A Master’s Project that Could Solve One of Physics’ Most Important Problems
The publication released recently in Proceedings of the National Academy of Sciences (PNAS) of the United States of America finds its source in a risky master’s project and ends with what may ultimately be the key to one physics’ most important problems: the mechanism of superconductivity in high-temperature superconductors.
Nicolas Kowalski arrived from Paris in April 2019 in freezing, snowy weather. He set out to explain the experimental observation of a correlation between the maximum temperature, at which superconductors formed from copper oxide become superconductors, and the probability that the electrons are on the oxygens rather than the coppers. The project was risky because it relied on the modification and use of a program developed by Patrick Sémon, when he was at Sherbrooke, based on a methodology different from those found in books on solid state physics. This methodology sometimes causes surprises since it comes up against enormous computation times in certain ranges of microscopic parameters.
Nicolas’ simulations finally found the correlation mentioned above. However, the range of parameters accessible to the calculations did not correspond exactly to the one that theoretically characterizes copper oxide superconductors.
“We used a method called Quantum Monte Carlo in continuous time. This method allows us to access the properties of materials at a non-zero temperature but brings some inconveniences. One of them, called the sign problem, comes from the fact that this type of algorithm tends to be less accurate, especially at low temperature and near phase transitions of the material. In some parameter regions – and in particular in the one corresponding to real materials – to reach a sufficient accuracy and to have exploitable results, it would be necessary to run the simulation program during an excessively long time. To overcome this problem, we chose microscopic parameters which corresponded to an idealized vision of the structure of copper oxides and allowed us to get rid of this sign problem,” says Nicolas.
This is where Sidhartha Dash and his thesis supervisor, David Sénéchal, joined the team. The approach developed by David Sénéchal allows to gauge the strength of superconductivity at zero temperature, which is a good measure of the transition temperature. This approach is applicable in the whole range of microscopic parameters.
David Sénéchal’s approach gave results consistent with those of Nicolas and allowed to explore the range of more physical parameters. This approach also allowed to demonstrate another experimentally observed correlation between the strength of superconductivity and the energy needed to add a second electron to the copper. More importantly, it showed the physical reasons why this correlation and the previous one are still connected.
“We found that the probability of electron occupation in oxygen orbitals is entirely controlled by the energy required to add a second electron in the copper orbitals. This energy also determines the effective super-exchange interaction between the copper orbitals, which is known to play a role in controlling the transition temperature. We also verified that this super-exchange controls the superconducting strength in our computations. Thus, we found that ultimately this super-exchange is behind the observed correlation between the electron occupation in oxygen orbitals and the transition temperature,” explains Sidharta.
However, one mystery remained: the strength of superconductivity depended on the strength of the chemical bond between copper and oxygen (covalency). This covalency is an important element that determines the value of the so-called super-exchange interaction, which in turn, thanks to neutron scattering experiments, had been found to determine the value of the superconducting transition temperature. “The calculations thus confirmed the determining role of covalency.”
Thus, three apparently distinct experiments concerning the maximum superconducting transition temperature are linked and explained in Oxygen hole content, charge-transfer gap, covalency, and cuprate superconductivity. The strength of the covalent bond between copper and oxygen is thus an important element that explains why copper is the only transition metal leading to high temperature superconductivity. This understanding of the mechanism leading to high-temperature superconductivity opens the way to the design of new materials with even higher transition temperatures. It was worth the effort and, thanks to this collaboration between IQ members, a good part of the mystery is solved.
In the quasi two-dimensional infinite lattice at the top, the atoms are represented by spheres and sticks. In the lattice dynamic mean field method, the cluster at the bottom of the figure is solved in a self-consistent way with the infinite lattice. The orbitals that are taken into account appear on this cluster. At the corners, the d-orbitals of copper and, on the links, the p-orbitals of oxygens. The electron wave function has a large amplitude in these orbitals when there is a strong repulsion on the coppers. Thus, the oxygens become witnesses that tell us about the strength of the interactions and the ultimate origin of the pairing mechanism leading to superconductivity.