Physicists from Russia and Brazil Unveil Mystery behind Complex Superconductor Patterns

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The mechanism is described by the Ginzburg–Landau equation at the Bogomolny point

Scientists at HSE MIEM and MIPT have demonstrated that highly complex spatial structures, similar to the intricate patterns found in nature, can emerge in superconductors. Mathematically, these patterns are described using the Ginzburg–Landau equation at a specific combination of parameters known as the Bogomolny point. The paper has been published in the Journal of Physics: Condensed Matter.

One of the most intriguing and not fully understood questions in science is how seemingly simple natural laws give rise to complex patterns, such as zebra stripes or fish scales. 

Scientists have long been trying to understand how such patterns emerge in nature. The first explanation was offered in 1952 by mathematician Alan Turing, one of the founders of computer science. According to Turing, complex patterns arise from the competition between simple interactions within a system. Thus, in chemical reactions, patterns are formed through two main mechanisms: diffusion (the distribution of substances) and autocatalysis (where the reaction accelerates itself). It soon became clear that while the Turing model can also describe the emergence of complex patterns in biology effectively, it does not account for all natural phenomena.

Scientists at HSE and MIPT, in collaboration with physicists at Universidade Federal de Pernambuco, Brazil, found that the formation of complex patterns in nature can also be explained using the Ginzburg–Landau equation that describes how the state of a superconductor changes in response to a magnetic field.

A superconductor is a material that conducts electric current without resistance, meaning there is no loss of electricity. Under the influence of a magnetic field, superconductors can exhibit different behaviours: they can either completely expel the magnetic field or allow it to penetrate their mass, forming spatial structures such as a lattice of vortices.

However, according to the theory of superconductivity, there exists a special combination of superconductor parameters—referred to as the Bogomolny point—where any structure can emerge. In this study, the scientists investigated how a magnetic field changes in response to external conditions near the Bogomolny point.

Alexei Vagov

Co-author of the paper, Professor, MIEM HSE

An infinite variety of intricate configurations, like monsters, lie dormant at the Bogomolny point, waiting to be unleashed as you move away from it. Depending on how you move away from it, certain types of configurations emerge. There are various methods to move away: altering the temperature, adjusting the sample size, initiating an electric current, or stacking two superconductors atop each other. This will produce a vast array of exotic patterns.

For example, structures emerge in superconductors where regions devoid of a magnetic field coexist with regions where the magnetic field forms lattices of vortices. A superconducting film can give rise to extremely exotic patterns resembling the distribution of cases in the COVID-19 pandemic.

Alexei Vagov

Co-author of the paper, Professor, MIEM HSE

Previously, superconductivity was not considered a phenomenon where complex patterns could occur, as a superconductor is a relatively simple physical system. However, it turns out that highly complex magnetic structures can indeed manifest in superconductors. Our research contributes to the current understanding of how complex patterns emerge in seemingly simple systems.

The scientists suggest that the effects observed in superconductors could be used in the development of measuring instruments. For instance, by monitoring changes in configurations within a superconductor, one can gauge the extent of temperature, current, or geometric alterations in the sample.

Vasily Stolyarov

Co-author of the paper, Director, Centre for Advanced Mesoscience and Nanotechnology, MIPT

Research in this field has been ongoing from both theoretical and experimental perspectives, as well as from a technological standpoint. Since 2018, we have been the pioneers in conducting and publishing a series of experimental studies that led to the discovery and description of the process of pattern formation on the mesoscopic scale in ferromagnetic superconductors. Now, we are actively searching for and devising new systems where superconducting patterns can be controlled, thus enabling their application in nanotechnology and nanodevices.