This CAREER award supports theoretical research and education focused on the study of unconventional quantum critical points around topological order. These quantum critical points are beyond the classic Landau-Ginzburg paradigm, and they carry important and experimentally testable information on the nature of the topological phases. In particular, the PI will pursue the following directions:
(1) Understanding the experimental candidates of strongly correlated topological states, for example frustrated spin-1/2 quantum magnets. The PI will identify the nature of the exotic states observed in these materials by studying the phase diagram of these materials under magnetic field, pressure, and other external fields.
(2) Investigating the quantum critical points driven by topological defects with nontrivial quantum numbers. In topological states such as a fractional topological insulator, a topological defect usually carries topologically protected quantum numbers such as charge, spin, and anyon statistics. The PI will develop a many-body theory of such topological defects, and understand the universality class and quantum entanglement at the quantum critical points driven by these defects.
(3) Exploring unconventional phases and quantum critical points of strongly interacting Dirac fermions. Dirac fermions are related to many topological states such as topological band insulators. The PI will explore the novel physics due to the interplay between the strong interaction and topology of Dirac fermions. For example, the PI will investigate the 5d transition metal oxides with both strong spin-orbit coupling and interaction.
This award also supports educational activities. These include developing new courses with emphasis on new techniques in condensed matter theory. The PI will organize group meetings and seminars for students, where the students will not only broaden their scientific disciplines, but also practice their presentation and communication skills. An interactive online Forum will be developed in order to stimulate discussions between students and to evaluate the effectiveness of education. The associated outreach activities include partnerships with a Research Experience for Teachers program, and California Alliance for Minority Participation program which will provide resources and opportunities in scientific research to secondary school teachers and under-represented students.
NON-TECHNICAL SUMMARY
This CAREER award supports theoretical research and education programs to study new states of matter called topological states that are exhibited by electrons in materials. An example of a topological state is a topological insulator. Like ordinary insulators, for example rubber, topological insulators do not conduct electricity though the interior of the material. Unlike ordinary insulators, topological insulators are able to conduct electricity on their edges or boundaries through the formation of a new state of matter. Among the known topological insulators are compounds made of the elements bismuth and selenium, and bismuth and tellurium. The PI aims to advance understanding of topological states of matter by investigating the transformations between states of matter than involve topological states. Topological states fundamentally differ from more familiar states of matter like insulators and metallic states. Transformations involving these states do not fit the standard theory of phase transitions. The PI aims to use transformations among states that occur at the absolute zero of temperature called quantum phase transitions to determine the properties of topological states and connect to experiments on materials that exhibit electronic states that are candidates for topological states and to computer simulations on model systems.
This research has immediate relevance to materials that are frustrated magnets. In these materials the interactions between fundamental microscopic units of magnetism, the electron spin, cannot be satisfied because of the geometric arrangement of atoms. The PI aims to understand the nature of these unconventional states by comparing the experimentally determined diagram of phases with the PI's theoretical predictions.
This award supports educational activities with the goal to improve creativity and innovation in research while students learn basic physics. New courses with emphasis on modern condensed matter theory will be developed. A new online forum will be designed to stimulate discussion, and evaluate teaching effectiveness. The PI will carry out outreach activities that provide research opportunities to secondary school teachers and under-represented students.
