Quantum interference directed chiral Raman scattering in two-dimensional enantiomers

The study investigates whether quantum interference between different Raman scattering pathways can generate chiral Raman responses in two-dimensional materials. While Raman frequencies reveal structural information, intensities are governed by electron–photon and electron–phonon interactions and can be modulated by interference among elementary pathways. Prior observations of quantum interference in Raman scattering have been limited and challenging. Rhenium dichalcogenides (ReX2, X = S or Se) possess triclinic symmetry and strong in-plane anisotropy due to distorted Re2 parallelograms. Previous work reported chiral Raman effects in thick ReS2 flakes, but the microscopic mechanism involving electron/photon/phonon interactions remained unclear. This work explores monolayer ReS2 and ReSe2, aiming to uncover the physical origin of chiral Raman scattering under circularly polarized excitation and to determine the role of inter-k quantum interference in producing circular intensity differences across Raman modes and excitation energies.

- Quantum interference effects in Raman scattering have been reported in electrostatically doped graphene and few-layer MoTe2, including resonance and antiresonance phenomena that modulate Raman cross-sections. - Rhenium dichalcogenides exhibit anisotropic properties (carrier mobility, photoluminescence, Raman) due to triclinic symmetry and Re2 structural distortions. - Prior chiral Raman scattering was observed in thicker ReS2 flakes where anisotropic optical effects contribute significantly. However, the fundamental microscopic interactions responsible for chirality in the monolayer limit were not established. - Planar chirality can arise in 2D systems when enantiomers confined to a plane cannot be interconverted by rotations within the plane; layered ReS2 on a substrate exhibits planar chirality despite being achiral in 3D due to inversion symmetry in the bulk.

Experimental: Monolayer ReS2 and ReSe2 were mechanically exfoliated onto fused silica substrates. Monolayer regions were identified by optical microscopy and thickness confirmed by AFM (monolayer ReS2 ~1.1 nm). Chiral Raman measurements employed a quarter-wave plate (QWP) to generate left- (LCP) or right-handed (RCP) circularly polarized excitation; scattered light passed through the same QWP and was collected without an analyzer. Raman spectra were recorded at room temperature using a JY Horiba HR800 system with 1.96 eV and 2.33 eV lasers, 100× objective (NA 0.9), and 1800 lines/mm grating. The QWP rotation angle was varied to map polarization dependence and extract circular intensity differences (CID). Planar enantiomer orientations, ReX2(+) and ReX2(−), were identified by ADF-STEM imaging, highlighting Re2/Re4 parallelogram orientation. STEM: ReS2 flakes were transferred onto SiNx grids via PPC/PDMS stamping, baked at 110 °C for adhesion, followed by PPC removal in acetone (24 h). ADF-STEM images were acquired on an FEI Titan Cubed Themis G2 300 kV microscope (convergence semi-angle 21.3 mrad; ADF collection 39–200 mrad; probe current 8 pA; dwell time 2 μs/pixel). Theory and computation: First-order Raman intensities and Raman tensors as functions of phonon energy and laser energy were computed using third-order perturbation theory. Calculations distinguished three cases: (i) full interference including inter-k and intra-k pathways; (ii) intra-k interference only (between different excited states at the same k); and (iii) no interference. Electronic band structures and phonon dispersions for monolayer ReS2 were obtained using QUANTUM ESPRESSO with LDA and norm-conserving pseudopotentials. Electron–phonon coupling matrix elements were computed using Wannier interpolation via EPW. k-point sampling used Monkhorst-Pack grids of 9×9×1 (electrons) and 5×5×1 (phonons), with an energy cutoff of 150 Ry, vacuum spacing of 20 Å, and structural relaxation until forces < 1e-5 Ry/Bohr and stress < 0.01 kbar. Matrix elements were interpolated on a 45×45×1 grid. DFT provided eigenvectors of Raman-active modes. Raman selection rules and tensors were evaluated to relate tensor elements to LCP/RCP intensities for the two enantiomeric orientations; mirror-related tensors predict opposite chiral responses (Δ(+) = −Δ(−)).

- Monolayer ReS2 exhibits strong chiral Raman response under circularly polarized excitation, with mode- and energy-dependent circular intensity differences (CID = (IR − IL)/(IR + IL)). - For 2.33 eV excitation in 1L ReS2, CID values for modes I–VI are 0.49, 0.33, 0.18, −0.05, 0.27, and −0.16, respectively (modes at ~132, 143, 153, 162, 212, and 235 cm−1). - For 1.96 eV excitation, mode III (153 cm−1) shows CID ≈ −0.43 and mode VI (235 cm−1) shows CID ≈ 0.34; other modes show negligible or smaller chirality at this energy. - The chiral response depends on the enantiomeric orientation: ReS2(+) and ReS2(−) show opposite trends in polarization-resolved maps and polar plots, consistent with Δ(+) = −Δ(−). - Theoretical calculations indicate identical optical absorption intensities across k-space for LCP and RCP; thus circular dichroism in absorption is absent. However, k-resolved phase distributions of complex transition amplitudes differ between LCP and RCP, producing distinct inter-k interference and thus chiral Raman intensities. - Only when full inter-k interference is included do simulations reproduce large CIDs and their excitation-energy dependence; intra-k interference alone or no interference cannot account for the observed chirality. - Similar chiral Raman phenomena are observed in monolayer ReSe2, with excitation-energy and orientation-dependent LCP/RCP intensity differences for specific modes (e.g., 119 cm−1 and 162 cm−1), and opposite polar patterns for ReSe2(+) versus ReSe2(−).

The findings demonstrate that chiral Raman scattering in monolayer triclinic ReX2 arises from quantum interference among first-order Raman pathways at different k-points. Although LCP and RCP excitations have the same absorption strength, they imprint different k-dependent phases on the electronic transition amplitudes, leading to constructive or destructive interference across k-space that depends on phonon mode and excitation energy. This mechanism explains the substantial, mode-specific CIDs and their inversion with crystal enantiomeric orientation. The approach bridges microscopic electron–photon–phonon interactions with macroscopic chiral Raman observables and suggests that such interference-driven chirality is a general feature of inelastic light scattering in materials when the excitation exceeds the bandgap and interference pathways dominate.

This work establishes chiral Raman spectra as a manifestation of quantum interference in monolayer triclinic ReS2 and ReSe2 enantiomers. Large, mode- and energy-dependent circular intensity differences are observed experimentally and quantitatively captured by first-principles-based perturbative calculations that include full inter-k interference. The enantiomer-dependent sign inversion of chirality follows directly from symmetry-related Raman tensors. These results provide a pathway to induce and control chiral optical responses via quantum interference in other two-dimensional and bulk materials. Future research could explore tuning interference through doping, strain, or dielectric environment, extending to different materials systems and higher-order scattering processes.

- The quantitative analysis for bulk triclinic crystals requires consideration of additional anisotropic optical effects beyond those in monolayers. - The pronounced interference-driven chiral response becomes evident when the excitation photon energy exceeds the material bandgap; behavior outside this regime was not explored in detail. - Optical birefringence effects are neglected for monolayers due to their ~1 nm thickness, an assumption that may not hold for thicker samples or complex substrates.