The quasiparticle band-gap renormalization induced by the doped carriers is an important and well-known feature in two-dimensional semiconductors, including transition-metal dichalcogenides (TMDs), and it is of both theoretical and practical interest
. To get a quantitative understanding of this effect, here we calculate the quasiparticle band-gap renormalization of the electron-doped monolayer MoS$_2$, a prototypical member of TMDs. The many-body electron-electron interaction induced renormalization of the self-energy is found within the random phase approximation and to account for the quasi-2D character of the Coulomb interaction in this system a Keldysh-type interaction with a nonlocal dielectric constant is used. Considering the renormalization of both the valence and the conduction bands, our calculations reveal a large and nonlinear band-gap renormalization upon adding free carriers to the conduction band. We find a 410 meV reduction of the band gap for the monolayer MoS$_2$ on SiO$_2$ substrate at the free carrier density $n=4.9times 10^{12} rm{cm^{-2}}$ which is in excellent agreement with available experimental results. We also discuss the role of exchange and correlation parts of the self-energy on the overall band-gap renormalization of the system. The strong dependence of the band-gap renormalization on the surrounding dielectric environment is also demonstrated in this work, and a much larger shrinkage of the band gap is predicted for the freestanding monolayer MoS$_2$.
We calculate the quasiparticle properties of $rm{MoS_2}$ monolayer at $T=0$ considering the dynamical electron-electron interaction effect within random-phase-approximation (RPA). The calculations are carried out for an electron-doped slab of $rm{MoS
_2}$ monolayer using a minimal massive Dirac Hamiltonian and the quasi-two-dimensional nature of the Coulomb interaction in this system is taken into account considering a modified interaction of Keldysh type. Having calculated the real and imaginary parts of the retarded self-energy, we find the spectral function and discuss the impact of extrinsic variables such as the dielectric medium and the charge carrier density on the appearance and position of the quasiparticle peaks. We also report the results of the renormalization constant and the effective Fermi velocity calculations in a broad range of the coupling constant and carrier density. We show that the effective Fermi velocity obtained solving the self-consistent Dyson equation has an absolutely different behavior from the one found from the on-shell approximation. Our results show that the nonlocal dielectric screening of the monolayer tends to stabilize the Fermi liquid picture in $rm{MoS_2}$ monolayer and that the interaction strength parameter of this system is a multivariable function of the coupling constant, carrier density, and also the screening length.
We investigate the magnetotransport properties of a two-dimensional electron gas with anisotropic k-cubic Rashba interaction at the $rm{LaAlO_3}$/$rm{SrTiO_3}$ interface. The Landau levels and density of states of the system as well as the magnetotra
nsport coefficients are evaluated. A somehow anomalous beating pattern in low magnetic field regime is found both in the density profile and magnetoresistivity. We discuss the impact of electron density, Landau level broadening and Rashba spin-orbit constant on the appearance of the beatings in low magnetic fields and find that at low electron concentrations and not very strong spin-orbit interactions the beatings smooth out. On the other hand, as the magnetic field increases, the Zeeman term becomes the dominant splitting mechanism leading to the spin-split peaks in SdH oscillations. We also show that the observation of the beatings in low magnetic fields needs a system with rather higher carrier concentration so that the beatings persist up to sufficiently large fields where the oscillations are not smoothed out by Landau level broadening. The quantum Hall plateaus are evaluated and we show the Chern number with both even and odd values is replaced by the odd numbers when two subband energies are close with spin degenerate energy levels. Along with the numerical evaluation of the magnetotransport properties, a perturbative calculation is also performed which can be used in the case of low densities and not very large filling factors.
