When Cubic Is Not Isotropic: Phonon-Exciton Decoupling in CuInSnS$_4$ Single Crystals

Abstract

Atomic-scale disorder can create hidden optical anisotropy even in crystals that are structurally cubic on average. Here, we show that CuInSnS$_4$ single crystals host locally symmetry-broken environments arising from intrinsic In/Sn cation disorder, which affect vibrational and excitonic properties in markedly different ways. Combining polarization- and temperature-dependent Raman spectroscopy, infrared near-field microscopy, steady-state and time-resolved photoluminescence, and first-principles calculations, we find that phonons remain largely symmetry-averaged and locally homogeneous on the nanoscale. In contrast, photoluminescence reveals a lower-energy band-tail emission with pronounced polarization anisotropy following a well-defined angular symmetry, highlighting the strong sensitivity of excitonic states to local symmetry breaking. This phonon-exciton decoupling reveals that intrinsic disorder can localize excitons while preserving vibrational coherence and dielectric homogeneity, thereby opening new opportunities for polarization-sensitive light sources, anisotropic photodetectors, and exciton-based optical functionalities even in nominally cubic multinary semiconductors.

Figures (8)

• Figure 1: Hidden anisotropy in a cubic structure of CuInSnS$_4$. Although the average crystal structure is cubic, phonons and excitons sense disorder in different ways. (a) Phonon modes reflect a symmetry-averaged lattice response consistent with the cubic structure. (b) In contrast, localized excitons are sensitive to local symmetry breaking associated with cation disorder and exhibit a preferred orientation. (c,d) The corresponding schematics illustrate an effectively isotropic vibrational response (c) and a pronounced anisotropic excitonic response (d) in CuInSnS$_4$.
• Figure 2: Synchrotron X-ray diffraction patterns of CuInSnS$_4$ obtained from crushed single crystals and reference peak positions for different structural models. The experimental diffraction pattern (black dots) is well described by an average cubic spinel structure ($Fd\bar{3}m$). Vertical marks indicate Bragg peak positions for an ordered octahedral Imma structure (purple), a disordered Imma-derived supercell (orange), and a disordered cubic $Fd\bar{3}m$ structure (blue), highlighting the limited sensitivity of conventional XRD to In/Sn ordering. The inset shows an optical image of the CuInSnS$_4$ single crystal used in this study.
• Figure 3: Structural models and lattice dynamics of CuInSnS$_4$. (a) Experimentally refined average cubic spinel structure (Fd$\bar{3}$m) obtained from XRD. (b) DFT-optimized ordered octahedral structure with Imma symmetry. (c) Disordered supercell derived from the Imma structure, with In and Sn quasi-randomly distributed over octahedral sites while preserving the cubic structure on average. (d,e) Calculated phonon dispersions and atom-projected phonon density of states (PDOS) for the ordered Imma structure and the disordered supercell, respectively.
• Figure 4: Multi-wavelength excitation-dependent Raman measurements of CuInSnS$_4$. (a) Schematic illustration of the excitation-wavelength-dependent penetration depth in CuInSnS$_4$, calculated from the absorption spectrum. (b) Raman spectra of CuInSnS$_4$ measured using 785, 532, 488, 405, and 325 nm excitation wavelengths, showing the evolution of first-order and higher-order phonon features with excitation energy. Representative deconvolution of the spectra is indicated in the Raman spectrum measured with 532 nm excitation. Vertical lines indicate the experimentally extracted peak positions (EXP) and the DFT-calculated phonon mode frequencies (DFT), as indicated in the bottom panel. The full list of DFT-calculated phonon modes, including their frequency and relative intensity, is given in Table S3 in the Supporting Information.
• Figure 5: Schematic illustration of the polarized Raman scattering geometry used in this work. Polarization-dependent Raman measurements were performed in backscattering configuration on the (010) basal plane, with the incident laser beam propagating normal to the surface. The polarization direction of the incident light $\hat{e}_i$ was rotated with respect to the crystallographic axes, while the scattered light was analyzed in parallel ($\hat{e}_i \parallel \hat{e}_s$) and crossed ($\hat{e}_i \perp \hat{e}_s$) configurations, as indicated by the blue and orange arrows, respectively. The crystallographic orientations are marked, and the atomic structure of CuInSnS$_4$ is shown for reference, with Cu, In/Sn, and S atoms indicated by different colors.