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

Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2

The fundamental properties of an exciton are determined by the spin, valley, energy, and spatial wavefunctions of the Coulomb-bound electron and hole. In van der Waals materials, these attributes can be widely engineered through layer stacking configuration to create highly tunable interlayer excitons with static out-of-plane electric dipoles, at the expense of the strength of the oscillating in-plane dipole responsible for light-matter coupling. Here we show that interlayer excitons in bi- and tri-layer 2H-MoSe2 crystals exhibit electric-field-driven coupling with the ground (1s) and excited states (2s) of the intralayer A excitons. We demonstrate that the hybrid states of these distinct exciton species provide strong oscillator strength, large permanent dipoles (up to 0.73 ± 0.01 enm), high energy tunability (up to ~200 meV), and full control of the spin and valley characteristics such that the exciton g-factor can be manipulated over a large range (from -4 to +14). Further, we observe the bi- and tri-layer excited state (2s) interlayer excitons and their coupling with the intralayer excitons states (1s and 2s). Our results, in good agreement with a coupled oscillator model with spin (layer)-selectivity and beyond standard density functional theory calculations, promote multilayer 2H-MoSe2 as a highly tunable platform to explore exciton-exciton interactions with strong light-matter interactions.

Hybrid Moiré Excitons and Trions in Twisted MoTe2-MoSe2 Heterobilayers

We report experimental and theoretical studies of MoTe2-MoSe2 heterobilayers with rigid moiré superlattices controlled by the twist angle. Using an effective continuum model that combines resonant interlayer electron tunneling with stacking-dependent moiré potentials, we identify the nature of moiré excitons and the dependence of their energies, oscillator strengths, and Landé g-factors on the twist angle. Within the same framework, we interpret distinct signatures of bound complexes among electrons and moiré excitons in nearly collinear heterostacks. Our work provides a fundamental understanding of hybrid moiré excitons and trions in MoTe2-MoSe2 heterobilayers and establishes the material system as a prime candidate for optical studies of correlated phenomena in moiré lattices.

Giant Faraday rotation in atomically thin semiconductors

Faraday rotation is a fundamental effect in the magneto-optical response of solids, liquids and gases. Materials with a large Verdet constant find applications in optical modulators, sensors and non-reciprocal devices, such as optical isolators. Here, we demonstrate that the plane of polarization of light exhibits a giant Faraday rotation of several degrees around the A exciton transition in hBN-encapsulated monolayers of WSe2 and MoSe2 under moderate magnetic fields. This results in the highest known Verdet constant of -1.9 × 107 deg T-1 cm-1 for any material in the visible regime. Additionally, interlayer excitons in hBN-encapsulated bilayer MoS2 exhibit a large Verdet constant (VIL ≈ +2 × 105 deg T-1 cm-2) of opposite sign compared to A excitons in monolayers. The giant Faraday rotation is due to the giant oscillator strength and high g-factor of the excitons in atomically thin semiconducting transition metal dichalcogenides. We deduce the complete in-plane complex dielectric tensor of hBN-encapsulated WSe2 and MoSe2 monolayers, which is vital for the prediction of Kerr, Faraday and magneto-circular dichroism spectra of 2D heterostructures. Our results pose a crucial advance in the potential usage of two-dimensional materials in ultrathin optical polarization devices.

Weak Dispersion of Exciton Landé Factor with Band Gap Energy in Lead Halide Perovskites: Approximate Compensation of the Electron and Hole Dependences

The optical properties of lead halide perovskite semiconductors in vicinity of the bandgap are controlled by excitons, so that investigation of their fundamental properties is of critical importance. The exciton Landé or g-factor gX is the key parameter, determining the exciton Zeeman spin splitting in magnetic fields. The exciton, electron, and hole carrier g-factors provide information on the band structure, including its anisotropy, and the parameters contributing to the electron and hole effective masses. Here, gX is measured by reflectivity in magnetic fields up to 60 T for lead halide perovskite crystals. The materials band gap energies at a liquid helium temperature vary widely across the visible spectral range from 1.520 up to 3.213 eV in hybrid organic-inorganic and fully inorganic perovskites with different cations and halogens: FA0.9Cs0.1PbI2.8Br0.2, MAPbI3, FAPbBr3, CsPbBr3, and MAPb(Br0.05Cl0.95)3. The exciton g-factors are found to be nearly constant, ranging from +2.3 to +2.7. Thus, the strong dependences of the electron and hole g-factors on the bandgap roughly compensate each other when combining to the exciton g-factor. The same is true for the anisotropies of the carrier g-factors, resulting in a nearly isotropic exciton g-factor. The experimental data are compared favorably with model calculation results.

Charge Transfer and Asymmetric Coupling of MoSe2 Valleys to the Magnetic Order of CrSBr

van der Waals heterostructures composed of two-dimensional (2D) transition metal dichalcogenides and vdW magnetic materials offer an intriguing platform to functionalize valley and excitonic properties in nonmagnetic TMDs. Here, we report magneto photoluminescence (PL) investigations of monolayer (ML) MoSe2 on the layered A-type antiferromagnetic (AFM) semiconductor CrSBr under different magnetic field orientations. Our results reveal a clear influence of the CrSBr magnetic order on the optical properties of MoSe2, such as an anomalous linear-polarization dependence, changes of the exciton/trion energies, a magnetic-field dependence of the PL intensities, and a valley g-factor with signatures of an asymmetric magnetic proximity interaction. Furthermore, first-principles calculations suggest that MoSe2/CrSBr forms a broken-gap (type-III) band alignment, facilitating charge transfer processes. The work establishes that antiferromagnetic-nonmagnetic interfaces can be used to control the valley and excitonic properties of TMDs, relevant for the development of opto-spintronics devices.

Optical Properties of MoSe2 Monolayer Implanted with Ultra-Low-Energy Cr Ions

This paper explores the optical properties of an exfoliated MoSe₂ monolayer implanted with Cr⁺ ions, accelerated to 25 eV. Photoluminescence of the implanted MoSe₂ reveals an emission line from Cr-related defects that is present only under weak electron doping. Unlike band-to-band transition, the Cr-introduced emission is characterized by nonzero activation energy, long lifetimes, and weak response to the magnetic field. To rationalize the experimental results and get insights into the atomic structure of the defects, we modeled the Cr-ion irradiation process using ab initio molecular dynamics simulations followed by the electronic structure calculations of the system with defects. The experimental and theoretical results suggest that the recombination of electrons on the acceptors, which could be introduced by the Cr implantation-induced defects, with the valence band holes is the most likely origin of the low-energy emission. Our results demonstrate the potential of low-energy ion implantation as a tool to tailor the properties of two-dimensional (2D) materials by doping.

Electronic and Excitonic Properties of MSi2 Z4 Monolayers

MA₂ Z₄ monolayers form a new class of hexagonal non-centrosymmetric materials hosting extraordinary spin-valley physics. While only two compounds (MoSi₂ N₄ and WSi₂ N₄ ) are recently synthesized, theory predicts interesting (opto)electronic properties of a whole new family of such two-dimensional (2D) materials. Here, the chemical trends of band gaps and spin-orbit splittings of bands in selected MSi₂ Z₄ (M = Mo, W; Z = N, P, As, Sb) compounds are studied from first-principles. Effective Bethe-Salpeter-equation-based calculations reveal high exciton binding energies. Evolution of excitonic energies under external magnetic field is predicted by providing their effective g-factors and diamagnetic coefficients, which can be directly compared to experimental values. In particular, large positive g-factors are predicted for excitons involving higher conduction bands. In view of these predictions, MSi₂ Z₄ monolayers yield a new platform to study excitons and are attractive for optoelectronic devices, also in the form of heterostructures. In addition, a spin-orbit induced bands inversion is observed in the heaviest studied compound, WSi₂ Sb₄ , a hallmark of its topological nature.

Signatures of Electric Field and Layer Separation Effects on the Spin-Valley Physics of MoSe2/WSe2 Heterobilayers: From Energy Bands to Dipolar Excitons

Multilayered van der Waals heterostructures based on transition metal dichalcogenides are suitable platforms on which to study interlayer (dipolar) excitons, in which electrons and holes are localized in different layers. Interestingly, these excitonic complexes exhibit pronounced valley Zeeman signatures, but how their spin-valley physics can be further altered due to external parameters-such as electric field and interlayer separation-remains largely unexplored. Here, we perform a systematic analysis of the spin-valley physics in MoSe2/WSe2 heterobilayers under the influence of an external electric field and changes of the interlayer separation. In particular, we analyze the spin (Sz) and orbital (Lz) degrees of freedom, and the symmetry properties of the relevant band edges (at K, Q, and Γ points) of high-symmetry stackings at 0° (R-type) and 60° (H-type) angles-the important building blocks present in moiré or atomically reconstructed structures. We reveal distinct hybridization signatures on the spin and the orbital degrees of freedom of low-energy bands, due to the wave function mixing between the layers, which are stacking-dependent, and can be further modified by electric field and interlayer distance variation. We find that H-type stackings favor large changes in the g-factors as a function of the electric field, e.g., from -5 to 3 in the valence bands of the Hhh stacking, because of the opposite orientation of Sz and Lz of the individual monolayers. For the low-energy dipolar excitons (direct and indirect in k-space), we quantify the electric dipole moments and polarizabilities, reflecting the layer delocalization of the constituent bands. Furthermore, our results show that direct dipolar excitons carry a robust valley Zeeman effect nearly independent of the electric field, but tunable by the interlayer distance, which can be rendered experimentally accessible via applied external pressure. For the momentum-indirect dipolar excitons, our symmetry analysis indicates that phonon-mediated optical processes can easily take place. In particular, for the indirect excitons with conduction bands at the Q point for H-type stackings, we find marked variations of the valley Zeeman (∼4) as a function of the electric field, which notably stands out from the other dipolar exciton species. Our analysis suggests that stronger signatures of the coupled spin-valley physics are favored in H-type stackings, which can be experimentally investigated in samples with twist angle close to 60°. In summary, our study provides fundamental microscopic insights into the spin-valley physics of van der Waals heterostructures, which are relevant to understanding the valley Zeeman splitting of dipolar excitonic complexes, and also intralayer excitons.

Magneto-Optical Chirality in a Coherently Coupled Exciton-Plasmon System

Chirality is a fundamental asymmetry phenomenon, with chiral optical elements exhibiting asymmetric response in reflection or absorption of circularly polarized light. Recent realizations of such elements include nanoplasmonic systems with broken-mirror symmetry and polarization-contrasting optical absorption known as circular dichroism. An alternative route to circular dichroism is provided by spin-valley polarized excitons in atomically thin semiconductors. In the presence of magnetic fields, they exhibit an imbalanced coupling to circularly polarized photons and thus circular dichroism. Here, we demonstrate that polarization-contrasting optical transitions associated with excitons in monolayer WSe₂ can be transferred to proximal plasmonic nanodisks by coherent coupling. The coupled exciton-plasmon system exhibits magneto-induced circular dichroism in a spectrally narrow window of Fano interference, which we model in a master equation framework. Our work motivates the use of exciton-plasmon interfaces as building blocks of chiral metasurfaces for applications in information processing, nonlinear optics, and sensing.

Distinctive g-Factor of Moiré-Confined Excitons in van der Waals Heterostructures

We investigated the valley Zeeman splitting of excitonic peaks in the microphotoluminescence (μPL) spectra of high-quality hBN/WS₂/MoSe₂/hBN heterostructures under perpendicular magnetic fields up to 20 T. We identify two neutral exciton peaks in the μPL spectra; the lower-energy peak exhibits a reduced g-factor relative to that of the higher energy peak and much lower than the recently reported values for interlayer excitons in other van der Waals (vdW) heterostructures. We provide evidence that such a discernible g-factor stems from the spatial confinement of the exciton in the potential landscape created by the moiré pattern due to lattice mismatch or interlayer twist in heterobilayers. This renders magneto-μPL an important tool to reach a deeper understanding of the effect of moiré patterns on excitonic confinement in vdW heterostructures.

Giant g-factor in Self-Intercalated 2D TaS2

Central to the application of spintronic devices is the ability to manipulate spins by electric and magnetic fields, which relies on a large Landé g-factor. The self-intercalation of layered transitional metal dichalcogenides with native metal atoms can serve as a new strategy to enhance the g-factor by inducing ferromagnetic instability in the system via interlayer charge transfer. Here, scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) are performed to extract the g-factor and characterize the electronic structure of the self-intercalated phase of 2H-TaS₂ . In Ta₇ S₁₂ , a sharp density of states (DOS) peak due to the Ta intercalant appears at the Fermi level, which satisfies the Stoner criteria for spontaneous ferromagnetism, leading to spin split states. The DOS peak shows sensitivity to magnetic field up to 1.85 mV T^-1 , equivalent to an effective g-factor of ≈77. This work establishes self-intercalation as an approach for tuning the g-factor.

Ultrafast pseudospin quantum beats in multilayer WSe2 and MoSe2

Layered van-der-Waals materials with hexagonal symmetry offer an extra degree of freedom to their electrons, the so-called valley index or valley pseudospin, which behaves conceptually like the electron spin. Here, we present investigations of excitonic transitions in mono- and multilayer WSe₂ and MoSe₂ materials by time-resolved Faraday ellipticity (TRFE) with in-plane magnetic fields, B_∥, of up to 9 T. In monolayer samples, the measured TRFE time traces are almost independent of B_∥, which confirms a close to zero in-plane exciton g factor g_∥, consistent with first-principles calculations. In contrast, we observe pronounced temporal oscillations in multilayer samples for B_∥ > 0. Our first-principles calculations confirm the presence of a non-zero g_∥ for the multilayer samples. We propose that the oscillatory TRFE signal in the multilayer samples is caused by pseudospin quantum beats of excitons, which is a manifestation of spin- and pseudospin layer locking in the multilayer samples.

Strain-Induced Exciton Hybridization in WS_{2} Monolayers Unveiled by Zeeman-Splitting Measurements

Mechanical deformations and ensuing strain are routinely exploited to tune the band gap energy and to enhance the functionalities of two-dimensional crystals. In this Letter, we show that strain leads also to a strong modification of the exciton magnetic moment in WS_{2} monolayers. Zeeman-splitting measurements under magnetic fields up to 28.5 T were performed on single, one-layer-thick WS_{2} microbubbles. The strain of the bubbles causes a hybridization of k-space direct and indirect excitons resulting in a sizable decrease in the modulus of the g factor of the ground-state exciton. These findings indicate that strain may have major effects on the way the valley number of excitons can be used to process binary information in two-dimensional crystals.

Chirality of Valley Excitons in Monolayer Transition-Metal Dichalcogenides

By enabling control of valley degrees of freedom in transition-metal dichalcogenides, valley-selective circular dichroism has become a key concept in valleytronics. Herein, we show that valley excitons, bound electron-hole pairs formed at the K or K̅ valleys upon absorption of circularly polarized light, are chiral quasiparticles characterized by a finite orbital angular momentum (OAM). We further formulate an ab initio many-body theory of valley-selective circular dichroism and valley excitons based on the Bethe-Salpeter equation. Besides governing the interaction with circularly polarized light, the OAM confers upon excitons a finite magnetization that manifests itself through an excitonic Zeeman splitting upon interaction with external magnetic fields. The good agreement between our ab initio calculations and recent experimental measurements of the exciton Zeeman shifts corroborates this picture, indicating that valley excitons can carry angular momentum even in their singlet state.

Revealing the impact of strain in the optical properties of bubbles in monolayer MoSe2

Strain plays an important role for the optical properties of monolayer transition metal dichalcogenides (TMDCs). Here, we investigate strain effects in a monolayer MoSe₂ sample with a large bubble region using μ-Raman, second harmonic generation (SHG), μ-photoluminescence and magneto μ-photoluminescence at low temperature. Remarkably, our results reveal the presence of a non-uniform strain field and the observation of emission peaks at lower energies which are the signatures of exciton and trion quasiparticles red-shifted by strain effects in the bubble region, in agreement with our theoretical predictions. Furthermore, we have observed that the emission in the strained region decreases the trion binding energy and enhances the valley g-factors as compared to non-strained regions. Considering uniform biaxial strain effects within the unit cell of the TMDC monolayer (ML), our first principles calculations predict the observed enhancement of the exciton valley Zeeman effect. In addition, our results suggest that the exciton-trion fine structure plays an important role for the optical properties of strained TMDC ML. In summary, our study provides fundamental insights on the behaviour of excitons and trions in strained monolayer MoSe₂ which are particularly relevant to properly characterize and understand the fine structure of excitonic complexes in strained TMDC systems/devices.

Valley-Dependent Interlayer Excitons in Magnetic WSe2/CrI3

Heterostructures of two-dimensional transition-metal dichalcogenides and ferromagnetic substrates are important candidates for the development of viable new spin- or valleytronic devices. For the prototypical bilayer of WSe₂ on top of a ferromagnetic layer of CrI₃, we find substantially different coupling of both WSe₂ K-valleys to the sublayer. Besides an energy splitting of a few meV, the corresponding excitons have significantly different interlayer character with charge transfer allowed at the K̅^- point but forbidden at K̅⁺. The different exciton wave functions result in a distinctly different response to magnetic fields with g factors of about -4.4 and -4.0, respectively. By means of ab initio GW/Bethe-Salpeter equation calculations, these findings establish g factors as tool for investigating the exciton character and shedding light on the detailed quantum-mechanical interplay of magnetic and optical properties which are essential for the targeted development of optoelectronic devices.

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.

Exciton g-factors in monolayer and bilayer WSe2 from experiment and theory

The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. Here, we present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe₂ monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton g-factors from first principles for all possible spin-valley configurations of excitons in monolayer and bilayer WSe₂ including valley-indirect excitons. Our theoretical and experimental findings shed light on some of the characteristic photoluminescence peaks observed for monolayer and bilayer WSe₂. In more general terms, the theoretical aspects of our work provide additional means for the characterization of single and few-layer transition metal dichalcogenides, as well as their heterostructures, in the presence of external magnetic fields.

Optical properties of charged excitons in two-dimensional semiconductors

Strong Coulomb interaction in atomically thin transition metal dichalcogenides makes these systems particularly promising for studies of excitonic physics. Of special interest are the manifestations of the charged excitons, also known as trions, in the optical properties of two-dimensional semiconductors. In order to describe the optical response of such a system, the exciton interaction with resident electrons should be explicitly taken into account. In this paper, we demonstrate that this can be done in both the trion (essentially, few-particle) and Fermi-polaron (many-body) approaches, which produce equivalent results, provided that the electron density is sufficiently low and the trion binding energy is much smaller than the exciton one. Here, we consider the oscillator strengths of the optical transitions related to the charged excitons, fine structure of trions, and Zeeman effect, as well as photoluminescence of trions illustrating the applicability of both few-particle and many-body models.