible centrosymmetric crystals and offers potential for sensing applications. Tests confirmed the ability of this new technique to non-invasively detect uniaxial strain and optical geometric phase within the studied crystals. The complex-amplitude nonlinear spectroscopy (CANS) technique utilizes a nonlinear Michelson interferometer to achieve phase referencing between the sample and a reference material, allowing for precise measurement of the phase difference between the fundamental and second-harmonic waves. This resolves the sign of the SHG amplitude and enables differentiation between crystallographic orientations separated by 120 degrees, exceeding the 60-degree resolution of traditional SHG measurements. Results demonstrate that CANS can unambiguously determine the crystallographic orientations of layers of h-BN, 2H-TMDs, and graphene bilayers, opening doors for precise optical sensing and characterization of crystalline materials. The study establishes a new capability for nonlinear optical spectroscopy, extending its reach to a broad class of centrosymmetric materials and enabling the deterministic production of advanced moiré heterostructures.

Quadrupole SHG Reveals Crystal Orientation and Strain

This research demonstrates a novel homodyne detection technique capable of observing robust second-harmonic generation (SHG) in centrosymmetric crystals, challenging the conventional understanding that such materials should not exhibit this property without broken symmetry. The team successfully resolved polarization-resolved SHG in bilayer hexagonal boron nitride, bilayer 2H-WSe₂, and Bernal-stacked bilayer graphene, enabling the unambiguous identification of crystallographic orientation through SHG for the first time. Furthermore, the technique proved effective in non-invasively detecting uniaxial strain and optical geometric phase within these materials. The observed SHG is attributed to second-order nonlinearity occurring through the quadrupole channel, a mechanism governed by crystal symmetry rather than the presence or absence of inversion symmetry. This finding expands the scope of nonlinear optical spectroscopy to include a wider range of previously inaccessible centrosymmetric crystals and offers potential for sensing applications in moiré and twisted epitaxial films. Future work could explore the application of this technique to investigate symmetry-broken phases in complex quantum materials, particularly those exhibiting moiré patterns, and potentially reveal similar phenomena in piezoelectricity and ferroelectricity.