The spin polarization induced by the spin Hall effect (SHE) in thin films typically points out of the plane. This is rooted on the specific symmetries of traditionally studied systems, not in a fundamental constraint. Recently, experiments on few-layer ${\rm MoTe}_2$ and ${\rm WTe}_2$ showed that the reduced symmetry of these strong spin-orbit coupling materials enables a new form of {\it canted} spin Hall effect, characterized by concurrent in-plane and out-of-plane spin polarizations. Here, through quantum transport calculations on realistic device geometries, including disorder, we predict a very large gate-tunable SHE figure of merit $λ_sθ_{xy}\sim 1\text{--}50$ nm in ${\rm MoTe}_2$ and ${\rm WTe}_2$ monolayers that significantly exceeds values of conventional SHE materials. This stems from a concurrent long spin diffusion length ($λ_s$) and charge-to-spin interconversion efficiency as large as $θ_{xy} \approx 80$\%, originating from momentum-invariant (persistent) spin textures together with large spin Berry curvature along the Fermi contour, respectively. Generalization to other materials and specific guidelines for unambiguous experimental confirmation are proposed, paving the way towards exploiting such phenomena in spintronic devices. These findings vividly emphasize how crystal symmetry and electronic topology can govern the intrinsic SHE and spin relaxation, and how they may be exploited to broaden the range and efficiency of spintronic materials and functionalities.
We present low temperature magneto-photoluminescence experiments which demonstrate the brightening of dark excitons by an in-plane magnetic field $B$ applied to monolayers of different semiconducting transition metal dichalcogenides. For both WSe$_2$ and WS$_2$ monolayers, the dark exciton emission is observed at $\sim$50 meV below the bright exciton peak and displays a characteristic doublet structure which intensity is growing with $B^2$, while no magnetic field induced emission peaks appear for MoSe$_2$ monolayer. Our experiments also show that the MoS$_2$ monolayer has a dark exciton groun…
We study the pseudo-spin of electron pair in superconducting transition-metal dichalcogenide monolayers and show that the pseudo-spin affects the electric transport property of lateral heterojunction of the superconducting and metallic monolayers. The pseudo-spins of two electrons forming a Cooper pair are parallel to each other unlike the real spins being anti-parallel. In the lateral heterojunction, the electronic transport with forming a Cooper pair, the Andreev reflection, is suppressed with the Fermi level crossing the valence band near the edge in the metallic monolayer. We numerically i…
We study the trion and biexciton in transition metal dichalcogenides monolayers within the framework of a nonrelativistic potential model using the method of hyperspherical harmonics (HH). We solve the three- and four-body Schrödinger equations with the Keldysh potential by expanding the wave functions of a trion and biexciton in terms of the antisymmetrized HH. Results of the calculations for the ground state energies are in good agreement with similar calculations for the Keldysh potential and in reasonable agreement with experimental measurements of trion and biexciton binding energies.
Intervalley scattering by atomic defects in monolayer transition metal dichalcogenides (TDMs; MX2) presents a serious obstacle for applications exploiting their unique valley-contrasting properties. Here, we show that the symmetry of the atomic defects can give rise to an unconventional protection mechanism against intervalley scattering in monolayer TMDs. The predicted defect-dependent selection rules for intervalley scattering can be verified via Fourier transform scanning tunneling spectroscopy (FT-STS), and provide a unique identification of, e.g., atomic vacancy defects (M vs X). Our find…
We study valley-dependent spin transport theoretically in monolayer transition-metal dichalcogenides in which a variety of spin and valley physics are expected because of spin-valley coupling. The results show that the spins are valley-selectively excited with appropriate carrier doping and valley polarized spin current (VPSC) is generated. The VPSC leads to the spin-current Hall effect, transverse spin accumulation originating from the Berry curvature in momentum space. The results indicate that spin excitations with spin-valley coupling lead to both valley and spin transport, which is promis…
Monolayer films of transition metal dichalcogenides (in particular, MoS2, MoSe2, WS2, and WSe2) can be considered as ideal systems for the studies of high-temperature electron-hole liquids. The quasi-two-dimensional nature of electrons and holes ensures their stronger interaction as compared to that in bulk semiconductors. The screening of the Coulomb interaction in monolayer heterostructures is significantly reduced, since it is determined by the permittivities of the environment (e.g., vacuum and substrate), which are much lower than those characteristic of the films of transition metal dich…
We study the refraction effect of electronic wave in hole-doped lateral heterojunctions of metallic and semiconducting transition-metal dichalcogenide monolayers. This effect is theoretically investigated in 2$H$-type MoSe$_2$-NbS$_2$ and WSe$_2$-NbS$_2$ junctions by combining the first-principles calculation and the lattice Green's function method. We show that the electronic waves change the direction of motion at the interface and collimate the velocity along two different directions depending on the spin. We find that the transmission probability increases with the charge density and that …
The direct gap interband transitions in transition metal dichalcogenides monolayers are governed by chiral optical selection rules. Determined by laser helicity, optical transitions in either the $K^+$ or $K^-$ valley in momentum space are induced. Linearly polarized laser excitation prepares a coherent superposition of valley states. Here we demonstrate the control of the exciton valley coherence in monolayer WSe2 by tuning the applied magnetic field perpendicular to the monolayer plane. We show rotation of this coherent superposition of valley states by angles as large as 30 degrees in appli…
Although single-layer transition-metal dichalcogenides with novel valley functionalities are promising candidate to realize valleytronic devices, the essential understanding of valley depolarization mechanisms is still incomplete. Based on pump-probe experiments performed for MoSe2 and WSe2 monolayers and corroborating analysis from density functional calculations, we demonstrate that coherent phonons at the K-point of the Brillouin zone can effectively mediate the valley transfer of electron carriers. In the MoSe2 monolayer case, we identify this mode as the flexural acoustic ZA(K) mode, whic…
Monolayer transition-metal dichalcogenides (TMDCs) have recently emerged as possible candidates for valleytronic applications, as the spin and valley pseudospin are directly coupled and stabilized by a large spin splitting. In these semiconducting materials, optically excited electron-hole pairs form tightly Coulomb-bound excitons with large binding energies. The selection rules for excitonic transitions allow for direct optical generation of a valley-polarized exciton population using resonant excitation. Here, we investigate the exciton valley dynamics in monolayers of three different TMDCs …
We derive a low-energy theory for edge states in transition metal dichalcogenide monolayers for a two-band $\bm{kp}$-Hamiltonian in case of uncoupled valleys. In the absence of spin-orbit interaction at the edge, these states possess a linear dispersion described by a single phenomenological parameter characterizing the edge structure. Depending on the sign of the parameter, the edge state spectrum can either cross the band gap or lie outside of it. In the first case, the presence of edge states leads to resonant enhancement of the second harmonic generation at frequencies about the half of th…
In the last few years, interest in monomolecular layers of transition metal dichalcogenides (TMDs) has been driven by their unusual electronic and optical properties, which are very attractive for designing functional elements of new generation nanoelectronics. Recently, experimental evidence has appeared for the formation of a high-temperature strongly bound electron-hole liquid (EHL) in TMD monolayers. Strong binding of charge carriers is due to a significant decrease in the screening of the Coulomb interaction in monolayer heterostructures. In this work, the gas--liquid phase transition in …
We show that H-phase transition metal dichalcogenides (TMDs) monolayers such as MoS$_2$ and WSe$_2$, are orbital Hall insulators. They present very large orbital Hall conductivity plateaus in their semiconducting gap, where the spin Hall conductivity vanishes. Our results open the possibility of using TMDs for orbital current injection and orbital torque transfers that surpass their spin-counterparts in spin-orbitronics devices. The orbital Hall effect (OHE) in TMD monolayers occurs even in the absence of spin-orbit coupling. It can be linked to exotic momentum-space Dresselhaus-like orbital t…
In heterostructures consisting of different transition-metal dichalcogenide monolayers, a staggered band alignment can occur, leading to rapid charge separation of optically generated electron-hole pairs into opposite monolayers. These spatially separated electron-hole pairs are Coulomb-coupled and form interlayer excitons. Here, we study these interlayer excitons in a heterostructure consisting of MoSe$_2$ and WSe$_2$ monolayers using photoluminescence spectroscopy. We observe a non-trivial temperature dependence of the linewidth and the peak energy of the interlayer exciton, including an unu…
We study theoretically the Coulomb interaction between excitons in transition metal dichalcogenide (TMD) monolayers. We calculate direct and exchange interaction for both ground and excited states of excitons. The screening of the Coulomb interaction, specific to monolayer structures, leads to the unique behavior of the exciton-exciton scattering for excited states, characterized by the non-monotonic dependence of the interaction as function of the transferred momentum. We find that the nontrivial screening enables the description of TMD exciton interaction strength by approximate formula whic…
The linear absorption spectra in monolayers of transition metal dichalcogenides show pronounced signatures of the exceptionally strong exciton-phonon interaction in these materials. To account for both exciton and phonon physics in such optical signals, we compare different theoretical methods to calculate the absorption spectra using the example of $\mathrm{MoSe_2}$. In this paper, we derive the equations of motion for the polarization either using a correlation expansion up to 4th Born approximation or a time convolutionless master equation. We show that the Born approximation might become p…
We theoretically investigate the chiral topological excitons emerging in the monolayer transition metal dichalcogenides, where a bulk energy gap of valley excitons is opened up by a position dependent external magnetic field. We find two emerging chiral topological nontrivial excitons states, which exactly connects to the bulk topological properties, i.e., Chern number =2. The dependences of the spectrum of the chiral topological excitons on the width of the magnetic field domain wall as well as the magnetic filed strength are numerically revealed. The chiral topological valley excitons are no…
The interaction between off-resonant laser pulses and excitons in monolayer transition metal dichalcogenides is attracting increasing interest as a route for the valley-selective coherent control of the exciton properties. Here, we extend the classification of the known off-resonant phenomena by unveiling the impact of a strong THz field on the excitonic resonances of monolayer MoS$_2$. We observe that the THz pump pulse causes a selective modification of the coherence lifetime of the excitons, while keeping their oscillator strength and peak energy unchanged. We rationalize these results theo…
The effect of a magnetic field on the optical absorption in semiconductors has been measured experimentally and modeled theoretically for various systems in previous decades. We present a new first-principles approach to systematically determine the response of excitons to magnetic fields, i.e. exciton $g$ factors. By utilizing the $GW$-Bethe-Salpeter equation methodology we show that $g$ factors extracted from the Zeeman shift of electronic bands are strongly renormalized by many-body effects which we trace back to the extent of the excitons in reciprocal space. We apply our approach to monol…
We investigate the electronic transport property of lateral heterojunctions of semiconducting and metallic transition-metal dichalcogenide monolayers, MoSe$_2$ and NbSe$_2$, respectively. We calculate the electronic transmission probability by using a multi-orbital tight-binding model based on the first-principles band structure. The transmission probability depends on the spin and valley degrees of freedom. This dependence qualitatively changes by the interface structure. The heterostructure with a zig-zag interface preserves the spin and the valley of electron in the transmission process. On…
We calculate the interference correction to the conductivity of doped transition metal dichalcogenide (TMDC) monolayers. Because of the interplay between valley structure and intrinsic spin-orbit coupling (SOC), these materials exhibit a rich weak localization (WL) behavior that is qualitatively different from conventional metals or similar two-dimensional materials such as graphene. Our results can also be used to describe graphene/TMDC heterostructures, where the SOC is induced in the graphene sheet. We discuss new parameter regimes that go beyond existing theories, and can be used to interp…
We develop an analytical theory for edge states in monolayers of transition metal dichalcogenides based on a general boundary condition for a two-band ${\bf kp}$-Hamiltonian in case of uncoupled valleys. Taking into account {\it edge} spin-orbit interaction we reveal that edge states, in general, have linear dispersion that is determined by three real phenomenological parameters in the boundary condition. In absence of the edge spin-orbit interaction, edge states are described by a single real parameter whose sign determines whether their spectra intersect the bulk gap or not. In the former ca…
In this work, we predict the emergence of the valley Edelstein Effect (VEE), which is an electric-field-induced spin polarization effect, in gated monolayer transition metal dichalcogenides (MTMDs). We found an unconventional valley-dependent response in which the spin-polarization is parallel to the applied electric field with opposite spin-polarization generated by opposite valleys. This is in sharp contrast to the conventional Edelstein effect in which the induced spin-polarization is perpendicular to the applied electric field. We identify the origin of VEE as combined effects of conventio…
The lack of inversion symmetry in semiconducting transition metal dichalcogenide monolayers (TMDMs) enables a considerable molecular-level intrinsic piezoelectricity, which opens prospects for atomically-thin piezotronics and optoelectronics. Here, based on the tight-binding (TB) approach and Berry phase polarization theory, we establish an atomic-scale TB theory for demonstrating piezoelectric physics in TMDMs. Using the TB piezoelectric theory, we predict their electronic Grüneisen parameters (EGP) which measure the electron-phonon couplings. By virtue of the constructed analytical piezoelec…
We study the anomalous Hall effect in monolayers of transition-metal dichalcogenides 2H-$MX_2$ ($M$=Mo, W, and $X$=S, Se, Te) under a proximity effect of ferromagnetic substrate. If a proximity-induced exchange field is introduced, the spin-polarized energy bands in $K$ and $K'$ valleys are shifted in the opposite directions, and it causes the Hall effect by breaking time-reversal symmetry. The induced Hall effect is the most prominent in the valence band which has a large intrinsic spin splitting. Moreover, we find that tilting the magnetization from the perpendicular direction gives rise to …
We derive the boundary conditions for MoS$_2$ and similar transition-metal dichalcogenide honeycomb (2H polytype) monolayers with the same type of $\mathbf{k}\!\cdot\!\mathbf{p}$ Hamiltonian within the continuum model around the K points. In an effective 2-band description, the electron-hole symmetry breaking quadratic terms are also taken into account. We model the effect of the edges with a linear edge constraint method that has been applied previously to graphene. Focusing mainly on zigzag edges, we find that different reconstruction geometries with different edge-atoms can generally be des…
Delamination of thin films from the supportive substrates is critical issues in thin film industry and technology. The emergent two-dimensional materials, atomic layered materials, such as transition metal dichalcogenides are highly flexible thus the buckles and wrinkles can be easily generated and play vital effects on the physical properties. Here we introduce one kind of patterned buckling behavior caused by the delamination from substrate initiated at the edges of the chemical vapor deposition synthesized monolayer transition metal dichalcogenides, mainly due to the thermal expansion misma…
We theoretically investigate the corrections of exciton binding energy in monolayer transition metal dichalcogenides (TMDs) due to the exciton-optical phonon coupling in the Fr$\ddot{o}$hlich interaction model by using the linear operator combined Lee-Low-Pines variational method. We not only consider the excitons couple with the intrinsic longitudinal optical (LO) phonon modes, but also the surface optical phonon modes that induced by the polar substrates underneath the TMDs. We find that exciton binding energies are corrected in a large scale due to these exciton-optical phonon couplings. We…
Strong spin-orbit coupling in transition metal dichalcogenide (TMDC) monolayers results in spin resolvable band structures about the $K$ and $K'$ valleys such that the eigenbasis of a 2D quantum dot (QD) in a TMDC monolayer in zero field is described by the Kramers pairs $|0\rangle_-=|K'\uparrow\rangle$, $|1\rangle_-=|K\downarrow\rangle$ and $|0\rangle_+=|K\uparrow\rangle$, $|1\rangle_+=|K'\downarrow\rangle$. The strong spin-orbit coupling limits the usefulness of single TMDC QDs as spin qubits. Possible regimes of spin-degenerate states, overcoming the spin-orbit coupling in monolayer TMDC QD…
The recent accessibility of high quality, charge neutral monolayer transition metal dichalcogenides with narrow exciton linewidths at the homogeneous limit provides an ideal platform to study excitonic many-body interactions. In particular, the possibility to manipulate coherent exciton-exciton interactions, which govern the ultrafast nonlinear optical response, by applying an external magnetic field has not been considered so far. We address this discrepancy by presenting a nonlinear microscopic theory in the coherent limit for optical excitations in the presence of out-of-plane, in-plane, an…
We study the electronic band structure in the K/K' valleys of the Brillouin zone of monolayer WSe2 and MoSe2 by optical reflection and photoluminescence spectroscopy on dual-gated field-effect devices. Our experiment reveals the distinct spin polarization in the conduction bands of these compounds by a systematic study of the doping dependence of the A and B excitonic resonances. Electrons in the highest-energy valence band and the lowest-energy conduction band have antiparallel spins in monolayer WSe2, and parallel spins in monolayer MoSe2. The spin splitting is determined to be hundreds of m…
Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTI), protected by $C_3$ rotation symmetry. In addition, theoretical calculations show an orbital Hall plateau in the insulating gap of TMDs, characterized by an orbital Chern number. We explore the correlation between these two phenomena in TMD monolayers in two structural phases: the noncentrosymmetric 2H and the centrosymmetric 1T. Using density functional theory, we confirm the characteristics of 2H-TMDs and reveal that 1T-TMDs are identifi…
The dependence of the excitonic photoluminescence (PL) spectrum of monolayer transition metal dichalcogenides (TMDs) on the tilt angle of an applied magnetic field is studied. Starting from a four-band Hamiltonian we construct a theory which quantitatively reproduces the available experimental PL spectra for perpendicular and in-plane magnetic fields. In the presence of a tilted magnetic field, we demonstrate that the dark exciton PL peaks brighten due to the in-plane component of the magnetic field and split for light with different circular polarization as a consequence of the perpendicular …
We perform a theoretical study of radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers. This decay necessarily involves an electronic spin flip. The intrinsic decay mechanism due to interband spin-flip dipole moment perpendicular to the monolayer plane, gives a rate about 100--1000 times smaller than that of bright excitons. However, we find that this mechanism also introduces an energy splitting due to a local field effect, and the whole oscillator strength is contained in the higher-energy component, while the lowest-energy state remains dark and needs a…
We describe a facile technique based on polymer encapsulation to apply several percent controllable strains to monolayer and few-layer Transition Metal Dichalcogenides (TMDs). We use this technique to study the lattice response to strain via polarized Raman spectroscopy in monolayer WSe2 and WS2. The application of strain causes mode-dependent redshifts, with larger shift rates observed for in-plane modes. We observe a splitting of the degeneracy of the in-plane E' modes in both materials and measure the Gruneisen parameters. At large strain, we observe that the reduction of crystal symmetry c…
We propose a physical model based on disordered (a hole punched inside a material) monolayer transition metal dichalcogenides (TMDs) to demonstrate a large-gap quantum valley Hall insulator. We find an emergence of bound states lying inside the bulk gap of the TMDs. They are strongly affected by spin-valley coupling, rest- and kinetic- mass terms and the hole size. In addition, in the whole range of the hole size, at least two in-gap bound states with opposite angular momentum, circulating around the edge of the hole, exist. Their topological insulator (TI) feature is analyzed by the Chern num…
Optical orientation of localized/bound excitons is shown to be effectively enhanced by the application of magnetic fields as low as 20 mT in monolayer WS$_2$. At low temperatures, the evolution of the polarization degree of different emission lines of monolayer WS$_2$ with increasing magnetic fields is analyzed and compared to similar results obtained on a WSe$_2$ monolayer. We study the temperature dependence of this effect up to $T=60$ K for both materials, focusing on the dynamics of the valley pseudospin relaxation. A rate equation model is used to analyze our data and from the analysis of…
Monolayer transition metal dichalcogenides are promising materials for valleytronic operations. They exhibit two inequivalent valleys in the Brillouin zone, and the valley populations can be directly controlled and determined using circularly polarized optical excitation and emission. The photoluminescence polarization reflects the ratio of the two valley populations. A wide range of values for the degree of circularly polarized emission, Pcirc, has been reported for monolayer WS2, although the reasons for the disparity are unclear. Here we optically populate one valley, and measure Pcirc to e…
Recent experimental studies of out-of-plane straining geometries of transition metal dichalchogenide (TMD) monolayers have demonstrated sufficient band gap renormalisation for device application such as single photon emitters. Here, a simple continuum-mechanical plate-theory approach is used to estimate the topography of TMD monolayers layered atop nanopillar arrays. From such geometries, the induced conduction band potential and band gap renormalisation is given, demonstrating a curvature of the potential that is independent of the height of the deforming nanopillar. Additionally, with a semi…
