Emergent correlated phases in rhombohedral trilayer graphene induced by proximity spin-orbit and exchange coupling

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing \emph{ab initio}-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr$_2$Ge$_2$Te$_6$ (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement field and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a \textit{spin-valley-coherent} phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magneto-correlation effect -- strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers

Three-particle states and brightening of intervalley excitons in a doped MoS2_2 monolayer

Optical spectra of two-dimensional transition-metal dichalcogenides (TMDC) are influenced by complex multi-particle excitonic states. Their theoretical analysis requires solving the many-body problem, which in most cases, is prohibitively complicated. In this work, we calculate the optical spectra by exact diagonalization of the three-particle Hamiltonian within the Tamm-Dancoff approximation where the doping effects are accounted for via the Pauli blocking mechanism, modelled by a discretized mesh in the momentum space. The single-particle basis is extracted from the {\it ab initio} calculations. Obtained three-particle eigenstates and the corresponding transition dipole matrix elements are used to calculate the linear absorption spectra as a function of the doping level. Results for negatively doped MoS$_2$ monolayer (ML) are in an excellent quantitative agreement with the available experimental data, validating our approach. The results predict additional spectral features due to the intervalley exciton that is optically dark in an undoped ML but is brightened by the doping. Our approach can be applied to a plethora of other atomically thin semiconductors, where the doping induced brightening of the many-particle states is also anticipated

Electrostatic and Environmental Control of the Trion Fine Structure in Transition Metal Dichalcogenide Monolayers

Charged excitons or trions are essential for optical spectra in low-dimensional doped monolayers (ML) of transitional metal dichalcogenides (TMDC). Using a direct diagonalization of the three-body Hamiltonian, we calculate the low-lying trion states in four types of TMDC MLs as a function of doping and dielectric environment. We show that the fine structure of the trion is the result of the interplay between the spin-valley fine structure of the single-particle bands and the exchange interaction. We demonstrate that by variations of the doping and dielectric environment, the fine structure of the trion energy can be tuned, leading to anticrossing of the bright and dark states, with substantial implications for the optical spectra of the TMDC ML

Nonlinear spectroscopy of excitonic states in transition metal dichalcogenides

Second-harmonic generation (SHG) is a well-known nonlinear spectroscopy method to probe electronic structure, specifically, in transition metal dichalcogenide (TMDC) monolayers. This work investigates the nonlinear dynamics of a strongly excited TMDC monolayer by solving the time evolution equations for the density matrix. It is shown that the presence of excitons qualitatively changes the nonlinear dynamics leading, in particular, to a huge enhancement of the nonlinear signal as a function of the dielectric environment. It is also shown that the SHG polarization angular diagram and its dependence on the driving strength are very sensitive to the type of exciton state. This sensitivity suggests that SHG spectroscopy is a convenient tool for analyzing the fine structure of excitonic states.Comment: 13 pages, 5 figure

Emergent Trion-Phonon Coupling in Atomically-Reconstructed MoSe2_2-WSe2_2 Heterobilayers

In low-temperature resonant Raman experiments on MoSe$_2$-WSe$_2$ heterobilayers, we identify a hybrid interlayer shear mode (HSM) with an energy, close to the interlayer shear mode (SM) of the heterobilayers, but with a much broader, asymmetric lineshape. The HSM shows a pronounced resonance with the intralayer hybrid trions (HX$^-$) of the MoSe$_2$ and WSe$_2$ layers, only. No resonance with the neutral intralayer excitons is found. First-principles calculations reveal a strong coupling of Q-valley states, which are delocalized over both layers and participate in the HX$^-$, with the SM. This emerging trion-phonon coupling may be relevant for experiments on gate-controlled heterobilayers.Comment: 6 pages, 3 figure

Strain control of exciton and trion spin-valley dynamics in monolayer transition metal dichalcogenides

The electron-hole exchange interaction is a fundamental mechanism that drives valley depolarization via intervalley exciton hopping in semiconductor multi-valley systems. Here, we report polarization-resolved photoluminescence spectroscopy of neutral excitons and negatively charged trions in monolayer MoSe$_2$ and WSe$_2$ under biaxial strain. We observe a marked enhancement(reduction) on the WSe$_2$ triplet trion valley polarization with compressive(tensile) strain while the trion in MoSe$_2$ is unaffected. The origin of this effect is shown to be a strain dependent tuning of the electron-hole exchange interaction. A combined analysis of the strain dependent polarization degree using ab initio calculations and rate equations shows that strain affects intervalley scattering beyond what is expected from strain dependent bandgap modulations. The results evidence how strain can be used to tune valley physics in energetically degenerate multi-valley systems

Trion induced photoluminescence of a doped MoS2 monolayer

We demonstrate that the temperature and doping dependencies of the photoluminescence (PL) spectra of a doped MoS2 monolayer have several peculiar characteristics defined by the trion radiative decay. While only zero-momentum exciton states are coupled to light, radiative recombination of non-zero momentum trions is also allowed. This leads to an asymmetric broadening of the trion spectral peak and redshift of the emitted light with increasing temperature. The lowest energy trion state is dark, which is manifested by the sharply non-monotonic temperature dependence of the PL intensity. Our calculations combine the Dirac model for the single-particle states, with parameters obtained from the first-principles calculations, and the direct solution of the three-particle problem within the Tamm-Dancoff approximation. The numerical results are well captured by a simple model that yields analytical expressions for the temperature dependencies of the PL spectra