Decoding Spatial Complexity in Strongly Correlated Electronic Systems

Purdue University, West Lafayette IN

Investigators

Abstract

NON-TECHNICAL SUMMARY This award supports theoretical and computational research, and education on materials with strong interactions among electrons which lead to strong correlations in the motions of electrons in the material. Inside conventional materials like metals and semiconductors, the electrons are evenly spread out, like tomato soup filling a container. But the electrons inside these strongly correlated materials act more like an exotic gumbo: nanoscale images show that the electrons clump into complicated shapes at the surface. These patterns and their formation may be a key to understanding the unusual electronic properties characteristic of strongly correlated materials and to the eventual mastery of these materials leading to technological applications. Most theoretical and experimental tools are designed for understanding and detecting homogeneous electronic states, and it is necessary to envision and explore new frameworks for understanding why patterns form in the distribution of electrons in strongly correlated materials. Combining theoretical tools from fractal mathematics and the statistical mechanics of disordered materials, the PI aims to develop new concepts and methods for interpreting and understanding the nanoscale electronic textures of these materials. The nanoscale is about two hundred thousand times smaller than the diameter of a human hair. The PI aims to develop geometric cluster analysis techniques that she introduced into the field, in order to better understand and eventually control these materials so that they can be successfully applied in the marketplace. The PI will continue to develop the mentoring program she began for graduate women in the physics program at her home institution. The PI will also continue to visit K-12 public schools to discuss her research. This outreach combines interactive hands-on superconductivity and magnetism demonstrations with education about current condensed matter research. In addition, the proposed work will also advance the training of one graduate student. TECHNICAL SUMMARY This award supports theoretical and computational research, and education on strongly correlated electron materials with an aim to advance understanding of patterns formed by inhomogeneous distribution of electrons. There is growing experimental evidence that many strongly correlated electronic systems such as nickelates, cuprates, and manganites exhibit nanoscale variations in local electronic properties. Describing the electronic behavior of these materials involves multiple degrees of freedom, including orbital, spin, charge, and lattice degrees of freedom. The interplay with disorder adds another dimension: not only can disorder destroy phase transitions, leaving mere crossovers in the wake; it can fundamentally alter ground states, often forbidding long range order. Especially in systems where different physical tendencies to order compete, disorder can provide nucleation points for competing ground states, leading to spatial pattern formation and complexity. The interplay of many degrees of freedom, strong correlations, and disorder can lead to a hierarchy of length scales and to pattern formation at the nanoscale. There is a need to design and develop new ways of understanding, detecting, and characterizing electronic pattern formation in strongly correlated electronic materials, especially in the presence of severe disorder effects. Resulting theoretical guidance will enable more direct contact between theory and experiment for a number of materials, and provide a path forward for understanding "disputed" regions of phase diagrams of strongly correlated materials. The PI aims to further develop the geometric cluster analysis techniques that she pioneered in the field of strongly correlated electronic systems, in order to maximize the information that can be extracted from experiments using these methods, and to facilitate the broad application of these techniques to various materials and image probes. In order to do this, the PI will develop theory of geometric criticality in random Ising models through numerical simulations. The resulting work is expected to connect to several experimental techniques and to yield new modes of data taking and analysis, and new methods enabling the detection and characterization of novel phases of matter. The PI will continue to develop the mentoring program she began for graduate women in the physics program at her home institution. The PI will also continue to visit K-12 public schools to discuss her research. This outreach combines interactive hands-on superconductivity and magnetism demonstrations with education about current condensed matter research. In addition, the proposed work will also advance the training of one graduate student.