SuMo - Superconductivity in the vicinity of Mott insulators

Materials with strong electronic correlations are amongst the most interesting topics at the forefront research in physics. The reason for this is that they exhibit a vast variety of fascinating phenomena with a high potential for applications, but they are still poorly understood by theory. One prototypical example is superconductivity, a pure quantum mechanism causing the electric resistance of a material to suddenly drop to zero upon cooling. In a certain class of superconductors, the so called cuprates, this transition from the metallic to the ideally conducting state can happen at temperatures of -138 C. This is quite remarkable since this temperature is above the boiling point of liquid nitrogen (-195 C), resulting this class of materials to be a perfect candidate for technological applications. On the other hand, the theoretical description of these systems is so challenging that no consistent theory could be established since their first discovery in 1987. Interestingly one can find many of these so-called unconventional superconductors if one introduces impurity atoms into systems, which would be insulators in the undoped configuration. This is quite puzzling, because naively one would think that the best way of achieving small electrical resistivity is by starting from a well conducting compound, i.e., a metal. Furthermore, these systems are not ordinary (band) insulators, but their insulating nature is a result of strong interactions between the electrons. In a certain analogy to a Sumo wrestler, by means of their mutual interactions, the electrons acquire a high mass, so that their ability to move through the crystal is immensely reduced. The description of these highly correlated systems is challenging, because it requires the simultaneous treatment of a high number of (interacting) electrons, making cutting-edge quantum field theories the method of choice. Within the research projects of the Erwin Schrodinger scholarship SuMo - superconductivity in the vicinity of Mott insulators, three systems with rich phase diagrams emerging from the vicinity to a Mott insulating phase will be investigated: the pseudogap phase of the cuprates, the superconducting phases of organic charge transfer salts and ad-atoms on a silicon surface. By analyzing these systems with one of the forefront numerical quantum field theoretical methods currently available, the triply irreducible local expansion method (TRILEX), novel insights for a better understanding of these phenomena are clearly foreseen.

Interactions between a large number of identical quantum particles, such as electrons in a solid, lead to fascinating collective phenomena. Upon changing temperature, pressure or introducing charge carriers, the very same piece of matter may exhibit magnetism, undergo a transition from a metal to an insulator or even lose its resistance entirely and become a superconductor. The Hubbard model is the paradigmatic model of this field, similar to what the drosophila is to genetics. It describes electrons hopping from one site of a crystal to another, with the electron-electron interaction only present when two electrons occupy the same site. Despite its simplicity, the Hubbard model presents a formidable challenge to computational and theoretical methods alike. In this Erwin-Schrödinger Fellowship, a series of aspects of this paradigmatic model have been investigated. With the original intent to assess various cutting-edge numerical methods available today, a collaboration of 26 world-leading experts has been establish to study the Hubbard model at small interaction values. Borrowing terminology from astrophysics, this work presents an extensive 'multi-method, multi-messenger' assessment of the wealth of computational methods that have been developed in recent years to determine the physical properties of the Hubbard model in two spatial dimensions. The nature and role of magnetic fluctuations present in this model has been elucidated and their implications for the theory of metallic materials with strong magnetic correlations have been explained. This work paves the way to the improvement of existing algorithms, and the development of new ones aiming at quantum systems with strong interactions. Furthermore, in order to push the boundaries of existing techniques, new algorithms based on extensions of the so-called dynamical mean-field theory have been developed. These algorithms are believed to push the frontier of our knowledge about the intriguing (and not yet understood) so-called pseudogap phase of copper ceramic compounds, which exhibit superconductivity at the relatively high temperature of about -137 C. This Fellowship not only has been successful in terms of its scientific outputs, but also regarding the career development of its Principal Investigator (PI, Dr. Thomas Schäfer). In particular, on the invitation of Prof. Antoine Georges, the PI has been a regular visitor to the Center for Computational Quantum Physics at the Flatiron Institute in New York City, a recently opened hub for the exchange with world leading experts in the field. The most outstanding advance, however, was the "Ruf" of the President of the Max-Planck Society to lead a newly established international research group on the "Theory of Strongly Correlated Quantum Matter" starting in September 2020 at the Max-Planck Institute for Solid State Research in Stuttgart, Germany.