Rydberg series of dark excitons and the conduction band spin-orbit splitting in monolayer WSe$_2$
Piotr Kapuscinski, Alex Delhomme, Diana Vaclavkova, Artur Slobodeniuk, Magdalena Grzeszczyk, Miroslav Bartos, Kenji Watanabe, Takashi Taniguchi, Clément Faugeras, Marek Potemski
Strong Coulomb correlations together with multi-valley electronic bands in the presence of spin-orbit interaction and possible new optoelectronic applications are at the heart of studies of the rich physics of excitons in semiconductor structures made of monolayers of transition metal dichalcogenides (TMD). In intrinsic TMD monolayers the basic, intravalley excitons are formed by a hole from the top of the valence band and an electron either from the lower or upper spin-orbit-split conduction band subbands: one of these excitons is optically active, the second one is "dark", although possibly observed under special conditions. Here we demonstrate the s-series of Rydberg dark exciton states in monolayer WSe$_2$, which appears in addition to a conventional bright exciton series in photoluminescence spectra measured in high in-plane magnetic fields. The comparison of energy ladders of bright and dark Rydberg excitons is shown to be a method to experimentally evaluate one of the missing band parameters in TMD monolayers: the amplitude of the spin-orbit splitting of the conduction band.
We report the experimental observation of radiative recombination from Rydberg excitons in a two-dimensional semiconductor, monolayer WSe2, encapsulated in hexagonal boron nitride. Excitonic emission up to the 4s excited state is directly observed in photoluminescence spectroscopy in an out-of-plane magnetic field up to 31 Tesla. We confirm the progressively larger exciton size for higher energy excited states through diamagnetic shift measurements. This also enables us to estimate the 1s exciton binding energy to be about 170 meV, which is significantly smaller than most previous reports. The…
Monolayer WSe$_2$ hosts a series of exciton Rydberg states denoted by the principal quantum number n = 1, 2, 3, etc. While most research focuses on their absorption properties, their optical emission is also important but much less studied. Here we measure the photoluminescence from the 1s - 5s exciton Rydberg states in ultraclean monolayer WSe$_2$ encapsulated by boron nitride under magnetic fields from -31 T to 31 T. The exciton Rydberg states exhibit similar Zeeman shifts but distinct diamagnetic shifts from each other. From their luminescence spectra, Zeeman and diamagnetic shifts, we dedu…
The results of magneto-optical spectroscopy investigations of excitons in a CVD grown monolayer of WSe2 encapsulated in hexagonal boron nitride are presented. The emission linewidth for the 1s state is of 4:7 meV, close to the narrowest emissions observed in monolayers exfoliated from bulk material. The 2s excitonic state is also observed at higher energies in the photoluminescence spectrum. Magneto-optical spectroscopy allows for the determination of the g-factors and of the spatial extent of the excitonic wave functions associated with these emissions. Our work establishes CVD grown monolaye…
Based on \emph{ab initio} theoretical calculations of the optical spectra of vertical heterostructures of MoSe$_2$ (or MoS$_2$) and WSe$_2$ sheets, we reveal two spin-orbit-split Rydberg series of excitonic states below the \textsl{A} excitons of MoSe$_2$ and WSe$_2$ with a significant binding energy on the order of 250\,meV for the first excitons in the series. At the same time, we predict crystalographically aligned MoSe$_2$/WSe$_2$ heterostructures to exhibit an indirect fundamental band gap. Due to the type-II nature of the MoSe$_2$/WSe$_2$ heterostructure, the indirect transition and the …
Layered 2D van der Waals materials, such as transition metal dichalcogenides, are promising for nanoscale spintronic and optoelectronic applications. Harnessing their full potential requires understanding both intrinsic transport and the dynamics of optically excited spin and charge carriers -- particularly the transition between excited spin polarization and the conduction band's intrinsic spin texture. Here, we investigate the spin polarization of the conduction bands of bulk WSe$_2$ using static and time-resolved spin-resolved photoemission spectroscopy, complemented by photocurrent calcula…
We study the screened dynamics of the nonequilibrium excitonic consensate forming in a bulk WSe$_{2}$ when illuminated by coherent light resonant with the lowest-energy exciton. Intervalley scattering causes electron migration from the optically populated K valley to the conduction band minimum at $Σ$. Due to the electron-hole unbalance at the K point a plasma of quasi-free holes develops, which efficiently screens the interaction of the remaining excitons. We show that this plasma screening causes an ultrafast melting of the nonequilibrium consensate and that during melting coherent excitons …
We present a high-resolution resonance Raman study of hBN encapsulated MoSe$_2$ and WSe$_2$ monolayers at 4 K using excitation energies from 1.6 eV to 2.25 eV. We report resonances with the WSe$_2$ A2s and MoSe$_2$ A2s and B2s excited Rydberg states despite their low oscillator strength. When resonant with the 2s states we identify new Raman peaks which are associated with intravalley scattering between different Rydberg states via optical phonons. By calibrating the Raman scattering efficiency and separately constraining the electric dipole matrix elements, we reveal that the scattering rates…
Strong optical nonlinearities play a central role in realizing quantum photonic technologies. In solid state systems, exciton-polaritons, which result from the hybridization of material excitations and cavity photons, are an attractive candidate to realize such nonlinearities. Here, the interaction between excitons forms the basis of the polaritonic nonlinearity. While the interaction between ground state excitons generates a notable optical nonlinearity, the strength of such ground state interactions is generally not sufficient to reach the regime of quantum nonlinear optics and strong single…
One of the main tasks in the investigation of 2-dimensional transition metal dichalcogenides is the determination of valley lifetimes. In this work, we combine time-resolved Kerr rotation with electrical transport measurements to explore the gate-dependent valley lifetimes of free conduction band electrons of monolayer WSe$_2$. When tuning the Fermi energy into the conduction band we observe a strong decrease of the respective valley lifetimes which is consistent with both spin-orbit and electron-phonon scattering. We explain the formation of a valley polarization by the scattering of opticall…
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…
Quantum spin Hall (QSH) insulator with large gap is highly desirable for potential spintronics application. Here we realize electrically tunable QSH insulator with large gap in van der Waals heterobilayer of monolayer transition metal dichalcogenide (TMD) and hexagonal BAs. When the type II band alignment gets inverted in an electric field, the hybridization by interlayer hopping between the spin-valley locked valence band edges in TMD and the BAs conduction band edges leads to a stacking-configuration dependent topological band inversion. In the non-interacting limit, the double spin degenera…
We report scanning tunneling microscopy (STM) and spectroscopy (STS) measurements of monolayer and bilayer WSe$_2$. We measure a band gap of 2.21 $\pm$ 0.08 eV in monolayer WSe$_2$, which is much larger than the energy of the photoluminescence peak indicating a large excitonic binding energy. We additionally observe significant electronic scattering arising from atomic-scale defects. Using Fourier transform STS (FT-STS), we map the energy versus momentum dispersion relations for monolayer and bilayer WSe$_2$. Further, by tracking allowed and forbidden scattering channels as a function of energ…
Moiré excitons are emergent optical excitations in 2D semiconductors with deep moiré superlattice potentials. While these excitations have been realized in several platforms, a system with dynamically tunable moiré potential to tailor the moiré exciton properties is yet to be realized. Here, we present a continuously tunable moiré potential in a monolayer WSe2 that is enabled by its proximity to twisted bilayer graphene (TBG) near the magic-angle. Due to its flat electronic bands, charge distribution is highly localized and forms a triangular lattice in TBG. Tuning the local charge density via…
A WSe2 monolayer of 1T' phase is a large band gap quantum spin Hall insulator, supporting dissipationless charge and spin transports through the topologically protected edge states. In this work, we explore the nanoribbon forms of 1T' phase WSe2 by first-principles density functional calculations and the many-body perturbation GW and Bethe-Salpeter equation method. We found that the 1T' WSe2 nanoribbon can show topological edge states with a ribbon width of ~4-6 nm. Those edge bands show crossing through the Fermi level an odd number of times, with one kind of spin-polarization connecting the …
Hybridisation of electronic bands of two-dimensional materials, assembled into twistronic heterostructures, enables one to tune their optoelectronic properties by selecting conditions for resonant interlayer hybridisation. Resonant interlayer hybridisation qualitatively modifies the excitons in such heterostructures, transforming these optically active modes into superposition states of interlayer and intralayer excitons. For MoSe$_2$/WSe$_2$ heterostructures, strong hybridization occurs between the holes in the spin-split valence band of WSe$_2$ and in the top valence band of MoSe$_2$, especi…
We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the $s$-type Rydberg series of excitonic states follows a simple energy ladder: $ε_n=-Ry^*/(n+δ)^2$, $n$=1,2,\ldots, in which $Ry^*$ is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is only accounted for by $δ$. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe$_2$ ML encaps…
We develop a many-body approach to the behavior of exciton bound states and the conduction electron band edge in a surrounding electron-hole plasma with a focus on the absorption spectrum of Rydberg excitons in cuprous oxide. The interplay of band edge and exciton levels is analyzed numerically, whereby the self-consistent solution is compared to the semiclassical Debye approximation. Our results provide criteria which allow to verify or rule out the different band edge models against future experimental data.
Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly-bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX$_2$ (X~being S or Se) spin-forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe$_2$ monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsi…
We report the direct observation of intervalley exciton between the Q conduction valley and $Γ$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Γ$ exciton lies at ~18 meV below the QK exciton and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton spectra at gate-tunable electric field, we reveal different interlayer electric dipole moments and Stark shifts between Q$Γ$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Γ$ and QK excitons. Both Q$Γ$ and QK excitons exhibit pronounced phonon re…
The functional form of Coulomb interactions in the transition metal dichalcogenides and other van der Waals solids is critical to many of their unique properties, e.g. strongly-correlated electron states, superconductivity and emergent ferromagnetism. This paper presents measurements of key excitonic energy levels in MoSe2/WSe2 heterostructures. These measurements are obtained from resonance Raman experiments on specific Raman peaks only observed at excited states of the excitons. This data is used to validate a model of the Coulomb potential in these structures which predicts the exciton ener…
The direct band gap character and large spin-orbit splitting of the valence band edges (at the K and K' valleys) in monolayer transition metal dichalcogenides have put these two-dimensional materials under the spot-light of intense experimental and theoretical studies. In particular, for Tungsten dichalcogenides it has been found that the sign of spin splitting of conduction band edges makes ground state excitons radiatively inactive (dark) due to spin and momentum mismatch between the constituent electron and hole. One might similarly assume that the ground states of charged excitons and biex…
Coulomb interaction between electrons lies at the heart of magnetism in solids. In contrast to conventional two-dimensional (2D) systems, electrons in monolayer transition metal dichalcogenides (TMDs) possess coupled spin and valley degrees of freedom by the spin-orbit interaction. The electrons are also strongly interacting even in the high-density regime because of the weak dielectric screening in two dimensions and a large band mass. The combination of these properties presents a unique platform for exploring spin and valley magnetism in 2D electron liquids. Here we report an observation by…
A monolayer of a transition metal dichalcogenide (TMD) such as WSe$_2$ is a two-dimensional (2D) direct band-gap valley-semiconductor having an effective Honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly-polarized light fields, suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom. Here we report such experiments that demonstrate the valley Zeeman effect -- strongly anisotropic lifting of the degeneracy of the valley pseudospi…
Monolayers and multilayers of semiconducting transition metal dichalcogenides (TMDCs) offer an ideal platform to explore valley-selective physics with promising applications in valleytronics and information processing. Here we manipulate the energetic degeneracy of the $\mathrm{K}^+$ and $\mathrm{K}^-$ valleys in few-layer TMDCs. We perform high-field magneto-reflectance spectroscopy on WSe$_2$, MoSe$_2$, and MoTe$_2$ crystals of thickness from monolayer to the bulk limit under magnetic fields up to 30 T applied perpendicular to the sample plane. Because of a strong spin-layer locking, the gro…
Understanding quasiparticle band structures of transition metal dichalcogenides (TMDs) is critical for technological advances of these materials for atomic layer electronics and photonics. Although theoretical calculations to date have shown qualitatively similar features, there exist subtle differences which can lead to important consequences in the device characteristics. For example, most calculations have shown that all single layer (SL) TMDs have direct band gaps, while some have shown that $SL-WSe_2$ have an indirect gap. Moreover, there are large variations in the reported quasiparticle…
Monolayer transition metal dichalcogenide (TMDC) crystals, as direct-gap materials with unusually strong light-matter interaction, have attracted much recent attention. In contrast to the initial understanding, the minima of the conduction band are predicted to be spin split. Because of this splitting and the spin-polarized character of the valence bands, the lowest-lying excitonic states in WX2 (X=S, Se) are expected to be spin-forbidden and optically dark. To date, however, there has been no direct experimental probe of these dark band-edge excitons, which strongly influence the light emissi…
Manipulation of spin and valley degrees of freedom is a key step towards realizing novel quantum technologies, for which atomically thin transition metal dichalcogenides (TMDCs) have been established as promising candidates. In monolayer TMDCs, the lack of inversion symmetry gives rise to a spin-valley correlation of the band structure allowing for valley-selective electronic excitation with circularly polarized light. Here we show that, even in centrosymmetric samples of 2H-WSe2, circularly polarized light can generate spin-, valley- and layer-polarized excited states in the conduction band. …
We report 65 tesla magneto-absorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor WSe$_2$. 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 magn…
Monolayer transition metal dichalcogenides in the distorted octahedral 1T$^\prime$ phase exhibit a large bulk bandgap and gapless boundary states, which is an asset in the ongoing quest for topological electronics. In single-layer tungsten diselenide (WSe$_2$), the boundary states have been observed at well ordered interfaces between 1T$^\prime$ and semiconducting (1H) phases. This paper proposes an effective 4-band theory for the boundary states in single-layer WSe$_2$,describing a Kramers pair of in-gap states as well as the behaviour at the spectrum termination points on the conduction and …
We report on nanosecond long, gate-dependent valley lifetimes of free charge carriers in monolayer WSe$_2$, unambiguously identified by the combination of time-resolved Kerr rotation and electrical transport measurements. While the valley polarization increases when tuning the Fermi level into the conduction or valence band, there is a strong decrease of the respective valley lifetime consistent with both electron-phonon and spin-orbit scattering. The longest lifetimes are seen for spin-polarized bound excitons in the band gap region. We explain our findings via two distinct, Fermi level-depen…
TMDCs have attracted a lot of attention in recent years due to their unique indirect to direct band gap transition from bulk to monolayer thickness. Strong confinement in the out-of-plane direction enhances the Coulomb potential between the charged particles (e-h pairs) and thus increases the exciton binding energy dramatically. The lattice inversion asymmetry in a monolayer creates two non-equivalent (but degenerate in energy) band edges protected by time reversal polarisation via pseudo-spin. However, the presence of strong spin-orbit coupling in the valence band and weak spin-splitting in t…
The emergence of transition metal dichalcogenides (TMDs) as 2D electronic materials has stimulated proposals of novel electronic and photonic devices based on TMD heterostructures. Here we report the determination of band offsets in TMD heterostructures by using microbeam X-ray photoelectron spectroscopy (μ-XPS) and scanning tunneling microscopy/spectroscopy (STM/S). We determine a type-II alignment between $\textrm{MoS}_2$ and $\textrm{WSe}_2$ with a valence band offset (VBO) value of 0.83 eV and a conduction band offset (CBO) of 0.76 eV. First-principles calculations show that in this hetero…
We investigate Landau-quantized excitonic absorption and luminescence of monolayer WSe$_2$ under magnetic field. We observe gate-dependent quantum oscillations in the bright exciton and trions (or exciton-polarons) as well as the dark trions and their phonon replicas. Our results reveal spin- and valley-polarized Landau levels (LLs) with filling factors $n = +0, +1$ in the bottom conduction band and $n = -0$ to $-6$ in the top valence band, including the Berry-curvature-induced $n = \pm0$ LLs of massive Dirac fermions. The LL filling produces periodic plateaus in the exciton energy shift accom…
Controlling the momentum of carriers in semiconductors, known as valley polarization, is a new resource for optoelectronics and information technologies. Materials exhibiting high polarization are needed for valley-based devices. Few-layer WS$_2$ shows a remarkable spin-valley polarization above 90%, even at room temperature. In stark contrast, polarization is absent for few-layer WSe$_2$ despite the expected material similarities. Here, we explain the origin of valley polarization in both materials based on the interplay between two indirect optical transitions. We show that the relative ener…
Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances which serve as a microscopic, non-invasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe$_2$). Here, we report an experimental investigation of excitonic luminescence properties of monolay…
Unveiling the Spin-Valley Structure of Dipolar Exciton Ladders in R-stacked WSe$_2$/WS$_2$ Moiré Heterobilayers
Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University（赫瑞-瓦特大学光子与量子科学研究所）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料纳米结构研究中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（电子与光学材料研究中心）
研究 R 堆叠 WSe₂/WS₂ 莫尔异质双层中偶极激子阶梯的自旋-谷结构，用螺旋度分辨磁光致发光确定其微观起源，明确不同电荷填充时各激子态情况，建立超越简单占据数物理的自旋-谷分辨图像。
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…
Energy relaxation of photo-excited charge carriers is of significant fundamental interest and crucial for the performance of monolayer (1L) transition metal dichaclogenides (TMDs) in optoelectronics. We measure light scattering and emission in 1L-WSe$_2$ close to the laser excitation energy (down to~$\sim$0.6meV). We detect a series of periodic maxima in the hot photoluminescence intensity, stemming from energy states higher than the A-exciton state, in addition to sharp, non-periodic Raman lines related to the phonon modes. We find a period $\sim$15meV for peaks both below (Stokes) and above …
Monolayer transition metal dichalcogenides have recently attracted great interests because the quantum dots embedded in monolayer can serve as optically active single photon emitters. Here, we provide an interpretation of the recombination mechanisms of these quantum emitters through polarization-resolved and magneto-optical spectroscopy at low temperature. Three types of defect-related quantum emitters in monolayer tungsten diselenide (WSe$_2$) are observed, with different exciton g factors of 2.02, 9.36 and unobservable Zeeman shift, respectively. The various magnetic response of the spatial…
Lifting the valley degeneracy of monolayer transition metal dichalcogenides (TMD) would allow versatile control of the valley degree of freedom. We report a giant valley exciton splitting of 18 meV/T for monolayer WS2, using the proximity effect from a ferromagnetic EuS substrate, which is enhanced by nearly two orders of magnitude from the 0.2 meV/T obtained by an external magnetic field. More interestingly, a sign reversal of the valley exciton splitting is observed as compared to that of WSe2 on EuS. Using first principles calculations, we investigate the complex behavior of exchange intera…
Proximity-induced spin-orbit coupling in graphene has led to the observation of intriguing phenomena like time-reversal invariant $\mathbb{Z}_2$ topological phase and spin-orbital filtering effects. An understanding of the effect of spin-orbit coupling on the band structure of graphene is essential if these exciting observations are to be transformed into real-world applications. In this research article, we report the experimental determination of the band structure of single-layer graphene (SLG) in the presence of strong proximity-induced spin-orbit coupling. We achieve this in high-mobility…
We investigate the twist-angle and gate dependence of the proximity-induced exchange coupling in the monolayer transition-metal dichalcogenides (TMDCs) MoSe$_2$ and WSe$_2$ due to the vdW coupling to the ferromagnetic semiconductor CrI$_3$, from first-principles calculations. A model Hamiltonian, that captures the relevant band edges at the $K/K^{\prime}$ valleys of the proximitized TMDCs, is employed to quantify the proximity-induced exchange. Upon twisting from 0° to 30°, we find a transition of the TMDC valence band (VB) edge exchange splitting from about $-2$ to $2$ meV, while the conducti…
The electron valley and spin degree of freedom in monolayer transition-metal dichalcogenides can be manipulated in optical and transport measurements performed in magnetic fields. The key parameter for determining the Zeeman splitting, namely the separate contribution of the electron and hole g-factor, is inaccessible in most measurements. Here we present an original method that gives access to the respective contribution of the conduction and valence band to the measured Zeeman splitting. It exploits the optical selection rules of exciton complexes, in particular the ones involving inter-vall…
