Most solid elements in Nature form crystal structures where atoms are arranged in regular lattices. The atoms consist of the heavy and positively charged nucleus surrounded by their electrons, and depending on the binding and interactions exhibited by the outermost electrons of the atoms, their collective behavior determines the diverse phases found in crystalline materials: metallic, semiconducting, insulating, magnetic or superconducting. When electrons are delocalized and free to move through the lattice, the properties are accurately described by the so-called Bloch theory. The success of this theory is linked to the overwhelming success of modern semiconductor device technology.
However, in a broad class of materials, including many magnets, insulators, and high-temperature superconductors, the electrons are tightly bound to their nucleus, and the Bloch theory fails. Instead, the so-called Hubbard model in principle captures the interactions among the localized electrons. The problem is, however, that the quantum nature of the electrons makes it impossible to solve the model or simulate the solution even the strongest supercomputers. Using electrons confined in semiconductors, researchers have instead tried to design quantum experiments that effectively simulate the Hubbard model. Until now, however, these experiments have failed because of the microscopic disorder inherent to conventional semiconductor electronics.
In this project, we take a new approach to such experiments by growing ultra-pure crystal lattices. The hypothesis is that the microscopic disorder can be eliminated by using position-controlled crystal growth instead of mechanically shaping existing crystals into the relevant geometries. This would enable us to perform quantum simulations of the Hubbard model to guide future developments of new materials such as high-temperature superconductors, which could revolutionize technology
