Towards the solution of the many- electron problem in real materials

Iron chalcogenides are a recently discovered family of superconductors. Professor Sandro Sorella of SISSA planned to investigate the nature of their superconductivity in a PRACE project, but soon realised that this would be impossible due to unforeseen factors. Instead, the project focused on investigating different methods for carrying out such simulations.

The discovery of iron-based high- temperature superconductors (FeSCs) in 2008, 20 years after the first discovery of high-temperature superconductivity in the cuprate family, has provided further evidence that a new theoretical framework is needed to understand this effect. New simulation techniques are needed to reproduce the present experimental results, with the final goal of being able to predict new superconducting materials for potential commercial applications using simulations.

Professor Sandro Sorella of SISSA in Italy has been leading a PRACE-supported project titled “HTESO-High Temperature Superconductivity in the iron chalcogenides family: a quantum Monte Carlo study”. The original aim of this project was to systematically study a number of materials in the iron chalcogenide family, with particular attention on iron selenide (FeSe). The iron chalcogenides have a simpler geometrical structure than iron pnictides, the first group of FeSCs to be discovered, but retain all the interesting properties of other FeSCs. This peculiarity makes chalcogenides a perfect laboratory for studying unconventional superconductivity both theoretically and experimentally.

The properties of iron chalcogenides cannot be explained easily using current techniques, as Sorella explains. “Near field theory cannot be used, so instead people tend to use density function theory, a computational quantum mechanical modelling method used to investigate the electronic structure of many-body systems. However, there are some limitations.

“For several years now, we have been trying to reach beyond the incredible success afforded by density functional theory and capture electron correlation effects with sufficient accuracy across different physical parameter regimes.”

Spin density from QMC calculations of nonacene, which reveals the spin- edge localisation. Bottom left panel: Contour plot of the spin destiny (the corresponding colour code is in the top-right box). Top left panel: Spin destiny projection on the long axis of the molecule. Bottom right panel: Spin destiny projection on the short molecule axis.

One of the grand challenges in modern science is the accurate treatment of interacting many-electron systems. In condensed phase materials, the challenge is increased by the need to account for the interplay between the electrons and the chemical and structural environment. Progress in addressing this challenge will be fundamental to the realisation of “materials genome” or materials by design initiatives.

The original aims of the project were to elucidate the connection between magnetism and superconductivity in bulk iron selenide by performing accurate first-principle calculations of the electron pairing function in the presence of collinear anti-ferromagnetism. On the other hand, the researchers were to investigate single layer iron selenide, as it has a remarkable record critical temperature in the 40-80K range on SrTiO3 and other polar substrates. Finally, Sorella and his colleagues were to investigate iron telluride (FeTe). Despite its structural similarity to iron selenide, it has different properties, with a long-range antiferromagnetic order at ambient conditions and no superconductivity. The project aimed to explore what the physical reasons behind this difference are.

However, the ambitious aims of the project were thwarted near the beginning of the project when Sorella and his group realised that there were a number of factors that would make their goals impossible to achieve at this point. “For instance, we realised that superconductivity in iron chalcogenides is mainly due to spin fluctuations. In order to study this, we would have had to simulate many more electrons than is possible at the moment, as spin fluctuation is an effect which involves many atoms.”

“Being provided with the possibility of using several thousand processors at once allows us to make huge amounts of progress in a short space of time”

So, Sorella and his colleagues instead carried out a comprehensive investigation of a simpler system of a hydrogen chain, deploying a vast suite of cutting-edge many-body numerical methodologies and obtaining a detailed and quantitative understanding of current computational capabilities for treating correlated quantum materials.

“Through the synergistic use of complementary methods, we accurately determined the ground-state energy as a function of interatomic distance. This serves as a proof of concept for a new mode of attack on correlated materials by ab initio calculations. The benchmark results will provide a reference on the state of the art in many-body computation of real materials.”

The study captured many of the salient features of predictive computations in real materials. The ability of each many-body method to correctly capture important physical properties depends on the material system under study. More benchmark studies of this kind will be highly desirable to broaden the understanding and identify further limitations as well as opportunities of development.

The computational cost of each method depends on various factors, including the degree to which the algorithm and codes have been optimised, the level to which one wishes to take the calculation (the order in perturbative or diagrammatic methods, or the statistical accuracy in Monte Carlo methods),

The benchmark results indicate that many of the methods tested were capable of reaching an accuracy of 5% of the cohesive energy or better, across wide parameter regimes of strong electron correlation.
A subset of these methods, among which the quantum Monte Carlo method was developed by Sorella and his team, predicts the equation of state systematically to sub-milli-Hartree accuracy. Further development may turn these into post-density functional theory methods of choice for ground-state studies, and a concerted effort to build open-source codes will be invaluable.

The PRACE allocation was extremely important for Sorella and his team as it provided them with a huge amount of computing power. “The techniques we are using are among the most accurate in existence, but are computationally very demanding,” he explains. “Being provided with the possibility of using several thousand processors at once allows us to make huge amounts of progress in a short space of time.”

For more information
Resources awarded by PRACE
Sandro Sorella was awarded 50 000 000 core hours on MARCONI hosted by CINECA, Italy