Disordered Materials Retain Stability Despite Broken Symmetry Rules

Scientists at KTH Royal Institute of Technology, led by Bikram Pain, have conducted a detailed investigation into Anderson localisation within disordered one-dimensional systems, revealing a notable resilience to perturbations in time-reversal symmetry. Their analytical work demonstrates a correlation-induced algebraic localisation that remains stable even when time-reversal symmetry is partially compromised. The research elucidates a clear transition between localisation and delocalisation, driven by the complex interplay between long-ranged correlated hopping, where the probability of an electron moving between sites depends on the distance between them, and the degree to which time-reversal symmetry is disrupted. This symmetry, fundamental in quantum mechanics, dictates that the laws of physics should remain the same if time were reversed. The study details how the breaking of this symmetry impacts the behaviour of electrons in disordered materials, and importantly, establishes a shift from subdiffusive to diffusive behaviour in wavepacket spreading as time-reversal symmetry is broken, offering new insights into the dynamics of these complex systems. Anderson localisation, a phenomenon where electrons become trapped due to disorder, is crucial for understanding the behaviour of materials and has implications for the development of novel electronic devices.

Wavepacket dynamics shift from subdiffusion to diffusion with broken time-reversal symmetry

A distinct transition in wavepacket spreading occurs, with the mean-squared displacement transitioning from subdiffusive to diffusive behaviour when time-reversal symmetry is broken; this occurs for any finite value of the time-reversal-symmetry-breaking parameter. Previously, establishing this precise change in wavepacket dynamics proved challenging due to the difficulty in disentangling the effects of correlated hopping and time-reversal symmetry. Wavepackets, representing the probability distribution of a particle, are used to model the propagation of quantum information. Subdiffusion describes a slower-than-normal rate of spreading, while diffusion represents standard spreading governed by Brownian motion. Researchers observed a distinct transition in wavepacket spreading, with the mean-squared displacement transitioning from subdiffusive to diffusive behaviour when time-reversal symmetry is broken. The findings clarify a direct link between these two factors, revealing how the disruption of time-reversal symmetry fundamentally alters the propagation of quantum information within disordered systems. Researchers validated these findings by examining wavepacket spreading at various disorder strengths, characterised by the parameter ‘a’, which governs the decay of hopping amplitudes with distance. Specifically, the hopping amplitude between sites decays as 1/r^a, where r is the distance between the sites. Analysis of the second moment of the wavepacket’s position revealed ballistic spreading, meaning initial expansion proportional to time, for values of ‘a’ less than 3/2. This indicates that the wavepacket initially expands rapidly before being constrained by the disorder. A system-size dependent prefactor diminishes when delocalized states are suppressed at ‘a’ greater than or equal to 3/2, signifying a change in the dominant mechanism governing wavepacket propagation. Detailed calculations demonstrated that the contribution from interactions between delocalized states scales as N^3-2a, where N represents the system size, providing a quantitative understanding of the transition.

Correlated electron behaviour shifts with minimal time-reversal symmetry disruption

Understanding electron behaviour within disordered materials is central to developing next-generation electronics and quantum technologies. The interplay between electron interactions, specifically correlated hopping where electrons influence each other’s movement, and the breaking of time-reversal symmetry, a concept relating to the direction of electron flow, is now better understood. Correlated hopping arises because electrons, being fermions, obey the Pauli exclusion principle, influencing the probability of other electrons occupying nearby sites. Researchers demonstrated that a strong form of electron confinement, algebraic localisation, persists until a critical point, proving surprisingly durable to disruptions in time-reversal symmetry. Algebraic localisation implies that the probability of finding an electron decays as a power law with distance, rather than exponentially as in typical localised systems, allowing for some degree of mobility. This resilience is particularly significant as it suggests that certain quantum properties can be maintained even in the presence of imperfections or external influences that break time-reversal symmetry.

This durability arises from the interplay between electron interactions and the long-range nature of their movement. The long-range correlated hopping allows electrons to ‘communicate’ over larger distances, effectively mitigating the effects of disorder. However, beyond a certain level of disruption to this symmetry, electrons inevitably spread out, transitioning to a delocalised state. The research establishes a localization-delocalization transition governed by the interaction between long-ranged correlated hopping and time-reversal symmetry breaking, demonstrating that even a minor alteration to time-reversal symmetry can fundamentally alter how electrons move within materials. This transition is not abrupt but rather a gradual shift in behaviour, with the degree of localisation decreasing as the time-reversal symmetry breaking parameter increases. Further investigation focused on the precise mechanisms driving this transition, revealing that collective electron behaviour maintains algebraic localisation even when the symmetry is partially broken. This suggests that the system can adapt to a certain degree of disorder and maintain some level of quantum coherence, which is essential for many quantum technologies. The findings have implications for the design of robust quantum devices that are less susceptible to environmental noise and imperfections.

The research demonstrated that a form of electron confinement, termed algebraic localisation, is robust to disruptions in time-reversal symmetry until a critical point is reached. This is significant because it suggests that quantum properties can be maintained even with imperfections or external influences. Researchers found that a transition from localisation to delocalisation occurs as the degree of time-reversal symmetry breaking increases, altering electron movement within materials. They investigated this transition by observing the behaviour of wavepackets and found a shift from subdiffusive to diffusive movement with even a small alteration to time-reversal symmetry.