The Kibble-Zurek (KZ) mechanism, which has been experimentally confirmed only for equilibrium phase transitions, is also applicable to non-equilibrium phase transitions, Tokyo Tech researchers now show in a landmark study. The KZ mechanism is characterized by the formation of topological defects during the continuous phase transition away from the adiabatic limit. This groundbreaking finding could open the doors to studying the mechanism for other out-of-equilibrium phase transitions.
Phase transitions describe various phenomena around us, from the transformation of water into ice, through magnetic transitions, to the superconducting transition, where electrical resistance vanishes. In superconductivity and magnetism, the phase transition is continuous, characterized by “symmetry breaking” leading to the formation of an ordered state. The ordered state is perfect (defect-free) when this transition is very slow, a regime called the “adiabatic limit”. For transitions that do not satisfy this limit, however, topological defects appear, the generation of which is described by the Kibble-Zurek (KZ) mechanism. Experimentally, the KZ mechanism manifests itself as a power-law dependence of the defect density on the cooling rate.
Interestingly, although the KZ mechanism has been extensively studied for thermal equilibrium phase transitions, it has not yet been demonstrated experimentally for non-equilibrium phase transitions. However, a recent simulation study has suggested that the KZ mechanism can be applied to dynamic order transitions between disordered and ordered flow states, a phenomenon that can be experimentally tested in superconducting vortex systems.
To this end, a research group from the Tokyo Institute of Technology (Tokyo Tech), Japan, led by Prof. Satoshi Okuma, recently showed that the state of motion of a collection of magnetic fluxes (vortices) permeating a superconductor changes in the non-equilibrium process There is a phase transition from disordered flow to ordered lattice flow, and the lattice defects appear spontaneously in accordance with the KZ mechanism. Their groundbreaking study was published in Physical Review Letters (selected as editorial proposal).
In their work, the team prepared a 330 nm thick amorphous Mo stripe filmxge1−x (x ≈ 0.78) on a silicon substrate and then cooled it down to enable a superconducting transition at 6.3 K. By applying a magnetic field perpendicular to the surface, the vortices were created and experiments were performed at 4.1 K and a field strength of 3.5 T.
The team drove the vortices with a drive current that was increased linearly at different quenching rates (i.e.,I/dt). Upon reaching the quench endpoint, the vortex configuration was frozen by abruptly shutting off the power.
“In our study, we tested the simulation predictions by experimentally examining the configuration order of eddies after the dynamic order as a function of the quenching rate,” explains Prof. Okuma.
The team found that the vortex configuration became less ordered as the quenching rate increased, indicating a phase transition. “We examined the lattice defects that occur during this transition and how they vary with the quench rate,” says Prof. Okuma. “We found that the defect density scales with the quenching rate as a power law, which is consistent with the concentration camp scenario,” he emphasizes. The team additionally estimated the exponent of the power law (≈ 0.4-0.5), which was close to the value predicted by the simulation (0.39).
“We also observed a momentum-adiabatic transition on the ordered side of the transition, another key prediction of the KZ mechanism,” adds Prof. Okuma.
Overall, this study extends the applicability of the Kibble-Zurek mechanism from equilibrium phase transitions to non-equilibrium phase transitions and opens the door to countless new investigations. In view of this landmark result, new developments in the research field of non-equilibrium phase transitions are expected.
Materials provided by Tokyo Technical Institute. Note: Content can be edited for style and length.