Dear colleagues,

The last email about the minicourse on topological quantum matter, to be delivered by Prof. Juricic from 21.10. to 24.10, has a strange-looking attachment. Therefore, we are sending here the detailed plan of the lectures.

Foundations: Berry phase & Chern number.

Bloch bands and Bloch bundle
Berry connection, curvature, and Zak phase
Chern number/TKNN invariant. Hall conductivity.
Bulk–boundary correspondence.
Minimal models: Su-Schrieffer-Heeger, Bernevig-Hughes-Zhang, Haldane

2. Time-Reversal Topological Insulators & Superconductors. Tenfold way.

Altland–Zirnbauer symmetry classes (TRS, PHS, chiral)
Fu–Kane parity criterion and Pfaffian formulation
3D topological insulators.. 3D TI surface Dirac cone
Kitaev chain and Majorana bound state

3. Crystalline Topology & Higher-Order Phases

Symmetry indicators and topological quantum chemistry.
Wannier obstruction and symmetry-protected topology.
Mirror/rotation/inversion invariants.
Higher-order TIs: hinge/corner states; fragile topology

4.Quantum Geometry & Responses

Quantum geometric tensor: Berry curvature + Fubini–Study metric
Modern theory of polarization and orbital magnetization
Anomalous Hall effect. Berry-curvature dipole and nonlinear Hall conductivity.
Superfluid weight and geometric contributions
Flat/near-flat Chern bands; moiré miniband geometry (overview)

5. Non-Hermitian Topology: NH Dirac fermions, Interactions, and flat bands.

Biorthogonal formalism. NH Bloch bands.
NH Dirac fermions.
Interaction effects.
Exceptional flat bands.

Best wishes,

Dušan Đorđević