Optical signatures of states bound to vacancy defects in monolayer MoS$_2$

We show that pristine MoS$_2$ single layer (SL) exhibits two bandgaps $E_{gparallel}=1.9$ eV and $E_{gperp}=3.2$ eV for the optical in-plane and out-of-plane susceptibilities $chi_parallel$ and $chi_perp$, respectively. In particular, we show that odd states bound to vacancy defects (VDs) lead to resonances in $chi_perp$ inside $E_{gperp}$ in MoS$_2$ SL with VDs. We use density functional theory, the tight-binding model, and the Dirac equation to study MoS$_2$ SL with three types of VDs: (i) Mo-vacancy, (ii) S$_2$-vacancy, and (iii) 3$times$MoS$_2$ quantum antidot. The resulting optical spectra identify and characterize the VDs.

Two-dimensional Fermionic Hong-Ou-Mandel Interference with Weyl Fermions

We propose a two-dimensional Hong-Ou-Mandel (HOM) type interference experiment for Weyl fermions in graphene and 3D topological insulators. Since Weyl fermions exhibit linear dispersion, similar to photons in vacuum, they can be used to obtain the HOM interference intensity pattern as a function of the delay time between two Weyl fermions. We show that while the Coulomb interaction leads to a significant change in the angle dependence of the tunneling of two identical Weyl fermions incident from opposite sides of a potential barrier, it does not affect the HOM interference pattern, in contrast to previous expectations. We apply our formalism to develop a Weyl fermion beam-splitter (BS) for controlling the transmission and reflection coefficients. We calculate the resulting time-resolved correlation function for two identical Weyl fermions scattering off the BS.