Valley Splitting and Polarization by Zeeman Effect in Monolayer MoSe2

Li, Yilei; Ludwig, Jonathan; Low, Tony; Chernikov, Alexey; Xu, Chonghai; Arefe, Ghidewon; Kim, Young Duck; Zande, Arend van der; Rigosi, Albert F.; Hill, Heather M.; Kim, Suk Hyun; Hone, James; Li, Zhiqiang; Smirnov, Dmitry; Heinz, Tony F.

doi:10.1007/978-3-319-25376-3_7

Cited by 113 publications

(194 citation statements)

References 42 publications

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“…V) and (ii) commercially available crystals. We also show that narrow linewidths can be achieved in other TMDC MLs via hBN encapsulation (3) The narrow linewidth allows us to distinguish spectrally the emission from the nonidentical valleys K þ and K − in MoS 2 as they are split by the valley Zeeman effect [43][44][45][46][47][48]. We are able to determine the longitudinal exciton Landé g factor in magnetic fields below 10 T in a commercial magnetocryostat.…”

Section: Introductionmentioning

confidence: 86%

“…Measuring the Landé g factor is important for spin-valley physics, as it determines the energy separation achievable between the different polarization states [43][44][45][46][47][48]. The g factor, closely related to the effective mass tensor, also gives a fingerprint of the impact of different bands on the optical transitions [45,48,84].…”

Section: B Valley Zeeman Splitting and Field-induced Valley Polarizamentioning

confidence: 99%

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Excitonic Linewidth Approaching the Homogeneous Limit in MoS2 -Based van der Waals Heterostructures

et al. 2017

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The strong light-matter interaction and the valley selective optical selection rules make monolayer (ML) MoS 2 an exciting 2D material for fundamental physics and optoelectronics applications. But, so far, optical transition linewidths even at low temperature are typically as large as a few tens of meV and contain homogeneous and inhomogeneous contributions. This prevented in-depth studies, in contrast to the bettercharacterized ML materials MoSe 2 and WSe 2 . In this work, we show that encapsulation of ML MoS 2 in hexagonal boron nitride can efficiently suppress the inhomogeneous contribution to the exciton linewidth, as we measure in photoluminescence and reflectivity a FWHM down to 2 meV at T ¼ 4 K. Narrow optical transition linewidths are also observed in encapsulated WS 2 , WSe 2 , and MoSe 2 MLs. This indicates that surface protection and substrate flatness are key ingredients for obtaining stable, high-quality samples. Among the new possibilities offered by the well-defined optical transitions, we measure the homogeneous broadening induced by the interaction with phonons in temperature-dependent experiments. We uncover new information on spin and valley physics and present the rotation of valley coherence in applied magnetic fields perpendicular to the ML.

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Section: Introductionmentioning

confidence: 86%

Section: B Valley Zeeman Splitting and Field-induced Valley Polarizamentioning

confidence: 99%

Excitonic Linewidth Approaching the Homogeneous Limit in MoS2 -Based van der Waals Heterostructures

et al. 2017

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“…During the preparation of the manuscript, we became aware of similar results by the University of Washington group 37 , Cornell group 38 and Columbia University group 39 .…”

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confidence: 82%

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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“…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).…”

mentioning

confidence: 99%

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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Valley Splitting and Polarization by Zeeman Effect in Monolayer MoSe2

Cited by 113 publications

References 42 publications

Excitonic Linewidth Approaching the Homogeneous Limit in MoS2 -Based van der Waals Heterostructures

Excitonic Linewidth Approaching the Homogeneous Limit in MoS2 -Based van der Waals Heterostructures

Valley Zeeman effect in elementary optical excitations of monolayer WSe2

Optical manipulation of valley pseudospin

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