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We show that band topology can dramatically change the photophysics of two-dimensional (2D) semiconductors. For systems in which states near the band extrema are of multiple orbitals character and the spinors describing the orbital components (pseudospins) pick up nonzero winding numbers (topological invariants) around the extremal k-point, the optical strength and nature (i.e., helicity) of the excitonic states are dictated by the optical matrix element winding number, a unique and heretofore unrecognized characteristic. We illustrate these findings in three gapped graphene systems - monolayer graphene with inequivalent sublattices and biased bi- and tri-layer graphene, where the pseudospin textures manifest into a unique optical matrix element winding pattern associated with different valley and photon circular polarization. This winding-number physics leads to novel exciton series and optical selection rules, with each valley hosting multiple bright excitons coupled to light of different helicity. This valley-exciton selective circular dichroism can be unambiguously detected using optical spectroscopy.
Various properties of the energy band structures (electronic, phonon, etc.), including systematic band degeneracy, sticking and extremes, following from the full line group symmetry of the single-wall carbon nanotubes are established. The complete se
Electron motion in crystals is governed by the coupling between crystal momentum and internal degrees of freedom such as spin implicit in the band structure. The description of this coupling in terms of a momentum-dependent effective field and the re
The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with four most important interlayer interactions taken into account. Since the main features of the wave functions are well depicted, the L
This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of edge states