Flat-band materials such as the kagome metals or moiré superlattices are of intense current
interest. Flat bands can result from the electron motion on numerous (special) lattices and …

Electronic correlation effects are manifested in quantum materials when either the on-site
Coulomb repulsion is large or the electron kinetic energy is small. The former is the …

Magnetic kagome materials provide a fascinating playground for exploring the interplay of
magnetism, correlation and topology. Many magnetic kagome systems have been reported …

Strange metals develop near quantum critical points (QCPs) in a variety of strongly
correlated systems. Some of the important issues include how the quantum critical state …

Lattice symmetries are central to the characterization of electronic topology. Recently, it was
shown that Green's function eigenvectors form a representation of the space group. This …

Flat electronic bands are expected to show proportionally enhanced electron correlations,
which may generate a plethora of novel quantum phases and unusual low-energy …

Moiré structures, along with line-graph-based d-electron systems, represent a setting to
realize flat bands. One form of the associated strong correlation physics is the Kondo effect …

Strange metals develop near quantum critical points in a variety of strongly correlated
systems. Some of the issues that are central to the field include how the quantum critical …

We demonstrate a procedure for constructing a maximally localized Wannier basis for a
subspace of bands with a non-zero Chern number. Bands with non-trivial topological indices …

This thesis is based on research conducted in Prof. Qimiao Si's group. Parts of the work
were performed in collaboration with Prof. Jennifer Cano's group at Stony Brook University …