Valley depolarization due to intervalley and intravalley electron-hole exchange interactions in monolayerMoS2

We consider the random-field O($N$) spin model with long-range exchange interactions which decay with distance $r$ between spins as $r^{-d-\sigma}$ and/or random fields which correlate with distance $r$ as $r^{-d+\rho}$, and reexamine the critical phenomena near the lower critical dimension by use of the perturbative functional renormalization group. We compute the analytic fixed points in the one-loop beta functions, and study their stability. We also calculate the critical exponents at the analytical fixed points. We show that the analytic fixed point which governs the phase transition in the system with the long-range correlations of random fields can be destabilized by the nonanalytic perturbation in both cases where the exchange interactions between spins are short ranged and long ranged. For the system with the long-range exchange interactions and uncorrelated random fields, we show that the $d\to d-\sigma$ dimensional reduction at the leading order of the $d-2\sigma$ expansion holds only for $N>2(4+3{\sqrt{3}})\simeq 18.3923\cdots$. Our investigation into the system with the long-range exchange interactions and uncorrelated random fields also gives the value of the boundary between critical behaviors in systems with long-range and short-range exchange interactions, which is identical to that predicted by Sak [Phys. Rev. B {\bf{8}}, 281 (1973)]. For the system with the long-range exchange interactions and the long-range correlated random fields, we show that the $d\to d-\sigma-\rho$ dimensional reduction does not hold within the present framework, as far as $N$ is finite.

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/rd+2−2α,α→0+,α→0+. Renormalization group calculations ind=du−e are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.

Exciton fine structures in cubic III-V semiconductor GaAs, InAs and GaN quantum dots are investigated systematically and the exciton spin relaxation in GaN quantum dots is calculated by first setting up the effective exciton Hamiltonian. The electron-hole exchange interaction Hamiltonian, which consists of the long- and short-range parts, is derived within the effective-mass approximation by taking into account the conduction, heavy- and light-hole bands, and especially the split-off band. The scheme applied in this paper allows the description of excitons in both the strong- and weak-confinement regimes. The importance of treating the direct electron-hole Coulomb interaction unperturbatively is demonstrated. We show in our calculation that the light-hole and split-off bands are negligible when considering the exciton fine structure, even for GaN quantum dots, and the short-range exchange interaction is irrelevant when considering the optically active doublet splitting. We point out that the long-range exchange interaction, which is neglected in many previous works, contributes to the energy splitting between the bright and dark states, together with the short-range exchange interaction. Strong dependence of the optically active doublet splitting on the anisotropy of dot shape is reported. Large doublet splittings up to 600 $\ensuremath{\mu}$eV, and even up to several meV for small dot size with large anisotropy, are shown in GaN quantum dots. The spin relaxation between the lowest two optically active exciton states in GaN quantum dots is calculated, showing a strong dependence on the dot anisotropy. Long exciton spin relaxation time is reported in GaN quantum dots. These findings are in good agreement with the experimental results.

We investigate the valley depolarization dynamics and valley Hall effect of exciton due to the electron-hole exchange interaction in mono- and bilayer MoS$_2$ by solving the kinetic spin Bloch equations. The effect of the exciton energy spectra by the electron-hole exchange interaction is explicitly considered. For the valley depolarization dynamics, in the monolayer MoS$_2$, it is found that in the strong scattering regime, the conventional motional narrowing picture is no longer valid, and a novel valley depolarization channel is opened. For the valley Hall effect of exciton, in both the mono- and bilayer MoS$_2$, with the exciton equally pumped in the K and K' valleys, the system can evolve into the equilibrium state where the valley polarization is parallel to the effective magnetic field due to the exchange interaction. With the drift of this equilibrium state by applied uniaxial strain, the exchange interaction can induce the {\it momentum-dependent} valley/photoluminesence polarization, which leads to the valley/photoluminesence Hall current. Specifically, the disorder strength dependence of the valley Hall conductivity is revealed. In the strong scattering regime, the valley Hall conductivity decreases with the increase of the disorder strength; whereas in the weak scattering regime, it saturates to a constant, which can be much larger than the one in Fermi system due to the absence of the Pauli blocking.

The low valley polarization of monolayer transition-metal dichalcogenides at room temperature poses a significant obstacle to the development of valleytronic devices, and a mechanistic insight into the valley depolarization in such systems is still lacking. In this study, we demonstrate that substitutional doping leading to alloyed monolayers offer an effective strategy for enhancing valley polarization at room temperature. The degree of valley polarization, as determined by helicity-resolved transient absorption spectroscopy, is 15% for Se-doped and 30% for Se- and V-doped monolayer layer $\mathrm{Mo}{\mathrm{S}}_{2}$ (referred to as MoSSe and VMoSSe, respectively). The valley polarization persists for longer durations in MoSSe (\ensuremath{\sim}15 ps) and VMoSSe (>500 ps) compared to pristine $\mathrm{Mo}{\mathrm{S}}_{2}$ (\ensuremath{\sim}1 ps). The prolonged valley depolarization in MoSSe is attributed to a reduction in long-range electron-hole exchange interactions due to thermal mixing of bright and dark excitons. However, the valley depolarization in VMoSSe takes place via intervalley scattering of carriers between hybridized and defect excitons. Our study elucidates that altering the exciton ground state through the inclusion of additional levels near the conduction-band or valence band edges via alloying can enhance and prolong valley polarization in $\mathrm{Mo}{\mathrm{S}}_{2}$. These findings are pivotal in realizing valleytronics devices at room temperature.

Long-range interactions in triple quantum dots (TQDs) in Kondo regime are investigated by accurately solving the three-impurity Anderson model. For the occupation configuration of (N1,N2,N3) = (1, 0, 1), a long-range antiferromagnetic exchange interaction (JAF) is demonstrated and induces a continuous phase transition from the separated Kondo singlet (KS) to the long-range spin singlet (LSS) state between edge dots. The expression of JAF is analytically derived and numerically verified, according to which JAF can be conveniently manipulated via gate control of the detuning energy. The long-range entanglement of Kondo clouds are proved to be quite robust at strong inter-dot coupling limit. Under equilibrium condition, it induces an unexpected peak in the spectral function of the middle dot whose singly occupied level keeps much higher than the Fermi level. Under nonequilibrium condition, higher inter-dot tunneling barrier induces an anomalous enhancement of current. These novel features can be observed in routine experiments.

Magnetic-field splitting of the ground state of a shallow direct exciton in a cubic semiconductor makes it possible to determine the electron–hole exchange interaction. The short-range exchange interaction is diagonal in the representation of the total angular momentum of an electron and a hole. The long-range exchange interaction is taken into account by the linear dielectric response formalism. The frequency–wave vector dispersion relationships of an exciton polariton in the presence of a magnetic field are derived for the Voigt and Faraday configurations.

Understanding high ordering temperature in Gd6FeBi2 magnet: Critical behavior, electronic structure and crystal-field analysis

To resolve the discrepancies in the exciton fine structure of aluminum nitride (AlN), polarization- and angle-resolved photoluminescence (PL) spectroscopies are performed. The excitonic PL spectra strongly depend on the optical polarization and detection angle. We propose that both the long-range and short-range electron-hole exchange interaction should be used to interpret the luminescence spectra. The theoretical framework fully explains the present and previous experimental results. The large longitudinal-transverse splitting energy obtained in this study suggests that AlN has strong light-matter coupling without quantum-confined structures.

We study the excitonic valley polarization and coherence in few-layer MoS2 by using circular- and linear-polarization-resolved photoluminescence. The valley polarization is largest in monolayer MoS2 and decreases with increasing number of layers or temperature. Contrary to the valley polarization, the linear polarization is negligibly small in monolayer MoS2 and increases with increasing number of layers or temperature. The temperature-dependent valley depolarization can be explained by the exciton center-of-mass momentum-dependent electron-hole exchange interaction. The valley decoherence in few-layer MoS2 is much faster than the valley depolarization at low temperature and is steady against increasing temperature or photoexcitation intensity, indicating that the decoherence process does not involve phonon or carrier-carrier scattering. The dominant valley decoherence has a pure dephasing origin and cannot be explained by the valley-depolarizing e-h exchange interaction.

Long-range corrected (LC) density functional theories (DFTs) were applied to the isomerization energy calculations of organic molecules to make clear why conventional DFTs including B3LYP have given poor isomerization reaction energies. Combining with local response dispersion (LRD) method, we performed LC-DFT calculations for the benchmark set of isomerization reactions. Consequently, we found that LC-DFT + LRD methods give accurate reaction energies equivalent to up-to-date DFTs containing many semi-empirical parameters. This result indicates that long-range exchange and intramolecular dispersion correlation interactions, which have been neglected in conventional DFTs, play prominent roles in isomerization reactions. However, we also found that these interactions are not sufficient to give accurate isomerization energies especially for cyclization reactions. Considering that Gaussian-attenuated LC-DFTs (LCgau-DFTs) give better isomerization reaction energies than LC-DFTs, we suggested that the isomerization energies will be further improved by correcting the short-range part of exchange functionals in DFT with keeping the whole long-range exchange interactions.

We model the inhomogeneous dielectric permittivity of a semiconductor nanocrystal by considering a dielectric sphere with a core and a concentric spherical shell of different permittivities. We show that the penetration of the electric field is resonantly enhanced when the laser frequency approaches an electromagnetic surface mode of the sphere. The absorption lines are shifted to higher energy and the transition oscillator strengths are changed by the resonance. The line shift is the same as the line shift that originates from the long-range electron-hole exchange interaction and was calculated by Goupalov and Ivchenko [1]. Taking into account both the short-range exchange interaction and the resonance shift, we find an excellent agreement with experimental data for CdSe nanocrystals. The line splitting in CdTe nanocrystals is calculated.

The properties of localized surface states in the one-magnon spectrum of Heisenberg ferromagnets with different types of lattices and exchange interactions are considered. The systems with “isotropic” as well as “anisotropic” exchange interaction are investigated. The case of “anisotropic” exchange determined by the long-range interaction between the spins arranged along a crystallographic axis is analyzed. The dispersion relations and damping decrements of localized surface waves are obtained without using the cumbersome apparatus of Green’s functions for simple and complex ferromagnets with “isotropic” exchange between nearest neighbors. The contribution of the surface to the magnon energy distribution function is determined. Spin-wave states localized at two-dimensional defects (like a free surface, foreign plane in an infinite lattice, or the boundary between two magnetic crystals are investigted for systems with a long-range exchange interaction. The long-range interaction is found to be essential for an analysis of stability of the ferromagnetic ordering in the defect plane in the case of alternating ferro- and antiferromagnetic “anisotropic” interaction. Surface-projectable spectral densities of one-magnon states are estimated.

Wurtzitic ZnO/(Zn,Mg)O quantum wells grown along the (0001) direction permit unprecedented tunability of the short-range spin exchange interaction. In the context of large exciton binding energies and electron-hole exchange interaction in ZnO, this tunability results from the competition between quantum confinement and giant quantum confined Stark effect. By using time-resolved photoluminescence we identify, for well widths under 3 nm, the redistribution of oscillator strengths between the A and B excitonic transitions, due to the enhancement of the exchange interaction. Conversely, for wider wells, the redistribution is cancelled by the dominant effect of internal electric fields, which dramatically reduce the exchange energy.

Using a many-body approach based on atomistic pseudopotential wave functions we show that the electron-hole exchange interaction in semiconductor quantum dots is characterized by a large, previously neglected long-range component, originating from monopolar interactions of the transition density between different unit cells. The calculated electron-hole exchange splitting of CdSe and InP nanocrystals is in good agreement with recent experimental measurements.