Local structural disorder in crystalline materials

TL;DR

This Perspective addresses local positional disorder in soft, anharmonic materials, challenging conventional monomorphous crystalline models in predicting electronic, vibrational, and transport properties. It advocates polymorphous and anharmonic frameworks to explicitly account for local symmetry breaking and to recalibrate electron-phonon interactions and phonon dynamics. The authors review and synthesize methods such as ASDM, SCP, TDEP, SSCHA, and related approaches, showing that including local disorder yields band-gap openings, strongly overdamped phonon spectra, and substantial band-gap renormalization with temperature. They propose integrating these frameworks with first-principles simulations and machine-learning force fields to enable predictive modeling for energy materials, while outlining current limitations and a roadmap for future experimental–theoretical validation.

Abstract

Local positional disorder in soft, anharmonic materials has emerged as a central factor in shaping their electronic, vibrational, optical, and transport properties. Viewed mainly as a source of performance degradation, recent theoretical insights reveal that local disorder profoundly influences the electronic structure and phonon dynamics, without inducing deep electronic traps or non-radiative recombination pathways. In this work, we highlight advances in modeling local disorder using polymorphous and anharmonic frameworks, showing how these methods explain experimental observations and predict new trends. We emphasize the role of disorder in the breakdown of the phonon quasiparticle picture and in modulating electron-phonon and phonon-phonon interactions, particularly in soft, anharmonic phases of matter, with significant effects on electrical and thermal transport. We outline opportunities for integrating these insights into predictive modeling for energy materials and propose combining advanced first-principles methods with machine learning.

Figures (4)

• Figure 1: Impact of local disorder on the electronic structure. (a) Schematic representation of the PES illustrating the high symmetry and locally disordered structures, and the corresponding energy lowering $\Delta U$. (b) Locally disordered (polymorphous) structures of cubic CsPbI$_3$ and CsSnI$_3$ obtained by the ASDM using a $4\times4\times4$ supercell and DFT geometry optimization. (c) Average DFT charge densities of high symmetry and locally disordered cubic CsSnI$_3$. (d) DFT electron spectral function of polymorphous CsSnI$_3$ calculated by band structure unfolding Zacharias2020. The band structure of the monomorphous model is shown as red. The band gap opening due to local disorder is $\Delta E_{\rm g} = 0.56$ eV. Data are from Refs. Zacharias2023npjZacharias2025b
• Figure 2: Impact of local disorder on structural and vibrational properties. (a) Calculated XRD patterns of monomorphous and polymorphous cubic SrTiO$_3$ compared to experiment. Reproduced from Ref. Zhao2021, copyright (2021), with permission from Elsevier. (b) Calculated PDF of monomorphous and polymorphous cubic MAPbI$_3$ compared with experiment. Reproduced with permission from Ref. Zhao2020, copyright (2020) by the American Physical Society. (c) Phonon spectral function of polymorphous CsPbI$_3$ obtained by phonon unfolding. Data extracted from Ref. Zacharias2023npj. (d) Phonon energies in reciprocal space measured for MAPbBr$_3$ with inelastic neutron scattering. Figure adapted from Ref. Ferreira2020 under CC BY 4.0. (e) Calculated Raman spectra of CsPbBr$_3$ by MD compared to experimental measurements. Reproduced with permission from Ref. Yaffe2017, copyright (2017) by the American Physical Society. (f) Calculated phonon DOS of monomorphous and polymorphous cubic Cu$_2$Se compared with experiment. Data from Ref. Wang2025.
• Figure 3: Impact of local disorder on electron-phonon coupling. (a,b,c) Locally disordered structure and diagrammatic representation of loop diagram contributing to temperature-dependent anharmonicity and the basic electron-phonon coupling process. Lines represent electrons with wavector ${\bf k}$ and ${\bf k + q}$ and the zigzag lines the anharmonic phonon. (d,e) Calculated band gap renormalization of monomorphous and polymorphous cubic CsPbI$_3$ and tetragonal/cubic CsPbBr$_3$ by ASDM compared with experiment. Data taken from Refs. Zacharias2025bZacharias2023npj. (f) Calculated electron and hole effective mass of monomorphous and polymorphous cubic CsPbCl$_3$. Data extracted from Ref. Zacharias2025b. Vertical dashed lines indicate temperatures where phase transitions take place.
• Figure 4: Impact of local disorder on transport and polaron formation. (a) Calculated electron mobility of monomorphous and polymorphous cubic SrTiO$_3$ compared with experiment. Reproduced with permission from Ref. Ranalli2024, copyright (2024) by the American Physical Society. (b) Calculated average charge-carrier mobility of orthorhombic MAPbI$_3$ and cubic CsPbI$_3$ compated with experiment. Reproduced with permission from Ref. Ponce2019, copyright (2019) by the American Chemical Society. (c) Polaron charge density in CsPbBr$_3$ calculated by PBE0 in a supercell after adding a negative charge. Figure adapted from Ref. Miyata2017, copyright (2017) by the American Association for the Advancement of Science.