Hysteresis and Pattern Formation in Electronic Phase Transitions in Quantum Materials

We furthermore propose new experimental tests based on hysteresis that can distinguish whether any two-dimensional electron nematic is in the XY universality class (as previously proposed in high fractional Landau levels), or in the Ising universality class (as we propose). Given the growing interest in electron nematics in many materials, we expect our proposed test of universality class to be of broad interest.

Whereas the XY model in two dimensions does not have a long-range ordered phase, the addition of uniaxial random field disorder induces a long-range ordered phase in which the spontaneous magnetization points perpendicular to the random field direction, via an order-by-disorder transition. We have shown that this spontaneous magnetization is robust against a rotating driving field, up to a critical driving field amplitude. Thus we have found evidence for a new non-equilibrium phase transition that was unknown before in this model. Moreover, we have discovered an incredible anomaly at this nonequilibrium phase transition: the critical region is accompanied by a cascade of period multiplication events. This physics is reminiscent of the period bifurcation cascade signaling the transition to chaos in nonlinear systems, and of the approach to the irreversibility transition in models of yield in amorphous solids~\cite{reichhardt-dahmen,leishangthem_yielding_2017}. This period multiplication cascade is surprising to be present in a statistical mechanics model, and suggests that the non-equilibrium transition as a function of driving field amplitude is part of a larger class of transitions in dynamical systems.

Moreover, we show that this multi-period behavior represents a new emergent classical discrete time-crystal, since the new period is robust against changes to initial conditions and low-temperature fluctuations over hundreds of driving period cycles.

We expect this work to be of broad interest, further encouraging cross-fertilization between the rapidly growing field of time-crystals with the well-established fields of nonequilibrium phase transitions and dynamical systems.

Geometrical configurations gave us a better understanding of the multi-period behavior of the limit-cycles.

Moreover, surface probes are continually evolving and generating vast amounts of spatially resolved data of quantum materials, which reveal a lot of detail about the microscopic and macroscopic properties of the system.

Materials undergoing a transition between two distinct states, phase separate.

These phase-separated regions form intricate patterns on the observable surface, which can encode model-specific information, including interaction, dimensionality, and disorder.

While there are rigorous methods for understanding these patterns, they turn out to be time-consuming as well as requiring expertise.

We show that a well-tuned machine learning framework can decipher this information with minimal effort from the user.

We expect this to be widely used by the scientific community to fast-track comprehension of the underlying physics in these materials.