Imperfections in the crystal structure, such as point defects, can strongly modify the optical and transport properties of materials. Here, we study the effect of point defects on the optical and DC conductivities of single layers of semiconducting t
ransition metal dichalcogenides with the form $M$S$_2$, where $M$=Mo or W. The electronic structure is considered within a six bands tight-binding model, which accounts for the relevant combination of $d$ orbitals of the metal $M$ and $p$ orbitals of the chalcogen $S$. We use the Kubo formula for the calculation of the conductivity in samples with different distributions of disorder. We find that $M$ and/or S defects create mid-gap states that localize charge carriers around the defects and which modify the optical and transport properties of the material, in agreement with recent experiments. Furthermore, our results indicate a much higher mobility for $p$-doped WS$_2$ in comparison to MoS$_2$.
The excitation spectrum and the collective modes of graphene antidot lattices (GALs) are studied in the context of a $pi$-band tight-binding model. The dynamical polarizability and dielectric function are calculated within the random phase approximat
ion. The effect of different kinds of disorder, such as geometric and chemical disorder, are included in our calculations. We highlight the main differences of GALs with respect to single-layer graphene (SLG). Our results show that, in addition to the well-understood bulk plasmon in doped samples, inter-band plasmons appear in GALs. We further show that the static screening properties of undoped and doped GALs are quantitatively different from SLG.
The electrodynamics of a two-dimensional gas of massless fermions in graphene is studied by a collisionless hydrodynamic approach. A low-energy dispersion relation for the collective modes (plasmons) is derived both in the absence and in the presence
of a perpendicular magnetic field. The results for graphene are compared to those for a standard two-dimensional gas of massive electrons. We further compare the results within the classical hydrodynamic approach to the full quantum mechanical calculation in the random phase approximation. The low-energy dispersion relation is shown to be a good approximation at small wave vectors. The limitations of this approach at higher order is also discussed.
We study collective electronic excitations in graphene in the integer quantum Hall regime, concentrating mainly on excitations with spin reversal such as spin-flip and spin-wave excitations. We show that these excitations are correctly accounted for
in the time-dependent Hartree-Fock and strong magnetic field approximations, in contrast to spin-conserving (magneto-exciton) modes which involve a strong Landau-level mixing at non-zero wave vectors. The collective excitations are discussed in view of prominent theorems, such as Kohns and Larmors. Whereas the latter remains valid in graphene and yields insight into the understanding of spin-dependent modes, Kohns theorem does not apply to relativistic electrons in graphene. We finally calculate the exchange correction to the chemical potential in the weak magnetic field limit.
The particle-hole excitation spectrum for doped graphene is calculated from the dynamical polarizability. We study the zero and finite magnetic field cases and compare them to the standard two-dimensional electron gas. The effects of electron-electro
n interaction are included within the random phase approximation. From the obtained polarizability, we study the screening effects and the collective excitations (plasmon, magneto-excitons, upper-hybrid mode and linear magneto-plasmons). We stress the differences with the usual 2DEG.
A doped graphene layer in the integer quantum Hall regime reveals a highly unusual particle-hole excitation spectrum, which is calculated from the dynamical polarizability in the random phase approximation. We find that the elementary neutral excitat
ions in graphene in a magnetic field are unlike those of a standard two-dimensional electron gas (2DEG): in addition to the upper-hybrid mode, the particle-hole spectrum is reorganized in linear magneto-plasmons that disperse roughly parallel to $omega=v_F q$, instead of the usual horizontal (almost dispersionless) magneto-excitons. These modes could be detected in an inelastic light scattering experiment.
The electron-electron interactions effects on the shape of the Fermi surface of doped graphene are investigated. The actual discrete nature of the lattice is fully taken into account. A $pi$-band tight-binding model, with nearest-neighbor hopping int
egrals, is considered. We calculate the self-energy corrections at zero temperature. Long and short range Coulomb interactions are included. The exchange self-energy corrections for graphene preserve the trigonal warping of the Fermi surface topology, although rounding the triangular shape. The band velocity is renormalized to higher value. Corrections induced by a local Coulomb interaction, calculated by second order perturbation theory, do deform anisotropically the Fermi surface shape. Results are compared to experimental observations and to other theoretical results.
