Optical selection rules of zigzag graphene nanoribbons

• Main Authors: Saroka, V. A, Shuba, M. V, Portnoi, M. E
• Format: Journal Article
• Language: English
• Published: 20-01-2018
• Subjects: Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.1705.00757

Phys. Rev. B 95, 155438 (2017); Phys. Rev. B 96, 199901(E) (2017) We present an analytical tight-binding theory of the optical properties of
graphene nanoribbons with zigzag edges. Applying the transfer matrix technique
to the nearest-neighbor tight-binding Hamiltonian, we derive analytical
expressions for electron wave functions and optical transition matrix elements
for incident light polarized along the structure axis. It follows from the
obtained results that optical selection rules result from the wave function
parity factor $(-1)^J$, where $J$ is the band number. These selection rules are
that $\Delta J$ is odd for transitions between valence and conduction subbands
and that $\Delta J$ is even for transitions between only valence (conduction)
subbands. Although these selection rules are different from those in armchair
carbon nanotubes, there is a hidden correlation between absorption spectra of
the two structures that should allow one to use them interchangeably in some
applications. The correlation originates from the fact that van Hove
singularities in the tubes are centered between those in the ribbons if the
ribbon width is about a half of the tube circumference. The analysis of the
matrix elements dependence on the electron wave vector for narrow ribbons shows
a smooth non-singular behavior at the Dirac points and the points where the
bulk states meet the edge states.