EAGER: Topological Semimetals, Insulators and Supersymmetry

Princeton University, Princeton NJ

Investigators

Abstract

NONTECHNICAL SUMMARY This EAGER award supports theoretical and computational research on new kinds of insulating and metallic materials. Materials can be generally classified as metals or insulators according to whether or not they conduct electricity. Recently, it was realized that the situation is not quite so simple because a new kind of insulators, called topological insulators, exist. The bulk of a topological insulator is insulating; however the same material behaves as a metal along its surfaces. Another recent discovery includes a new kind of metallic state called a Weyl semimetal, which has electrons that in a sense appear to be massless and have a "handedness" derived from the direction of their motion relative to the direction of intrinsic magnetism of the electron. This project involves the investigation of other theoretically possible insulating and metallic states. One of the main focuses of this project will be to study insulators called "Cohomological Insulators." These are materials that do not conduct electricity in the bulk but conduct electricity perfectly on several, but not all, of their surfaces. A local probe that measures current flow as a result of an applied voltage would see no flow if the probe is buried in the bulk of the material; however, it would see perfect flow of current on some surfaces of the sample. Moreover, it would measure different "perfect" current flow on different sides. Symmetries of the crystal ensure the perfect current flows are robust. Symmetries refer to transformations of the crystal that leave it unchanged. For example a cubic crystal rotated by 90 degrees in certain ways looks the same as it did before the rotation. Symmetries are encoded in the fundamental microscopic description of the electrons and atoms in the crystal, have experimentally observable consequences, and enrich the possibilities for new kinds of topological insulators. The PI will use sophisticated mathematical methods involving the concepts of symmetry, and cohomology in particular, to explore the properties of these remarkable states of matter. Another main focus of the research will be to investigate the possibility that supersymmetry exists in a series of newly discovered semimetals. Supersymmetry is a fundamental theoretical, yet unproven, property of matter, and several high-energy physics experiments actively seek evidence for supersymmetry among the collisions of fast-moving subatomic particles. It has also been recently argued on the basis of theory that supersymmetry can appear in materials, and specifically in Weyl semimetals; the research team recently predicted several crystalline materials are Weyl semimetals. It is thought that if Weyl semimetals can be made to undergo a transformation to a special kind of superconductivity, then hints of supersymmetry can appear at the onset of superconductivity. Superconductivity is a quantum mechanical state of matter involving the cooperative motion of many electrons that can conduct electricity without resistance. The PI will investigate the conditions necessary for the appearance of supersymmetry, and aims to propose the first realistic materials system where it could be observed. This project contains a component focused on informing the public about these fundamental states of electronic matter that occur in materials, their potential applications, and their relevance to the understanding of the universe we live in. TECHNICAL SUMMARY This EAGER award supports theoretical and computational research to uncover new phenomena in topological insulators and semimetals. The research team aims to predict materials and systems where new topological phenomena can be uncovered. The PI plans to classify and realize the last remaining topological insulators protected by non-symmorphic symmetries. These are point-group symmetries followed by a fractional translation of the lattice. These materials are bulk insulators but exhibit protected edge metals. The first kind of such non-symmorphic topological insulator has been recently predicted, by the research team, to exist in the potassium-mercury-antimony compound, KHgSb. The electronic edge states of this insulator can take a shape that resembles that of an hourglass as observed by experiment. The PI aims to characterize the possible different kinds of non-symmorphic topological insulators and predict materials where they can be realized. Their response to external electric and magnetic fields will also be analyzed. Several other new and distinct types of surface Fermions may be discovered in the course of the research. The team also proposes work on interactions in semimetals, specifically on how to realize supersymmetry at the transition point between a Weyl semimetal and a pair-density wave state. Recent theory suggests that this would involve first making a two-Weyl only system, which would then need to be made superconducting with a specific order parameter. The team will perform the theoretical design of such a system. Using first-principles and topological calculations, the team will predict semimetals with only two Weyl nodes. The team will then use Functional Renormalization Group methods to establish the parameter range for pair density wave instability in the Weyl system. Finally, the team will propose new systems in which tunable interactions can achieve critical points with different symmetry properties. This project contains a component focused on informing the public about these fundamental states of electronic matter that occur in materials, their potential applications, and their relevance to the understanding of the universe we live in.