Spatiotemporal observation of quantum crystallization of electrons

Crystallization, the transition from a liquid to a solid state, is a fundamental process across various materials. Typically, this process follows classical dynamics, involving nucleation and growth of crystal seeds. However, the recent discovery of electron glasses and their crystallization in molecular materials raises fundamental questions about the role of quantum mechanics in this process. This study focuses on the crystallization of Coulomb interacting electrons on charge-frustrated triangular lattices, a system known to exhibit supercooled liquid and glass states with quantum characteristics. The research question is: How does the quantum nature of the electrons influence the crystallization process, which is usually described by classical dynamics and thermodynamics? The importance of this research lies in understanding the fundamental principles governing crystallization, expanding our knowledge beyond the classical framework and potentially impacting diverse fields involving condensed matter physics and materials science. The authors aim to unveil universal features of crystallization applicable across systems while highlighting features unique to quantum systems.

Previous studies on θ-(BEDT-TTF)₂X organic conductors, featuring quasi-triangular lattices, have demonstrated the competitive emergence of charge order (CO) and charge glass (CG) states depending on lattice anisotropy. The CG state, characterized by slow fluctuations and medium-scale correlation, exhibits hallmarks of classical glasses but also reveals an itinerant electron character, suggesting a quantum-classical energetic hierarchy. θ-(BEDT-TTF)₂RbZn(SCN)₄ (θ-RbZn) acts as a key material, exhibiting a transition to CO at ~200 K under slow cooling, while rapid cooling leads to a supercooled charge liquid (SCL) that freezes into CG at low temperatures. Prior investigations using transport and NMR measurements suggested different crystallization profiles, highlighting the unique aspects of this electronic glass former. Recent theoretical work has successfully explained the properties of charge glass through quantum simulations.

The researchers employed Raman microspectroscopy to directly observe the spatiotemporal evolution of electronic crystallization. Specifically, they utilized ¹³C-enriched single crystals of θ-RbZn to enhance the charge sensitivity of the Raman signal by focusing on the charge-sensitive C=C stretching modes (ν₂ mode). The Raman spectra distinguish between CO and SCL/CG states. The time evolution of the Raman spectra was analyzed using a linear combination of CO and SCL/CG spectra to determine the volume fraction of CO (φ) as a function of time. Raman microspectroscopy provided real-space imaging with a spatial resolution of 6.5 µm, allowing the visualization of crystal growth. Experiments were conducted at various temperatures to explore the temperature dependence of the crystallization process. The observation depth was about 1 µm, determined by considering both the microscope's depth resolution and the light's penetration depth in the sample. The Avrami equation was used to model the time evolution of the CO volume fraction (φ), enabling the determination of the Avrami exponent (n) and the rate constant (K). The growth rate (v) was determined by analyzing the time evolution of the Raman images, fitting the data with a phenomenological equation. The temperature dependence of the growth rate was then investigated and compared with theoretical models, such as the Wilson-Frenkel model.

The study's key findings are: (1) Real-space and real-time imaging of electronic crystallization using Raman microspectroscopy revealed distinct crystallization profiles at high and low temperatures. (2) At high temperatures (above the nose temperature of ~165 K), crystallization proceeds via a rapid growth of a single nucleation site. (3) At low temperatures (below 165 K), crystallization occurs more homogeneously, with numerous small nucleation events. (4) The growth rate (v) exhibits a nearly linear dependence on ΔT = Tco - T near Tco and saturates at low temperatures. (5) The experimental growth rates are orders of magnitude faster than predicted by the conventional Wilson-Frenkel model, suggesting a significant role for quantum effects in the crystallization process. (6) Analysis of the Avrami equation indicated two-dimensional crystal growth at lower temperatures. (7) The observed rapid growth is possibly explained by considering the quantum nature of the electrons and the change in wave function behavior between SCL and CO. (8) The speed of sound in the material is much greater than the observed crystallization speed, suggesting that the lattice distortion doesn't control the crystallization rate. Numerical simulations of the charge glass on a rigid lattice support the observed behavior. The experimental results point to the pivotal involvement of quantum effects in the process.

The significantly faster crystallization rate observed compared to conventional models points to a mechanism unique to quantum systems. The quantum nature of the electrons in the SCL or CG state, indicated by moderate conductivity, suggests a significant role for the wavefunction's behavior. While classical crystallization involves particle rearrangement, the transition from SCL/CG to CO involves a substantial shrinking of wave functions and a drastic change in the electronic quantum state. This constitutes a novel form of quantum crystallization. The discrepancy between experimental growth rates and the predictions of the Wilson-Frenkel model, a cornerstone of classical crystallization theory, underscores the limitations of classical models in explaining this quantum phenomenon. The study highlights the influence of the quantum nature of electrons and the significant difference between classical and quantum crystallization mechanisms.

This research successfully utilized Raman microspectroscopy to directly image the spatiotemporal evolution of electronic crystallization, unveiling distinct high and low-temperature crystallization profiles consistent with the nucleation and growth mechanism. The remarkably faster-than-expected growth rate suggests a dominant role for the quantum nature of electrons. This discovery opens new avenues for research into crystallization in quantum systems, motivating future theoretical work to fully elucidate the microscopic mechanism of this fast growth.

The spatial resolution of the Raman microspectroscopy limits the ability to resolve very small nucleation events. The study primarily focuses on one specific material, and the generality of the findings to other quantum systems requires further investigation. The precise role of lattice distortion in the crystallization remains an open question for future research.