Quantum materials host a variety of electronic states with remarkable potential for technological applications. Among those, high-temperature superconductors have attracted both fundamental and applied scientists for their ability to carry currents without dissipation above the liquid nitrogen boiling temperature. Because most quantum materials displaying this unconventional state also show other types of electronic order nearby, elucidating the interplay between them has become a key challenge to understand and possibly design new superconductors. Another unique state of quantum matter, which contrasts sharply with superconductivity, is the Mott insulator, in which electron-electron interactions localize the charge carriers, thus strongly suppressing conduction.
In previous years, this research involved classical and quantum Monte Carlo simulations that captured the intertwining between superconductivity, nematicity, Mott insulating behavior, and antiferromagnetism. More recently, the role of structural disorder has been one of the main research thrusts. The motivation comes from the fact that lattice defects are ubiquitous in even the cleanest crystals, which inevitably impacts the electronic ordered states displayed by quantum materials. In 2024, the group will continue Monte Carlo studies on the role that the structure plays in quantum materials. One research thrust will focus on the impact of elastic deformations generated by dilute defects, such as dislocations, resulting in a long-ranged and correlated distribution of local strains. A second research thrust will shed light on electronic orders that emerge in quasicrystalline systems, which lack the periodicity of ordered crystals. Both problems are analytically intractable and will require extensive supercomputing resources to be addressed.