Research

Periodically phases or Floquet phases can achieve exotic phenomena that are unavailable in any static lattices. An important open question that I am investigating is the role of spatial crystalline symmetry in supporting Floquet topological phenomena. In a recent work, we propose to use Floquet engineering to generate tunable fragile topological phases. We also established a general theoretical framework to understand, classify, and characterize anomalous Floquet higher-order topological phenomena that are inherently dynamical (i.e. statically impossible). An on-going work that will appear soon develops a complete symmetry indicator theory for Floquet crystalline topological phases. We are also working closely with our experimental colleagues at Maryland to realize an anomalous Floquet higher-order topological insulator in the experimental settings.

Protected by crystalline symmetry, 3D Dirac semimetals (DSM) are known for their stable gapless nodes that are four-fold degenerate in the bulk energy spectrum. An interesting question is how stable these bulk Dirac points are. We studied the instability problem of these bulk Dirac nodes and identified two possible gapping scenarios: (i) developing charge-density-wave (CDW) order with spontaneously translational symmetry breaking; (ii) developing nematic order with rotational symmetry breaking. The order parameters are in general complex. This is highly nontrivial in a Dirac system since the phase angle in the complex mass terms acts as a dynamic axion field. Consequently, a topological defect structure (e.g. vortex) in the order parameter configuration hosts gapless chiral modes (axion string), even though bulk Dirac points are removed by nematic/CDW ordering.

Along with my experimental collaborators in U.K., we found that introducing inhomogeneity to a Weyl metamaterial amounts to inducing a gauge field coupled to the bulk Weyl photons. The induced gauge field generates a large artificial magnetic field, which creates chiral pseudo-Landau levels as one-way propagation channels in the bulk. This serves as the first direct experimental observation of zeroth chiral Landau levels in Weyl systems.

The inability of developing long-range order makes 1D quantum systems unique from their higher-dimensional counterparts. This is why I like to think about 1D problems with Luttinger liquid theory. Lots of my theories on the edge physics of a 2D topological state involve bosonization technique and Luttinger liquid analysis. In particular, I found that strong correlation effects in a Dirac semimetal nanowire can surprisingly lead to Majorana end modes, even when no long-range superconductivity is present. This proposal is intrinsically distinct from the well-known platform of superconducting Rashba nanowire, where superconducting proximity effect is a necessity.

Valleytronics is one of the promising candidates that can potentially replace the current paradigm of silicon-based electronics. In collaboration with my experiment colleagues at Penn State, we achieved an important milestone in valleytronics and realized a gate-controlled four-way valley router in a gated bilayer graphene sample. Specifically, our router device realizes the operations of an electron waveguide, a valley valve, and an electron beam splitter, all of which are well-explained by my theoretical modeling. Our work offers a fundamental building block for future scalable valleytronics devices. A pedagogical video explanation of our work can be found at this website.