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Superconductivity, the effortless transport of electric charge, has many potential technological applications. Unfortunately, most materials that show superconductive behavior only do so at very low temperatures. An international group of physicists, among which UvA-Institute of Physics researcher Philippe Corboz, has now made important progress in simulating unconventional materials which are superconducting at higher temperatures. Their results were published in Science this week.

Period-8 stripe. Image: B-X. Zheng et al.

One of the grand open problems in physics is understanding high-temperature superconductivity, which was discovered more than 30 years ago in so-called cuprates. Superconductive materials are substances that completely lose their electrical resistance below a certain transition temperature. Typically, these temperatures are close to the absolute zero of the temperature scale, 273 degrees Celsius below zero. In cuprates, however, this temperature is much higher. Understanding the mechanism behind this phenomenon is the key to design new materials with an even higher transition temperature - the ultimate dream would be room temperature - which would pave the way for groundbreaking technological applications.

Computational advances

In early attempts to gain understanding on this issue, it was proposed that a very simple model of interacting electrons moving on a two-dimensional lattice - called the Hubbard model - could capture the relevant physics of high temperature superconductivity. Despite the simplicity of the Hubbard model, it has been one of the major challenges in computational physics to accurately simulate it on a computer, in order to determine what type of ordering of the electrons is realized. However, thanks to major advances in computational methods for quantum many-body systems, the solution of the Hubbard model has recently become within reach.

By combining the latest numerical methods in large-scale simulations, the researchers have now found a definite answer on the ordering, namely a so-called "stripe" state (see image) in which the electron density is not uniform, but modulated in space. Stripes had also been found in previous studies, but not with the required level of precision to distinguish them from solutions with uniform density. The new simulations qualitatively reproduce some of the main features of the stripes observed in the cuprates. At the same time, they show that for a quantitative agreement with real materials, more realistic models beyond the simplest Hubbard model are required.

Period-8 stripe obtained in the simulations. The arrows show the local magnetic moment on each site, and the green dots indicate the local density of electron-holes. A clear vertical stripe pattern is visible in the green dots. Image: B-X. Zheng et al.


The work, which was published in Science this week, demonstrates the power of modern numerical methods. It provides the optimistic perspective that solving more advanced models of the cuprates is within reach. The researchers have high hopes that their techniques are strong enough to fully uncover the mechanism behind high temperature superconductivity in the near future.


B-X. Zheng, C-M. Chung,  P. Corboz, G. Ehlers, M-P. Qin, R. M. Noack, H. Shi, S. R. White, S. Zhang and G. K-L. Chan, Stripe order in the underdoped region of the two-dimensional Hubbard model, Science 01 (Dec 2017) Vol. 358, Issue 6367, pp. 1155-1160. DOI: 10.1126/science.aam7127/.

Link to the online version of the paper