Floquet topology

     The Floquet topological phases refer to the dynamical change of a material’s topology with ultrafast photons. In this context, the Floquet effect mainly manifests in the following three aspects. First, it generates the Floquet replica bands; Second, it breaks time-reversal symmetry with circular polarized light; Third, it can break crystalline or magnetic symmetries if a particular bosonic (phonon or magnon) mode is activated by resonant pumping through infrared photons or stimulated Raman processes. Such tunability allows us to control the topological phase on an ultrafast time scale. Examples are described as below:

    3D Floquet topological phases: In 3D, the Floquet-induced transient band structure (both bulk bands and surface states) can be directly probed by time-resolved ARPES. For instance, by pumping an infrared active phonon (Au, Bu, Eu or Tu) mode of a 3D Dirac semimetal, one can break its inversion symmetry and therefore obtain a Weyl semimetal. 

   2D Floquet topological phases: In 2D, time-resolved ARPES can only detect the 2D bulk bands but not the 1D edge states. However, the edge states can be probed by an ultrafast on-chip optoelectronic spectroscopy. For instance, by pumping 2D Dirac fermions (e.g. Bi2Se3 thin film or graphene) with mid-infrared circularly polarized pump light, a gap is expected to open due to time-reversal breaking. This results in a 2D Chern insulator with chiral edge states, which can be measured by an ultrafast on-chip optoelectronic spectroscopy. 

   The Floquet experiments can be generalized to more complex quantum systems such as unconventional superconductors (cuprates and FeSe), magic-angle twisted bilayer graphene and Mott insulators (1T-TaS2, YTiO3 and -RuCl3). In contrast to the above cases, the Floquet phenomena in these correlated materials are not well understood even theoretically. However, there are exciting possibilities that can be directly tested in experiments. For instance, by breaking time-reversal symmetry with mid-infrared circularly polarized light, one may gap out the superconducting nodal points in cuprates and realize a d+id topological superconductor. In magic-angle twisted bilayer graphene, pumping with THz pulse (on-chip) may make the Moiré flat band even flatter, leading to Floquet induced/enhanced electronic instabilities. In antiferromagnetic Mott insulators, the Floquet effect may provide a means to cant the magnetization, control the exchange coupling or turn a Mott insulator into a chiral quantum spin liquid.

Topological magnets

      Magnetism is one of the most important topics in condensed matter physics. Its physics is extremely broad. Primary magnetic phenomena include ferromagnetism, anti-ferromagnetism, spin density waves, skyrmions, multiferroics, spin ice, Mott insulator, spin liquid, etc. Since most of these magnetic phenomena have been discovered before the explosion of topological physics, exploring the interplay of topology and magnetism is a new territory with ample possibilities to discover fundamental physics. Moreover, magnetic materials are the basis for countless technologies including spintronics, memories, magnetic sensing, etc. By taking advantage of topological protection, we may be able to make magnetic properties more robust or make relevant transport dissipationless. 

       Recent theoretical advances have proposed a wide range of new topological magnets both in 3D and in 2D including magnetic Weyl semimetals, antiferromagnetic Dirac semimetals, axion insulators, 2D quantum anomalous Hall (QAH) effect, and 2D magnetic spin polarized Dirac semimetals. While the QAH effect has been realized in magnetically doped TI thin films, other topological magnetic phases remain largely unknown and await exploration. Candidate materials include PrAlGe, Y2Mn2O7, Gd4Sb3, GdN, Co3Sn2Se2, Co2MnSi (magnetic Weyl semimetals), CuMnAs, GdPtBi, EuP3 (AFM semimetals), Co1-xFexSi (magnetic Weyl coexisting with skyrmion), CeBi, MnBi2Te4 (axion insulators) and ZrTe5/CrI3 (2D magnetic spin polarized Dirac semimetals). 

    It is interesting to explore how nontrivial topology affects important magnetic responses such as the spin Hall conductivity, spin transfer torque, spin diffusion, etc. These magnetic responses are intimately related to the Berry phase properties. For instance, the spin Hall conductivity is determined by the spin Berry curvature. In these topological magnets, the interplay of time-reversal symmetry breaking, topological band structures (Weyl nodes, Dirac fermions, etc.) and non-collinear or chiral spin texture can give rise to singular quantum geometry and diverging Berry curvatures. Such unconventional Berry phase properties can strongly modify the above-described magnetic responses.  

Topological superconductors

    Topological superconductors (TSC) are of great interest because they host Majorana fermions (MF) as protected boundary modes and are hence relevant for topological quantum computation. Current research has been focused on hybrid structures via SC proximity effect, which involve an s-wave SC, an external magnetic field, and certain non-SC material.  Our group will explore new routes to TSC that is different in terms of material platforms, topological classification and verification, i.e., searching for TSC in naturally occurring SCs. Over the past century, researchers have discovered many natural SCs. To date, only a handful has been explored in depth as candidates of TSCs. A well-known example is the proposed chiral p+ip SC in Sr2RuO4. By contrast, most of SCs have not been studied thoroughly and their pairing symmetry remains unknown. Therefore, there are ample opportunities to discover new TSCs.