In the past decade, there has been remarkable progress in our understanding of topological states of matter. A quantum state is topological if its ground state wave function bears a distinctive character that can be specified by a topological invariant—a discrete quantity that remains unchanged upon adiabatic deformations of the system. Since the 1980s, quantum Hall systems have been recognized to be topological, but it was long believed that such topological states are rather exceptional in nature and only exist in quantum liquids under extreme conditions (requiring high magnetic fields and low temperatures). However, after the discovery of topological insulators (TIs), it has come to be widely recognized that topological states of matter can actually be widespread. In this sense, TIs have established a new paradigm about topological materials and opened up an interdisciplinary field at the crossroad between physics,quantum chemistry and material science.

The goal of this research is to discover two new types of TSMs in magnetic and photo-driven systems respectively, and explore their novel properties. First, magnetic TSMs consist of itinerant electrons that form the Dirac/Weyl point in k-space and localized moment that generates magnetism. The exchange coupling between the two is expected to catalyze a plethora of novel correlated phenomena, including an anomalous Hall effect induced by Berry curvature, an axion electromagnetic response, tunable Weyl point creation/annihilation, and metal-insulator transitions. Despite intensive searches, magnetic TSMs have not been experimentally found. The PIs will combine theoretical and experimental efforts to search for magnetic TSMs in correlated electron systems.

Second, the PIs propose a new topological phase of matter in photon-electron hybrid states, which they term the Floquet topological semimetal. Recent experiments lead by the PI Gedik has demonstrated that Bloch states in solids can be “dressed” by intense laser light, forming “Floquet-Bloch states” that are completely coherent and behave like real bands. When these states form topologically robust band crossings in energy-momentum space, the photo-excited system is expected to become a Floquet topological semimetal. The PI Fu will theoretically determine the photon polarization and frequency required for this new phase, while Checkelsky will provide the necessary materials platform and Gedik use well-established time resolved photoemission techniques to uncover these Floquet TSMs.

**I. Magnetic Topological Semimetals**

An important class of TSMs, known as Weyl semimetals, is proposed to materialize in magnetic topological insulators, where time-reversal symmetry is spontaneously broken. Fu’s group will use first-principles calculations to identify such magnetically driven TSMs in candidate materials and predict their emergent phenomena. Checkelsky’s group will synthesize samples and characterize their transport and magnetic properties, which will then be studied by Gedik’s group using angle-resolved photoemission spectroscopy (ARPES) to directly observe the Dirac/Weyl point in the bulk and the topological surface states with Fermi arc. Gedik’s group will further perform optical and magneto-optical measurements to thoroughly characterize the electronic structure. In addition to its scientific value, the discovery of TSMs may enable new spintronic device application, where electrical properties can be efficiently tuned by magnetization.**II. Floquet Topological Semimetals**

Besides the static optical and photoemission measurements probing the equilibrium, Gedik will also study the dynamics of the material in response to photoexcitation by light. Gedik has recently showed that by shining light with energy below the bulk band gap of a topological insulator, hybrid photon-electron states can be created. These states are called Floquet-Bloch states, which are the Bloch states “dressed” by the intense laser light. Surface electrons coherently can emit and absorb multiple laser photons giving rise to replicas of the original dispersion separated by integer multiples of photon energy. These new states are completely coherent and behave like real bands for practical purposes. When these bands cross they can hybridize and open up band gaps along certain directions. Considering the fact that material properties are largely determined by electronic dispersion, this ability to manipulate the electronic band structure with light is a novel way to engineer novel quantum phases of matter. There have been a number of proposals for inducing phase transitions using Floquet methods, such as inducing a Floquet topological insulator from a trivial insulator.

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