An understanding of the phase transitions at the nanoscale is essential in state-of-the-art engineering^1,2,3,4,5, instead of simply averaging the heterogeneous domains formed during phase transitions^6,7. However, as materials are scaled down, the steepness of the phase transition rapidly increases^{8,9,10,11,12,13} and requires extremely high precision in the control method. Here, a three-terminal device, which could precisely control the phase transition electrically^{14,15,16,17,18,19}, was applied for the first time to a scaled-down metal-insulator transition material VO₂. The crossover from continuous to binary transitions with the scaled-down material was clarified, and the critical channel length was successfully elucidated via phase boundary energy. Notably, below the critical channel length, the spatial degrees of freedom degenerated, and the impact of drain voltage application disappeared in the phase transition, indicating zero-dimensionality of the VO₂ channel. This zero-dimensionality could be the fundamental property in the scaled-down phase transition and have a significant impact on various fields that need nanoscale engineering.

在最先进的工程中，了解纳米级的相变至关重要^1,2,3,4,5，而不是简单地平均相变过程中形成的异质域^6,7。然而，随着材料尺寸的缩小，相变的陡度迅速增加^{8,9,10,11,12,13}，对控制方法的精度要求极高。这里，一种可以精确电控制相变的三端器件^{14,15,16,17,18,19}首次应用于按比例缩小的金属-绝缘体过渡材料 VO ₂。阐明了按比例缩小的材料从连续转变到二元转变的交叉，并且通过相界能量成功阐明了临界沟道长度。值得注意的是，低于临界沟道长度，空间自由度退化，并且漏极电压施加的影响在相变中消失，表明VO 2 沟道的零维_性。这种零维性可能是缩小相变的基本特性，并对需要纳米级工程的各个领域产生重大影响。