CAREER: Facets of gapless quantum matter: new phenomena, new tools, and new platforms

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education focused on understanding the organization of interacting electrons in solid-state materials and the non-traditional ways in which their properties can change abruptly when specific conditions are adjusted. The traditional framework to understand electronic organizations and their transformations is based on the idea of symmetry, which in essence comes from intuition in classical physics. In recent years, it has been realized that the quantum mechanical nature of electrons allows for novel electronic states that differ by their so-called "topological" properties. For instance, some materials of the same symmetry that do not conduct electricity through their bulk can possess electronic states that allow them to conduct electricity on their surfaces, but with significantly different surface conducting properties. To comprehend the transitions between these fundamentally new electronic states, a fresh theoretical framework is essential, one that integrates the principles of quantum mechanics that dictate electron behavior. The aim of this project is to delve into the uncharted phenomena that can occur in these transformations, craft innovative theoretical tools to understand their properties, and design experimental setups to test these novel physics concepts. This research could lead to a general understanding of the diverse behavior of electrons in materials and potentially lay the groundwork for the material platforms for next-generation quantum devices.This award also supports educational activities which include mentoring graduate students and postdocs and developing new courses with emphasis on modern techniques in condensed matter theory. In addition to these educational activities, the PI will introduce a new outreach initiative named “Quantum Echoes: Uncovering Diverse Narratives in Physics”, a pioneering oral history project devoted to amplifying diverse voices in the physics community. The PI will organize students to conduct oral history interviews with underrepresented minority students and faculty members. The mission of the project is to provide a reservoir of encouragement, inspiration, and mentorship for young scientists, especially underrepresented students, and to humanize the realm of scientific discovery.TECHNICAL SUMMARYThis CAREER award supports theoretical research and education focused on the study of the diverse quantum critical phenomena and gapless phases inherent in quantum many-body systems. Understanding the quantum critical fluctuations in a gapless state provides a universal understanding of its nearby phases and their finite temperature properties. These universal predictions are not only mathematically elegant but also readily testable in experiments.The PI and his team will focus on the following directions: 1) Exploring novel phenomena for phase transitions diverging from Landau’s paradigm by systematically constructing models of topological phase transitions which demonstrate the so-called multi-path quantum criticality where the same phase transition can have multiple paths each described by a distinct universality class; 2) Developing innovative tools to characterize quantum phase transitions in strongly correlated systems and non-Fermi liquid states. The PI will develop generalized network models, encompassing more complex low energy fluctuations and symmetry constrains, to describe quantum phase transitions between crystalline topological phases with strong interactions as well as non-Fermi liquid states with spatial and internal symmetries; and 3) Designing experimental platforms that offer precision and control for an in-depth exploration of strongly correlated gapless systems. The PI will show that twisted trilayer transition metal dichalcogenides can be an ideal system to realize moiré Kagome metals within certain conditions. This award also supports educational activities which include mentoring graduate students and postdocs and developing new courses with emphasis on modern techniques in condensed matter theory. In addition to these educational activities, the PI will introduce a new outreach initiative named “Quantum Echoes: Uncovering Diverse Narratives in Physics”, a pioneering oral history project devoted to amplifying diverse voices in the physics community. The PI will organize students to conduct oral history interviews with underrepresented minority students and faculty members. The mission of the project is to provide a reservoir of encouragement, inspiration, and mentorship for young scientists, especially underrepresented students, and to humanize the realm of scientific discovery.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.