Silicon atoms on cooled surfaces pair into structures known as dimers. At temperatures above 190 Kelvin (-83 oC), these dimers fluctuate between two tilted states. Below this critical temperature, they settle-or "freeze"-into one orientation, marking a clear phase transition. "They are effectively frozen by this phase transition," said Dr. Gernot Schaller, who leads Quantum Information Technology research at HZDR.
These dimer pairs also influence each other, forming patterns based on the direction of their coupling. Fast cooling-greater than 100 Kelvin per microsecond-leads to one-dimensional zigzag chain formations. Slower cooling allows dimers to organize into two-dimensional domains with a honeycomb structure. "And the slower the cooling, the larger the domains," explained Schaller.
To describe the behavior, researchers used the anisotropic Ising model, which reduces the silicon dimer tilt behavior to a binary system-ideal for modeling phase transitions. Their theoretical findings aligned with actual high-resolution scanning tunneling microscope images, showing both zigzag chains and honeycomb domains.
Prof. Ralf Schutzhold, director of HZDR's Institute of Theoretical Physics, noted that the dimer formations reflect the Kibble-Zurek mechanism. Originally used to describe defect formation in the cooling early universe, this theory was later applied to superfluid helium. Now, it appears to govern behavior in flash-frozen silicon. "The way the silicon dimers behave exhibits parallels with the so-called Kibble-Zurek mechanism," Schutzhold said.
Their work may open new approaches for creating defect-free silicon structures, while also bridging quantum theory, materials science, and cosmology in novel ways.
Research Report:Kibble-Zurek Dynamics in the Anisotropic Ising Model of the Si(001) Surface
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