Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides

Yu, Hongyi; Liu, Gui-Bin; Gong, Pan; Xu, Xiaodong; Yao, Wang

doi:10.1038/ncomms4876

Cited by 338 publications

(423 citation statements)

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“…We observe that, as we increase transmission NA from 0.1 to 0.55, the extinction drops from 0.9 down to 0.6, while the exciton linewidth increases from 3 to 6 meV. We tentatively attribute this strong NA dependence to electron-hole exchange interaction induced modification of the exciton spectrum: it has been theoretically predicted that, due to this interaction, the p-polarized excitons would have a Dirac-conelike dispersion, leading to an energy splitting of s-and p-polarized excitons of order 3 meV for k ∼ ω exc =c [26,27]. To the best of our knowledge, the NA-dependent increase in linewidth that we report here provides the first evidence for this striking theoretical prediction.…”

Section: (C)mentioning

confidence: 88%

Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using MonolayerMoSe2

et al. 2018

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Advent of new materials such as van der Waals heterostructures, propels new research directions in condensed matter physics and enables development of novel devices with unique functionalities. Here, we show experimentally that a monolayer of MoSe 2 embedded in a charge controlled heterostructure can be used to realize an electrically tunable atomically-thin mirror, that effects 90% extinction of an incident field that is resonant with its exciton transition. The corresponding maximum reflection coefficient of 45% is only limited by the ratio of the radiative decay rate to the linewidth of exciton transition and is independent of incident light intensity up to 400 Watts/cm 2 . We demonstrate that the reflectivity of the mirror can be drastically modified by applying a gate voltage that modifies the monolayer charge density. Our findings could find applications ranging from fast programmable spatial light modulators to suspended ultra-light mirrors for optomechanical devices.A plethora of ground-breaking experiments have established monolayers of transition metal dichalcogenides (TMD) such as MoSe 2 or WSe 2 as a new class of two dimensional (2D) direct 1

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confidence: 88%

Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using MonolayerMoSe2

et al. 2018

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“…Polarization-resolved PL measurements yielded a valley-contrasting circular dichroism of less than 20% for both X 0 and X − resonances in all the flakes that were measured. As we argue below, the electron-hole exchange-induced mixing of the two valleys is possibly responsible for reducing the degree of circular dichroism 21,23 . Figure 2a shows the behaviour of X 0 at various B up to 8.4 T in the Faraday geometry (B z).…”

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“…The absence of valley coherence of the X − peak in monolayer WSe 2 has been attributed to the fast phase-rotation associated with this energy splitting 22 . Recently, it was theoretically shown that the corresponding exchange-induced modification of the trion dispersion ensures that the trion states with centre-ofmass momentum ∼ ±K carry a large Berry curvature 21 . If the trion can be considered as a strongly bound, charged quasi-particle, the exchange-induced Berry curvature (k) will be accompanied by a contribution to the orbital magnetic moment that is given by µ(k) = (e/2h) (k)δ ex for k ±K; here δ ex is the exchangeinduced splitting of the trion resonances.…”

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confidence: 99%

“…On the other hand, it is well known that the optical excitation spectra of TMDs are strongly modified by Coulomb interactions, leading to strongly bound neutral and charged exciton (trion) resonances with non-hydrogenic excited states [15][16][17][18][19][20] . Moreover, it has been recently shown that the electronhole exchange interaction couples the ±K valleys 21 . It is therefore not a priori clear to what extent predictions about circular dichroism or orbital magnetic moments that are based on a non-interacting particle picture remain valid in optical measurements probing exciton or trion resonances.…”

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Valley Zeeman effect in elementary optical excitations of monolayer WSe2

et al. 2015

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A monolayer of a transition metal dichalcogenide such as WSe 2 is a two-dimensional direct-bandgap valley-semiconductor 1,2 having an e ective honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly polarized light fields 3-5 , suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom 6-8 . Here we report such experiments that demonstrate the valley Zeeman e ect-strongly anisotropic lifting of the degeneracy of the valley pseudospin degree of freedom using an external magnetic field. The valley-splitting measured using the exciton transition deviates appreciably from values calculated using a three-band tight-binding model 9 for an independent electron-hole pair at ±K valleys. We show, on the other hand, that a theoretical model taking into account the strongly bound nature of the exciton yields an excellent agreement with the experimentally observed splitting. In contrast to the exciton, the trion transition exhibits an unexpectedly large valley Zeeman e ect that cannot be understood within the same framework, hinting at a di erent contribution to the trion magnetic moment. Our results raise the possibility of controlling the valley degree of freedom using magnetic fields in monolayer transition metal dichalcogenides or observing topological states of photons strongly coupled to elementary optical excitations in a microcavity 10 .Charge carriers in two-dimensional (2D) layered materials with a honeycomb lattice, such as graphene and transition metal dichalcogenides (TMDs), have a twofold valley degree of freedom labelled by ±K-points of the Brillouin zone, which are related to each other by time-reversal symmetry 7 . In TMDs, the low-energy physics takes place in the vicinity of ±K-points of the conduction and valence bands with Bloch states that are formed primarily from d z 2 and d x 2 −y 2 , d xy orbitals of the transition metal, respectively 9 . The magnetic moment of charged particles in a monolayer TMD arises from two distinct contributions: the intracellular component stems from the hybridization of the d x 2 −y 2 and d xy orbitals as d x 2 −y 2 ± id xy , which provide the Bloch electrons at ±K in the valence band an azimuthal angular momentum along z of l z = ±2h (Fig. 1a). The second-intercellular-contribution originates from the phase winding of the Bloch functions at ±K-points 11-14 . This latter contribution to orbital magnetic moment is different for conduction and valence bands owing to breakdown of electronhole symmetry. Both contributions yield magnetic-field-induced splitting with an opposite sign in the two valleys.In a 2D material such as a monolayer TMD, the current circulation from the orbitals can only be within the plane; as a consequence, the corresponding orbital magnetic moment can only point out-of-plane. A magnetic field (B) along z distinguishes the sense of circulation in 2D, causing opposite energy shifts (− µ· B) in ±K val...

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“…This information allows us to estimate the ratio between T 1 and T 2 , leaving only two independent parameters in the model (Supplementary Section I). (We note that the partial degree of linear polarization has several possible origins, including intervalley scattering induced by defects/impurities, intravalley scattering, and the exchange interaction between excitons [23][24][25] . Within our model, we neglect possible initial depolarization effects in creating the valley excitation, in accord with the near-resonant character of our optical excitation.)…”

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Optical manipulation of valley pseudospin

Ye¹,

Sun²,

Heinz³

2016

Nature Phys

233

223

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The coherent manipulation of spin and pseudospin underlies existing and emerging quantum technologies, including quantum communication and quantum computation 1,2 . Valley polarization, associated with the occupancy of degenerate, but quantum mechanically distinct valleys in momentum space, closely resembles spin polarization and has been proposed as a pseudospin carrier for the future quantum electronics 3,4 . Valley exciton polarization has been created in the transition metal dichalcogenide monolayers using excitation by circularly polarized light and has been detected both optically 5-7 and electrically 8 . In addition, the existence of coherence in the valley pseudospin has been identified experimentally 9 . The manipulation of such valley coherence has, however, remained out of reach. Here we demonstrate all-optical control of the valley coherence by means of the pseudomagnetic field associated with the optical Stark e ect. Using below-bandgap circularly polarized light, we rotate the valley exciton pseudospin in monolayer WSe 2 on the femtosecond timescale. Both the direction and speed of the rotation can be manipulated optically by tuning the dynamic phase of excitons in opposite valleys. This study unveils the possibility of generation, manipulation, and detection of the valley pseudospin by coupling to photons.The broken inversion symmetry in monolayer transition metal dichalcogenide (TMDC) crystals in the semiconducting MX 2 (M = Mo, W; X = S, Se) family gives rise to a nontrivial Berry phase at the K and K valleys in momentum space 10 , where the optically accessible direct bandgap occurs in these materials 11,12 . This Berry phase, together with the angular momentum of the atomic orbitals, leads to different optical selection rules for the two valleys: excitons in the K valley couple to left-circularly polarized photons, while excitons in the K valley couple to right-circularly polarized photons, thus permitting the optical generation of valley polarization through control of the helicity of light [5][6][7] . Moreover, when a TMDC monolayer is excited with linearly polarized light, a coherent superposition state is established between the K and K valley excitons 9 . Such a coherent state can, in principle, be manipulated by lifting the energy degeneracy between valleys through the breaking of time-reversal symmetry in the material. In this regard, d.c. magnetic fields have been applied to achieve a valley splitting of a few meV [13][14][15][16] . Circularly polarized light also breaks time-reversal symmetry, and researchers have used it to create larger valley splittings, corresponding to pseudomagnetic fields up to 60 T (refs 17,18). In addition, this optical approach permits us to access the ultrafast timescale: in this work, we demonstrate the coherent manipulation of the valley pseudospin on the femtosecond timescale.The optical Stark effect has been applied to manipulate the spin/pseudospin in quantum systems, such as atomic quantum gases 19 , quantum dots 20,21 , and III-V quantum wells 22 . H...

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Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides

Cited by 338 publications

References 42 publications

Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using MonolayerMoSe2

Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using MonolayerMoSe2

Valley Zeeman effect in elementary optical excitations of monolayer WSe2

Optical manipulation of valley pseudospin

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