Design Principles for Negative Thermal Expansion in Two-Dimensional Materials

ConspectusNegative thermal expansion (NTE) is a counterintuitive property in metamaterials that can be observed upon excitation of certain low-frequency vibrational modes. Conventional materials expand upon heating, showing positive thermal expansion (PTE), whereas NTE materials contract, which is unusual. NTE challenges conventional lattice-dynamical concepts and is of significant importance for a wide range of applications such as in composite material for dental filling, glass-ceramic cooktops, etc. Over the past three decades, major efforts have focused on discovering and tuning NTE compounds. NTE has been reported in a wide range of materials in bulk and low-dimensional systems. To date, the vast majority of experimentally and theoretically identified NTE materials belong to bulk crystalline systems, whereas discovery of two-dimensional (2D) NTE systems is limited. Nevertheless, this phenomenon is remarkably amplified due to reduced dimensionality, enhanced anharmonicity, and unconventional phonon dynamics. Quantum confinement alters electronic, optical, mechanical, and thermal properties significantly in these systems. They sustain large NTE over exceptionally wide temperature ranges, often attributed to rigid-unit modes (RUMs) in framework structures. NTE in 2D materials can arise from several mechanisms including flexural phonons, structural transition, anisotropic bonding, conformational changes, geometric flexibility, electronegativity differences, spin-crossover, etc. We demonstrate a comprehensive and mechanism-oriented overview of NTE in 2D materials, encompassing elemental monolayers such as in graphene and graphyne analogues, h-boron nitride, transition-metal dichalcogenides, metal phosphides, arsenides and other emerging 2D materials. Beyond intrinsic mechanisms, we discuss tunability strategies unique to atomically thin systems, including pore size modulation, heteroatom substitution, defect modification, and magnetic or electronic-state control. Recent studies link NTE in 2D materials to phonon transport and topology-driven lattice responses and reveal trade-offs between thermal expansion and lattice thermal conductivity (TC). Most low-TC 2D systems exhibit pronounced NTE and vice versa. Spontaneous symmetry breaking in 2D-materials is associated with pseudo Jahn-Teller (PJT) distortions. The machine-learning (ML)-based predictions highlight the strong structural dependence of NTE in 2D materials. Despite growing interest in NTE materials across diverse applications, rational structural design and controlled tuning of lattice expansion remain challenging. This Account assesses current limitations and outlines future directions based on high-throughput calculations, ML, and topology-guided design for realizing enhanced NTE in 2D systems.