Research interests

A full list of previous works can be found on
Google scholar
and on
arXiv. A concept map of recent interests is illustrated below. To learn more
about each concept, head down to a
collection of representative papers.

**Delicate topology**: a new paradigm of *crystalline topological matter*.
[2]
Contrast with the more established notions of *stable* and
*fragile topology*, with respective examples
[3]
and
[4].

Topological principles in nonlinear optics, e.g., solar-cell photovoltaics.

**Foundational band theory**: *geometric Berry-phase* properties of wave functions over
momentum space are tied to *localizability* of wave functions
over real space.
[2]

**Topo-fermiology**: geometric-topological characterization of the
*Fermi surfaces* of *metals*.
[2]

**Magnetic quantum effects:**
*Landau quantization*
and
magnetic-field induced *tunneling*
in *topological metals*.

Topology in magnetic bandstructure:
*diabolical* touchings
between magnetic energy levels.

Phenomenology of topological materials:
glide-resolved *photoemission spectroscopy*,
**magnetic quantum oscillations** in thermodynamic/transport quantities, ultrasound absorption in metals.

Topology meets *magnetism*:
**quantized surface magnetism**.