  Experiments using ARPES, which is based on the photoelectric effect, show
that the surface states in 3D topological insulators (TI) are helical. Here we
consider Weyl interface fermions due to band inversion in narrow-bandgap
semiconductors, such as Pb$_{1-x}$Sn$_{x}$Te. The positive and negative energy
solutions can be identified by means of opposite helicity in terms of the spin
helicity operator in 3D TI as
$\hat{h}_{\textrm{TI}}=\left(1/\left|p_{\bot}\right|\right)\beta\left(\boldsymbol{\sigma}_{\perp}\times\boldsymbol{p}_{\perp}\right)\cdot\boldsymbol{\hat{z}}$,
where $\beta$ is a Dirac matrix and $\boldsymbol{\hat{z}}$ points perpendicular
to the interface. Using the 3D Dirac equation and bandstructure calculations we
show that the transitions between positive and negative energy solutions,
giving rise to electron-hole pairs, obey strict optical selection rules. In
order to demonstrate the consequences of these selection rules, we consider the
Faraday effect due to Pauli exclusion principle in a pump-probe setup using a
3D TI double interface of a PbTe/Pb$_{0.31}$Sn$_{0.69}$Te/PbTe heterostructure.
For that we calculate the optical conductivity tensor of this heterostructure,
which we use to solve Maxwell's equations. The Faraday rotation angle exhibits
oscillations as a function of probe wavelength and thickness of the
heterostructure. The maxima in the Faraday rotation angle are of the order of
millirads.
