Magnetooptics of Exciton Rydberg States in a Monolayer Semiconductor

Abstract

We report 65 tesla magneto-absorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor WSe2. The strongly field-dependent and distinct energy shifts of the 2s, 3s, and 4s excited neutral excitons permits their unambiguous identification and allows for quantitative comparison with leading theoretical models. Both the sizes (via low-field diamagnetic shifts) and the energies of the ns exciton states agree remarkably well with detailed numerical simulations using the non-hydrogenic screened Keldysh potential for 2D semiconductors. Moreover, at the highest magnetic fields the nearly-linear diamagnetic shifts of the weakly-bound 3s and 4s excitons provide a direct experimental measure of the exciton's reduced mass, mr = 0.20 ± 0.01 m0.The burgeoning interest in atomically-thin transitionmetal dichalcogenide (TMD) semiconductors such as monolayer MoS 2 and WSe 2 derives in part from their direct optical bandgap and very strong light-matter coupling [1, 2]. In a pristine TMD monolayer, the fundamental optical excitation -the ground-state neutral "A" exciton (X 0 )-can, remarkably, absorb >10% of incoming light [3]. Moreover, in doped or highly excited monolayers distinct resonances due to charged excitons or multiexciton states can develop in optical spectra [4][5][6][7][8][9]. The ability to spectrally resolve these and other features depends critically on material quality, which has markedly improved in recent years as techniques for synthesis, exfoliation, and surface passivation have steadily progressed.The optical quality of exfoliated WS 2 and WSe 2 monolayers has recently improved to the point where signatures of the much weaker excited Rydberg states of X 0 (2s, 2p, 3s, etc.) have been reported based on various linear and nonlinear optical spectroscopies [10][11][12][13][14][15][16]. Correct identification and quantitative measurements of excited excitons are of critical importance in this field, because they provide direct insight into the non-hydrogenic attractive potential between electrons and holes that is believed to exist in 2D materials due to dielectric confinement and nonlocal screening [17][18][19][20][21]. This potential leads, for example, to an unconventionally-spaced Rydberg series of excited excitons and can generate an anomalous ordering of (s, p, d ) levels [10]. Crucially, these excited states allow one to directly estimate the free-particle bandgap and binding energy of the X 0 ground state [10][11][12][13][14][15], both key material parameters that are otherwise difficult to measure in monolayer TMDs, and which are necessarily very sensitive to the surrounding dielectric environment [14,21,22,24]. Greatly desired, therefore, are incisive experimental tools for detailed studies of excited excitons in 2D semiconductors.Historically, optical spectroscopy in high magnetic fields B has provided an especially powerful way to identify and quantify excited excitons [25][26][27][28][29], because each excited state shifts very differently with B. Crucially, these shift...

Superior Valley Polarization and Coherence of 2s Excitons in Monolayer WSe2

“…If we assume the 0.8meV linewidth difference is mostly due to faster population decay, and take the 1s luminescence decay time to be 2ps from a recent study [35], we infer a 2s lifetime of about 0.6ps. Further the 2s oscillator strength is about 15 times weaker than 1s from absorption spectra in Fig.1, consistent with the value from a recent diamagnetic shift measurement [36], while the low temperature 1s intensity is about 60 times stronger than 2s (Fig.1c). This suggests a decay rate ratio of 4, in reasonable agreement with the above estimation from linewidth difference.…”

“…For the 1s exciton this is given approximately by 1/ 2 , where 36] is the exciton Bohr radius. In the case of 2s excitons, a recent measurement found that the electron-hole separation in 2s is about 6.6nm [36]. Assuming that the 1s and 2s excitons have about the same mass, the 2s exchange interaction is then about 15 times weaker.…”

Valley phonons and exciton complexes in a monolayer semiconductor

“…S1. Monolayer WSe2 hosts a rich spectrum of excitonic species [23][24][25][26][27][28] . Several previously identified excitonic states are indicated in the figure, including the neutral bright exciton ( 0 ), bright trions ( ± ) [29][30][31][32][33] , the intravalley spinforbidden dark exciton ( 0 ) 17-20, 34 , and dark trions ( ± ) 18, 35 .…”

Dynamical screening effects of substrate phonons on two-dimensional excitons

“…For the coupling between 2d carriers and environmental phonons in WSe 2 , the band structure around the K-point is approximated by electron and hole effective masses m e = m h = 0.4m 0 yielding a reduced exciton mass µ r = 0.2m 0 . [42] We limit carrier-phonon scattering to intra-valley processes neglecting coupling to dark excitons that involve large momentum transfer q. [32] This is justified by the 1/q-scaling behavior of the Fröhlichtype coupling considered here.…”

“…[32] This is justified by the 1/q-scaling behavior of the Fröhlichtype coupling considered here. We use a layer thickness of h 2d = 0.66 nm, a dielectric constant ε 2d = 14.6 corresponding to a screening length r 0 = 4.5 nm [42] and a broadening Γ = 10 meV. For the inter-layer distance, we choose h int = 0.2 nm.…”