Pseudospin is of central importance in governing many unusual transport properties of graphene and other artificial systems which have pseudospins of 1/2. These unconventional transport properties are manifested in phenomena such as Klein tunneling, and collimation of electron beams in one-dimensional external potentials. Here we show that in certain photonic crystals (PCs) exhibiting conical dispersions at the center of Brillouin zone, the eigenstates near the “Dirac-like point” can be described by an effective spin-orbit Hamiltonian with a pseudospin of 1. This effective Hamiltonian describes within a unified framework the wave propagations in both positive and negative refractive index media which correspond to the upper and lower conical bands respectively. Different from a Berry phase of π for the Dirac cone of pseudospin-1/2 systems, the Berry phase for the Dirac-like cone turns out to be zero from this pseudospin-1 Hamiltonian. In addition, we found that a change of length scale of the PC can shift the Dirac-like cone rigidly up or down in frequency with its group velocity unchanged, hence mimicking a gate voltage in graphene and allowing for a simple mechanism to control the flow of pseudospin-1 photons. As a photonic analogue of electron potential, the length-scale induced Dirac-like point shift is effectively a photonic potential within the effective pseudospin-1 Hamiltonian description. At the interface of two different potentials, the 3-component spinor gives rise to distinct boundary conditions which do not require each component of the wave function to be continuous, leading to new wave transport behaviors as shown in Klein tunneling and supercollimation. For examples, the Klein tunneling of pseudospin-1 photons is much less anisotropic with reference to the incident angle than that of pseudospin-1/2 electrons, and collimation can be more robust with pseudospin-1 than pseudospin-1/2. The special wave transport properties of pseudospin-1 photons, coupled with the discovery that the effective photonic “potential” can be varied by a simple length-scale change, may offer new ways to control photon transport. We will also explore the difference between pseudospin-1 photons and pseudospin-1/2 particles when they encounter disorder.
Owing to their reduced dimensionality, the behavior of quasi-one-dimensional systems is often strongly influenced by
electron-electron interactions. We discuss some recent work on using theory and computation to understand and predict
the electronic structure and the linear optical response of several one-dimensional (1D) nanostructures. The calculations
are carried out employing a first-principles interacting-electron Green's function approach. It is shown that exciton
states in the semiconducting carbon nanotubes have binding energies that are orders of magnitude larger than bulk
semiconductors and hence they dominate the optical spectrum at all temperature, and that strongly bound excitons can
exist even in <i>metallic</i> carbon nanotubes. In addition to the optically active (bright) exciton states, theory predicts a
number of optically inactive or very weak oscillator strength (dark) exciton states. These findings demonstrate the
importance of an exciton picture in interpreting optical experiments and in the possible applications of the carbon
nanotubes. Our studies show that many-electron interaction (self-energy and excitonic) effects are equally dominant in
the electronic structure and optical response of other potentially useful quasi-1D nanostructures such as the BN
nanotubes, Si nanowires, and graphene nanoribbons.