Momentum-Resolved Exciton Coupling and Valley Polarization Dynamics in Monolayer WS$_2$
Alice Kunin, Sergey Chernov, Jin Bakalis, Ziling Li, Shuyu Cheng, Zachary H. Withers, Michael G. White, Gerd Schönhense, Xu Du, Roland K. Kawakami, Thomas K. Allison
备注：
16 pages: 8 pages main text with 5 figures, 8 pages SI with 6 figures
Coupling between exciton states across the Brillouin zone in monolayer transition metal dichalcogenides can lead to ultrafast valley depolarization. Using time- and angle-resolved photoemission, we present momentum- and energy-resolved measurements of exciton coupling in monolayer WS$_2$. By comparing full 4D ($k_x, k_y, E, t$) data sets after both linearly and circularly polarized excitation, we are able to disentangle intervalley and intravalley exciton coupling dynamics. Recording in the exciton binding energy basis instead of excitation energy, we observe strong mixing between the B$_{1s}$ exciton and A$_{n>1}$ states. The photoelectron energy and momentum distributions observed from excitons populated via intervalley coupling (e.g. K$^-$ $\rightarrow$ K$^+$) indicate that the dominant valley depolarization mechanism conserves the exciton binding energy and center-of-mass momentum, consistent with intervalley Coulomb exchange. On longer timescales, exciton relaxation is accompanied by contraction of the momentum space distribution.
Coherent control and manipulation of quantum degrees of freedom such as spins forms the basis of emerging quantum technologies. In this context, the robust valley degree of freedom and the associated valley pseudospin found in two-dimensional transition metal dichalcogenides is a highly attractive platform. Valley polarization and coherent superposition of valley states have been observed in these systems even up to room temperature. Control of valley coherence is an important building block for the implementation of valley qubit. Large magnetic fields or high-power lasers have been used in th…
Heterostructures comprising different monolayer semiconductors provide a new system for fundamental science and device technologies, such as in the emerging field of valleytronics. Here, we realize valley-specific interlayer excitons in monolayer WSe2-MoSe2 vertical heterostructures. We create interlayer exciton spin-valley polarization by circularly polarized optical pumping and determine a valley lifetime of 40 nanoseconds. This long-lived polarization enables the visualization of the expansion of a valley-polarized exciton cloud over several microns. The spatial pattern of the polarization …
Excitons, Coulomb bound electron-hole pairs, are composite bosons and their interactions in traditional semiconductors lead to condensation and light amplification. The much stronger Coulomb interaction in transition metal dichalcogenides such as WSe$_2$ monolayers combined with the presence of the valley degree of freedom is expected to provide new opportunities for controlling excitonic effects. But so far the bosonic character of exciton scattering processes remains largely unexplored in these two-dimensional (2D) materials. Here we show that scattering between B-excitons and A-excitons pre…
Single-layer transition metal dichalcogenides (TMDs) provide a promising material system to explore the electron's valley degree of freedom as a quantum information carrier. The valley degree of freedom in single-layer TMDs can be directly accessed by means of optical excitation. The rapid valley relaxation of optically excited electron-hole pairs (excitons) through the long-range electron-hole exchange interaction, however, has been a major roadblock. Theoretically such a valley relaxation does not occur for the recently discovered dark excitons, suggesting a potential route for long valley l…
In this work, we provide a detailed derivation of Foldy-Wouthuysen (FW) transformation for two-dimensional (2D) gapped Dirac fermions under external fields and apply the formalism to study valley excitons in 2D semiconducting materials. Similar to relativistic quantum few-body problem, the gapped Dirac equation can be transformed into a Schrödinger equation with "relativistic" correction terms. In this 2D materials system, the correction terms can be interpreted as the Berry-curvature effect. The Hamiltonian for a valley exciton in external fields can be written based on the FW transformed Dir…
We developed a comprehensive theoretical framework focusing on many-body effects of exciton species in monolayer WS$_2$, including bright and dark excitons, and intra- and inter-valley biexcitons, to investigate valley dynamics in monolayer WS$_2$ subjected to a tilted magnetic field B. In particular, the evolution of the exciton population densities and the many-body particle scatterings are considered to calculate the valley polarization (V P ) as a function of the magnetic field. We found valley splittings for the dark exciton and biexciton energy levels that are larger than those of bright…
Interlayer valley excitons in bilayer MoS2 feature concurrently large oscillator strength and long lifetime, and hence represent an advantageous scenario for valleytronic applications. However, control of valley pseudospin of interlayer excitons in pristine bilayer MoS2, which lies at the heart of valleytronics, has remained elusive. Here we report the observation of highly circularly polarized photoluminescence from interlayer excitons of bilayer MoS2 with both optical and magnetic addressability. Under excitation of circularly polarized light near exciton resonance, interlayer excitons of bi…
Electron valleys in transition-metal dichalcogenide monolayers drive novel physics and allow designing multifunctional architectures for applications. We propose to manipulate the electron valleys in these systems for spin/valley filter and valve devices through band engineering. Instead of the magnetic proximity effect that has been extensively used in previous studies, in our strategy, the electron valleys are directly coupled to the spin-polarized states of the two-dimensional ferromagnets. We find that this coupling results in a valley-selective gap opening due to the spin-momentum locking…
Monolayer 2D semiconductors provide an attractive option for valleytronics due to the valley-addressability by helicity-specific light beam. But the short valley lifetime for excitons have hindered potential valleytronic applications. In this paper, we demonstrate a strategy for prolonging the valley lifetime by converting excitons to trions through effective gate control and by taking advantage of much longer valley lifetime for trions than for excitons. In continuous-wave experiments, we found the valley polarization increases as gate voltage is tuned away from the charge neutrality, with th…
The presence of two spin-split valleys in monolayer (1L) transition metal dichalcogenide (TMD) semiconductors supports versatile exciton species classified by their spin and valley quantum numbers. While the spin-0 intravalley exciton, known as the "bright" exciton, is readily observable, other types of excitons, such as the spin-1 intravalley (spin-dark) and spin-0 intervalley (momentum-dark) excitons, are more difficult to access. Here we develop a waveguide coupled 1L tungsten diselenide (WSe2) device to probe these exciton species. In particular, TM coupling to the atomic layer's out-of-pl…
Manipulating and reserving the valley pseudospin of excitons is one core aim in the two-dimensional transition metal dichalcogenides (TMDs). However, due to the strong electron-hole exchange and spin-orbit coupling interactions, the exciton recombination lifetime is subject to picosecond timescale intrinsically, and the valley polarization is hardly modulated by a moderate magnetic field. It is fortunate that interlayer and defect-localized excitons promise to overcome these difficulties by suppressing the above interactions. Here we clearly reveal that the valley polarization can be reversed …
Valleytronics is a rising topic to explore the emergent degree of freedom for charge carriers in energy band edges and has attracted a great interest due to many intriguing quantum phenomena and potential application in information processing industry. Creation of permanent valley polarization, i.e. unbalanced occupation at different valleys, is a chief challenge and also urgent question to be solved in valleytronics. Here we predict that the spin-orbit coupling and magnetic ordering allow spontaneous valley Zeeman-type splitting in pristine monolayer of VAgP2Se6 by using first-principles calc…
Single layers of transition metal dichalcogenides are two-dimensional direct bandgap semiconductors with degenerate, but inequivalent, `valleys' in the electronic structure that can be selectively excited by polarized light. Coherent superpositions of light and matter, exciton-polaritons, have been observed when these materials are strongly coupled to photons, but these hybrid quasiparticles do not harness the valley-sensitive excitations of monolayer transition metal dichalcogenides. Here, we demonstrate evidence for valley polarized exciton-polaritons in monolayers of MoS$_2$ embedded in a d…
We propose a new family of the d0 orbital XY (X = K, Rb, Cs; Y = N, P, As, Sb, Bi) monolayers with abundant and novel topology and valley properties. The KN, RbN, RbP, RbAs, CsP, CsAs, and CsSb monolayers possess remarkable quantum anomalous Hall effect (QAHE). CsSb monolayer also exhibits extraordinary valley QAHE with giant splitting. Moreover, the topological properties of XY monolayers can be effciently tuned by the in-plane strain, owing to the strain-induced band inversion between the px;y and pz orbitals. Our findings suggest that the d0 orbital XY monolayers can be good candidates for …
Exciton Valley Hall effect is the spatial separation of the valley-tagged excitons in the presence of a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering mechanisms. We develop microscopic theory of the exciton valley Hall effect in the presence of synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current …
Calculations combining first-principles electron-phonon ($e$-ph) interactions with the Boltzmann equation enable studies of ultrafast carrier and phonon dynamics. However, in materials with weak Coulomb screening, electrons and holes form bound excitons and their scattering processes become correlated, posing additional challenges for modeling nonequilibrium physics. Here we show calculations of ultrafast exciton dynamics and related time-domain spectroscopies using $ab~initio$ exciton-phonon (ex-ph) interactions together with an excitonic Boltzmann equation. Starting from the nonequilibrium e…
While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster time scale in MoSe$_2$ bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the $K$ va…
Ferrovalley materials can achieve manipulation of the valley degree of freedom with intrinsic spontaneous valley polarization introduced by their intrinsic ferromagnetism. A good ferrovalley material should possess perpendicular magnetic anisotropy (PMA), valence band maximum (VBM)/conduction band minimum (CBM) at valley points, strong ferromagnetic (FM) coupling and proper valley splitting. In this work, the monolayer $\mathrm{GdCl_2}$ is proposed as a potential candidate material for valleytronic applications by the first-principles calculations. It is proved that monolayer $\mathrm{GdCl_2}$…
As hosts for tightly-bound electron-hole pairs carrying quantized angular momentum, atomically-thin semiconductors of transition metal dichalcogenides provide an appealing platform for optically addressing the valley degree of freedom. In particular, the valleytronic properties of neutral and charged excitons in these systems have been widely investigated. Meanwhile, correlated quantum states involving more particles are so far elusive and controversial. Here we present experimental evidence for valleytronic four-particle biexcitons and five-particle exciton-trions in high-quality monolayer tu…
We investigate with polarized microphotoluminescence the optical pumping of the valley degree of freedom in charge-tunable MoS2 monolayers encapsulated with hexagonal boron nitride at cryogenic temperatures. We report a large steady state valley polarization of the different excitonic complexes following circularly-polarized laser excitation 25 meV above the neutral exciton transition. For the first time in this material we reveal efficient valley pumping of positively-charged trions, which were so far elusive in non-encapsulated monolayers due to defect and laser-induced large electron doping…
The valley degree of freedom is a sought-after quantum number in monolayer transition-metal dichalcogenides. Similar to optical spin orientation in semiconductors, the helicity of absorbed photons can be relayed to the valley (pseudospin) quantum number of photoexcited electrons and holes. Also similar to the quantum-mechanical spin, the valley quantum number is not a conserved quantity. Valley depolarization of excitons in monolayer transition-metal dichalcogenides due to long-range electron-hole exchange typically takes a few ps at low temperatures. Exceptions to this behavior are monolayers…
We quantitatively illustrate the fundamental limit that exciton-exciton annihilation (EEA) may impose to the light emission of monolayer transition metal dichalcogenide (TMDC) materials. The EEA in TMDC monolayers shows dependence on the interaction with substrates as its rate increases from 0.1 cm2/s (0.05 cm2/s) to 0.3 cm2/s (0.1 cm2/s) with the substrates removed for WS2 (MoS2) monolayers. It turns to be the major pathway of exciton decay and dominates the luminescence efficiency when the exciton density is beyond 1010 cm-2 in suspended monolayers or 1011 cm-2 in supported monolayers. This …
The exciton valley dynamics in van der Waals heterostructures with transition metal dichalcogenides monolayers is driven by the long-range exchange interaction between the electron and the hole in the exciton. It couples the states active in the opposite circular polarizations resulting in the longitudinal-transverse splitting of excitons propagating in the monolayer plane. Here we study theoretically the effect of the dielectric environment on the long-range exchange interaction and demonstrate how the encapsulation in the hexagonal boron nitride modifies the exciton longitudinal-transverse s…
The coupling between spin, charge, and lattice degrees of freedom plays an important role in a wide range of fundamental phenomena. Monolayer semiconducting transitional metal dichalcogenides have emerged as an outstanding platform for studying these coupling effects because they possess unique spin-valley locking physics for hosting rich excitonic species and the reduced screening for strong Coulomb interactions. Here, we report the observation of multiple valley phonons, phonons with momentum vectors pointing to the corners of the hexagonal Brillouin zone, and the resulting exciton complexes…
Spin-valley coupling in monolayer transition metal dichalcogenides gives rise to valley polarization and coherence effect, limited by intervalley scattering caused by exciton-phonon, exciton-impurity, and electron-hole exchange interaction (EHEI). We explore an approach to tune the EHEI by controlling excitons center of mass momentum (COM) utilizing the photon distribution of higher-order optical vortex beam. By virtue of this, we have observed excitons COM-dependent valley depolarization and decoherence which gives us the ability to measure the timescale associated with valley dynamics in the…
We investigate the optical control possibilities of spin-valley qubit carried by single electrons localized in nanostructures of monolayer TMDs, including small quantum dots formed by lateral heterojunction and charged impurities. The quantum controls are discussed when the confinement induces valley hybridization and when the valley hybridization is absent. We show that the bulk valley and spin optical selection rules can be inherited in different forms in the two scenarios, both of which allow the definition of spin-valley qubit with desired optical controllability. We also investigate nucle…
Using time-resolved optical Kerr rotation, we measure the low temperature valley dynamics of resident electrons and holes in exfoliated WSe$_2$ monolayers as a systematic function of carrier density. In an effort to reconcile the many disparate timescales of carrier valley dynamics in monolayer semiconductors reported to date, we directly compare the doping-dependent valley relaxation in two electrostatically-gated WSe$_2$ monolayers having different dielectric environments. In a fully-encapsulated structure (hBN/WSe$_2$/hBN, where hBN is hexagonal boron nitride), valley relaxation is found to…
Valleytronic materials, characterized by local extrema (valley) in their bands, and topological insulators have separately attracted great interest recently. However, the interplay between valleytronic and topological properties in one single system, likely to enable important unexplored phenomena and applications, has been largely overlooked so far. Here, by combining a tight-binding model with first-principles calculations, we find the large-band-gap quantum spin Hall effects (QSHEs) and valley Hall effects (VHEs) appear simultaneously in the Bi monolayers decorated with halogen elements, de…
Using time-resolved Kerr rotation, we measure the spin/valley dynamics of resident electrons and holes in single charge-tunable monolayers of the archetypal transition-metal dichalcogenide (TMD) semiconductor WSe2. In the n-type regime, we observe long (70 ns) polarization relaxation of electrons that is sensitive to in-plane magnetic fields $B_y$, indicating spin relaxation. In marked contrast, extraordinarily long (2 microsecond) polarization relaxation of holes is revealed in the p-type regime, that is unaffected by $B_y$, directly confirming long-standing expectations of strong spin-valley…
Heterobilayers consisting of MoSe$_2$ and WSe$_2$ monolayers can host optically bright interlayer excitons with intriguing properties such as ultralong lifetimes and pronounced circular polarization of their photoluminescence due to valley polarization, which can be induced by circularly polarized excitation or applied magnetic fields. Here, we report on the observation of an intrinsic valley-magnetophonon resonance for localized interlayer excitons promoted by invervalley hole scattering. It leads to a resonant increase of the photoluminescence polarization degree at the same field of 24.2 Te…
Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer $\mathrm{CSb_{1.5}Bi_{1.5}}$ with dynamic, mechanical and thermal stabilities. The inequivalent valleys have opposite Berry curvature and spin moment, which can produce a spin-valley Hall effect. In the center of Brillouin zone, a Rashba-type spin splitting can be observed due to missing horizont…
Semiconducting transition metal dichalcogenide monolayers have emerged as promising candidates for future valleytronics-based quantum information technologies. Two distinct momentum-states of tightly-bound electron-hole pairs in these materials can be deterministically initialized via irradiation with circularly polarized light. Here, we investigate the ultrafast dynamics of such a valley polarization in monolayer tungsten diselenide by means of time-resolved Kerr reflectometry. The observed Kerr signal in our sample stems exclusively from charge-neutral excitons. Our findings support the pict…
