I review my recent progress and develop a geometrical approach in the quantum with light
as a guide, from the vector potential in classical physics, revealing that topological …

We have recently identified a protected topological semimetal in graphene which presents a
zeroenergy edge mode robust to disorder and interactions. Here, we address the …

For bosons with flat energy dispersion, condensation can occur in different symmetry
sectors. Here, we consider bosons in a kagome lattice with π-flux hopping, which, in the …

Orbital degrees of freedom play an important role in understanding the emergence of
unconventional quantum phases. Ultracold atomic gases in optical lattices provide a …

Here, we reveal our recent progress on a geometrical approach of quantum physics and
topological crystals linking with Dirac magnetic monopoles and gauge fields through …

We have constructed a new type of topological end mode, named η, satisfying η†= i η, η 2=−
i, and demonstrate the topological characteristics of a quantum chain with isolated η modes …

We study the interplay of attractive electron interactions and topological states in strained
kagome lattices with spin-orbit coupling via a Hubbard Hamiltonian in the mean-field …

We theoretically study topological lattice models relevant to current experimental solidstate
and artificial systems. We develop an explicit analytical computation of the Chern number in …