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

Abstract

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.

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

“…These distinct g -factors provide valuable insights into the intricate interplay between electronic and magnetic degrees of freedom, underscoring the importance of considering the magnetic state of CrSBr in understanding the behavior of excitonic systems in this heterostructure. The changes in the magnitude of the g -factors are consistent with proximity effects due to the hybridization between the layers, as previously demonstrated in MoSe 2 /WSe 2 , , WSe 2 /CrI 3 , and WS 2 /graphene systems . A systematic analysis of the microscopic features behind the asymmetric g -factors is beyond the scope of the current manuscript; however, we point out that asymmetric signatures in valley Zeeman splitting have recently been observed in MoSe 2 /CrBr 3 heterostructures at zero magnetic field.…”

Hybrid Moiré Excitons and Trions in Twisted MoTe2–MoSe2 Heterobilayers

“…We employed ab initio calculations for theoretical estimates of the exciton g -factor in monolayer MoTe 2 and moiré excitons in MoTe 2 –MoSe 2 heterostructures. − For the fundamental exciton X A in monolayer MoTe 2 , we obtained g A = −4.6 from g normalA = 2 ( L c − L v ) with the orbital angular momenta of the lowest conduction band and the highest valence band L c and L v . For moiré excitons, we decompose the g -factors into the individual contributions of interlayer and intralayer excitons according to hybridization-induced admixing as g i ( R ) = 2 false( 0.0ex0.0ex0.1em f i 0.0ex0.0ex0.1em false( normalX false) L c + f i 0.0ex0.0ex0.1em false( normalI normalX false) L c false′ − L v false) g i false( normalH false) = 2 ( f i ( X ) L c − f i ( I X )…”

“…with the orbital angular momenta of the lowest conduction band and the highest valence band L c and L v . For moireé xcitons, we decompose the g-factors into the individual contributions of interlayer and intralayer excitons 33 according to hybridization-induced admixing as…”

“…We employed ab initio calculations for theoretical estimates of the exciton g -factor in monolayer MoTe 2 and moiré excitons in MoTe 2 –MoSe 2 heterostructures. − For the fundamental exciton X A in monolayer MoTe 2 , we obtained g A = −4.6 from with the orbital angular momenta of the lowest conduction band and the highest valence band L c and L v . For moiré excitons, we decompose the g -factors into the individual contributions of interlayer and intralayer excitons according to hybridization-induced admixing as where i = 1, 2 indicates the hybrid X i exciton, L c ′( c ′+1) is the first (second) conduction band in the MoSe 2 layer as shown in the insets of Figure a and b, and f i (X) ( f i (IX) ) is the fraction of X (IX) exciton. Using the calculated values of the orbital angular momenta in Table S2 and the respective exciton fractions deduced from our effective model, we obtain g 1 (R) = −4.2 and g 2 (R) = −4.4 for X 1 and X 2 moiré excitons in heterostacks with a 2° twist, as well as g 1 (H) = −8.0 and g 2 (H) = −6.8 in stacks with a 58° twist angle.…”

Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications

“…The purpose of this Special Issue entitled "Excitons and Phonons in Two-Dimensional Materials: From Fundamental to Applications" is to provide a unique international forum and to cover the entire range of fundamental and applied research associated with excitonic complexes and phonon modes in two-dimensional layered materials. This Special Issue is composed of nine published papers [6][7][8][9][10][11][12][13][14] devoted to investigations of different 2D materials, such as S-TMDs, perovskites, and the multilayered structure of thin films, with theoretical [7,9,11,13] and experimental [10] approaches, as well as their combination [6,8,12,14].…”