Landau-Quantized Excitonic Absorption and Luminescence in a Monolayer Valley Semiconductor

Versatile optical manipulation of trions, dark excitons and biexcitons through contrasting exciton-photon coupling

Various exciton species in transition metal dichalcogenides (TMDs), such as neutral excitons, trions (charged excitons), dark excitons, and biexcitons, have been individually discovered with distinct light-matter interactions. In terms of valley-spin locked band structures and electron-hole configurations, these exciton species demonstrate flexible control of emission light with degrees of freedom (DOFs) such as intensity, polarization, frequency, and dynamics. However, it remains elusive to fully manipulate different exciton species on demand for practical photonic applications. Here, we investigate the contrasting light-matter interactions to control multiple DOFs of emission light in a hybrid monolayer WSe2-Ag nanowire (NW) structure by taking advantage of various exciton species. These excitons, including trions, dark excitons, and biexcitons, are found to couple independently with propagating surface plasmon polaritons (SPPs) of Ag NW in quite different ways, thanks to the orientations of transition dipoles. Consistent with the simulations, the dark excitons and dark trions show extremely high coupling efficiency with SPPs, while the trions demonstrate directional chiral-coupling features. This study presents a crucial step towards the ultimate goal of exploiting the comprehensive spectrum of TMD excitons for optical information processing and quantum optics.

Six-Body and Eight-Body Exciton States in Monolayer WSe_{2}

In the archetypal monolayer semiconductor WSe_{2}, the distinct ordering of spin-polarized valleys (low-energy pockets) in the conduction band allows for studies of not only simple neutral excitons and charged excitons (i.e., trions), but also more complex many-body states that are predicted at higher electron densities. We discuss magneto-optical measurements of electron-rich WSe_{2} monolayers and interpret the spectral lines that emerge at high electron doping as optical transitions of six-body exciton states ("hexcitons") and eight-body exciton states ("oxcitons"). These many-body states emerge when a photoexcited electron-hole pair interacts simultaneously with multiple Fermi seas, each having distinguishable spin and valley quantum numbers. In addition, we explain the relations between dark trions and satellite optical transitions of hexcitons in the photoluminescence spectrum.

Theory of magnetic-field effect on trions in two-dimensional materials

In this work, we present a theoretical method to study the effect of magnetic field on trions in two-dimensional materials. The trion is modeled by a three-particle Schrödinger equation and the magnetic-field interaction is included by means of a vector potential in symmetric gauge. By using a coordinate transformation and a unitary transformation, the trion Hamiltonian can be converted into the sum of a translational term describing the Landau quantization for the trion center-of-mass motion, an internal term describing the trion binding, and a translational-internal coupling term depending linearly on the magnetic-field strength. The trion eigenenergy and wavefunction can then be calculated efficiently by using a variational method, and the quantum numbers of trions in magnetic fields can be assigned. The eigenenergies, binding energies, and correlation energies of three trion branches, which correspond to the ground-state trion and two excited-state trions solved from the trion Hamiltonian in zero magnetic field, are studied numerically in finite magnetic fields. The present method is applied to study the magnetic-field dependence of trion energy levels in hole-doped WSe₂ monolayers. The binding energies and correlation energies of positive trions in WSe₂ are investigated over a range of magnetic fields up to 25 T.

Anomalous Magneto-Optical Response and Chiral Interface of Dipolar Excitons at Twisted Valleys

An anomalous magneto-optical spectrum is discovered for dipolar valley excitons in twisted double-layer transition metal dichalcogenides, where the in-plane magnetic field induces a sizable multiplet splitting of exciton states inside the light cone. Chiral dispersions of the split branches make possible an efficient optical injection of the unidirectional exciton current. We also find an analog effect with a modest heterostrain replacing the magnetic field for introducing large splitting and chiral dispersions in the light cone. Angular orientation of the photoinjected exciton flow can be controlled by strain, with left-right unidirectionality selected by circular polarization.

Optical Detection of Long Electron Spin Transport Lengths in a Monolayer Semiconductor

Using a spatially resolved optical pump-probe experiment, we measure the lateral transport of spin-valley polarized electrons over very long distances (tens of micrometers) in a single WSe_{2} monolayer. By locally pumping the Fermi sea of 2D electrons to a high degree of spin-valley polarization (up to 75%) using circularly polarized light, the lateral diffusion of the electron polarization can be mapped out via the photoluminescence induced by a spatially separated and linearly polarized probe laser. Up to 25% spin-valley polarization is observed at pump-probe separations up to 20  μm. Characteristic spin-valley diffusion lengths of 18±3  μm are revealed at low temperatures. The dependence on temperature, pump helicity, pump intensity, and electron density highlight the key roles played by spin relaxation time and pumping efficiency on polarized electron transport in monolayer semiconductors possessing spin-valley locking.

Many-Body Exciton and Intervalley Correlations in Heavily Electron-Doped WSe2 Monolayers

In monolayer transition-metal dichalcogenide semiconductors, many-body correlations can manifest in optical spectra when electron-hole pairs (excitons) are photoexcited into a 2D Fermi sea of mobile carriers. At low carrier densities, the formation of charged excitons (X^±) is well documented. However, in WSe₂ monolayers, an additional absorption resonance, often called X^-', emerges at high electron density. Its origin is not understood. Here, we investigate the X^-' state via polarized absorption spectroscopy of gated WSe₂ monolayers in magnetic fields to 60T. Field-induced filling and emptying of the lowest optically active Landau level in the K' valley causes repeated quenching of the corresponding optical absorption. Surprisingly, these quenchings are accompanied by absorption changes to higher Landau levels in both K' and K valleys, which are unoccupied. These results cannot be reconciled within a single-particle picture, and demonstrate the many-body nature and intervalley correlations of the X^-' quasiparticle state.

Exciton-polaron Rydberg states in monolayer MoSe2 and WSe2

Exciton polaron is a hypothetical many-body quasiparticle that involves an exciton dressed with a polarized electron-hole cloud in the Fermi sea. It has been evoked to explain the excitonic spectra of charged monolayer transition metal dichalcogenides, but the studies were limited to the ground state. Here we measure the reflection and photoluminescence of monolayer MoSe₂ and WSe₂ gating devices encapsulated by boron nitride. We observe gate-tunable exciton polarons associated with the 1 s–3 s exciton Rydberg states. The ground and excited exciton polarons exhibit comparable energy redshift (15~30 meV) from their respective bare excitons. The robust excited states contradict the trion picture because the trions are expected to dissociate in the excited states. When the Fermi sea expands, we observe increasingly severe suppression and steep energy shift from low to high exciton-polaron Rydberg states. Their gate-dependent energy shifts go beyond the trion description but match our exciton-polaron theory. Our experiment and theory demonstrate the exciton-polaron nature of both the ground and excited excitonic states in charged monolayer MoSe₂ and WSe₂.

An exciton polaron is a quasiparticle composed of an exciton dressed with an electron-hole cloud, and this concept has been used to explain the ground excitonic states in charged monolayer transition metal dichalcogenides. Here the authors present experimental and theoretical evidence of exciton-polaron Rydberg states in monolayer MoSe₂ and WSe₂.

Excitonic and Valley-Polarization Signatures of Fractional Correlated Electronic Phases in a WSe_{2}/WS_{2} Moiré Superlattice

We have measured the reflectance contrast, photoluminescence, and valley polarization of a WSe_{2}/WS_{2} heterobilayer moiré superlattice at gate-tunable charge density. We observe absorption modulation of three intralayer moiré excitons at filling factors ν=1/3 and 2/3. We also observe luminescence modulation of interlayer trions at around a dozen fractional filling factors, including ν=-3/2, 1/4, 1/3, 2/5, 2/3, 6/7, 5/3. Remarkably, the valley polarization of interlayer trions is suppressed at some fractional fillings. These results demonstrate that electron crystallization can modulate the absorption, emission, and valley dynamics of the excitonic states in a moiré superlattice.

Signatures of moiré trions in WSe2/MoSe2 heterobilayers

Moiré superlattices formed by van der Waals materials can support a wide range of electronic phases, including Mott insulators^1-4, superconductors^5-10 and generalized Wigner crystals². When excitons are confined by a moiré superlattice, a new class of exciton emerges, which holds promise for realizing artificial excitonic crystals and quantum optical effects^11-16. When such moiré excitons are coupled to charge carriers, correlated states may arise. However, no experimental evidence exists for charge-coupled moiré exciton states, nor have their properties been predicted by theory. Here we report the optical signatures of trions coupled to the moiré potential in tungsten diselenide/molybdenum diselenide heterobilayers. The moiré trions show multiple sharp emission lines with a complex charge-density dependence, in stark contrast to the behaviour of conventional trions. We infer distinct contributions to the trion emission from radiative decay in which the remaining carrier resides in different moiré minibands. Variation of the trion features is observed in different devices and sample areas, indicating high sensitivity to sample inhomogeneity and variability. The observation of these trion features motivates further theoretical and experimental studies of higher-order electron correlation effects in moiré superlattices.

Measurement of Conduction and Valence Bands g-Factors in a Transition Metal Dichalcogenide Monolayer

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 intervalley phonons, avoiding strong renormalization effects that compromise single particle g-factor determination in transport experiments. These studies yield a direct determination of single band g factors. We measure g_{c1}=0.86±0.1, g_{c2}=3.84±0.1 for the bottom (top) conduction bands and g_{v}=6.1±0.1 for the valence band of monolayer WSe_{2}. These measurements are helpful for quantitative interpretation of optical and transport measurements performed in magnetic fields. In addition, the measured g factors are valuable input parameters for optimizing band structure calculations of these 2D materials.

Spontaneous Valley Polarization of Interacting Carriers in a Monolayer Semiconductor

We report magnetoabsorption spectroscopy of gated WSe_{2} monolayers in high magnetic fields up to 60 T. When doped with a 2D Fermi sea of mobile holes, well-resolved sequences of optical transitions are observed in both σ^{±} circular polarizations, which unambiguously and separately indicate the number of filled Landau levels (LLs) in both K and K^{'} valleys. This reveals the interaction-enhanced valley Zeeman energy, which is found to be highly tunable with hole density p. We exploit this tunability to align the LLs in K and K^{'}, and find that the 2D hole gas becomes unstable against small changes in LL filling and can spontaneously valley polarize. These results cannot be understood within a single-particle picture, highlighting the importance of exchange interactions in determining the ground state of 2D carriers in monolayer semiconductors.

Ab Initio Studies of Exciton g Factors: Monolayer Transition Metal Dichalcogenides in Magnetic Fields

The effect of a magnetic field on the optical absorption in semiconductors has been measured experimentally and modeled theoretically for various systems in previous decades. We present a new first-principles approach to systematically determine the response of excitons to magnetic fields, i.e., exciton g factors. By utilizing the GW-Bethe-Salpeter equation methodology we show that g factors extracted from the Zeeman shift of electronic bands are strongly renormalized by many-body effects which we trace back to the extent of the excitons in reciprocal space. We apply our approach to monolayers of transition metal dichalcogenides (MoS_{2}, MoSe_{2}, MoTe_{2}, WS_{2}, and WSe_{2}) with strongly bound excitons for which g factors are weakened by about 30%.

Multipath Optical Recombination of Intervalley Dark Excitons and Trions in Monolayer WSe_{2}

Excitons and trions (or exciton polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer WSe_{2}. We observe the intervalley dark excitons, which can recombine by the assistance of defect scattering or chiral-phonon emission. We also reveal that a trion can decay in two distinct paths-through intravalley or intervalley electron-hole recombination-into two different final valley states. Although these two paths are energy degenerate, we can distinguish them by lifting the valley degeneracy under a magnetic field. In addition, the intra- and inter-valley trion transitions are coupled to zone-center and zone-corner chiral phonons, respectively, to produce distinct phonon replicas. The observed multipath optical decays of dark excitons and trions provide insight into the internal quantum structure of trions and the complex excitonic interactions with defects and chiral phonons in monolayer valley semiconductors.