Spin-layer locking of interlayer excitons trapped in moir\'e potentials

TL;DR

This paper reports the discovery of spin-layer locking in interlayer excitons within moiré potentials in TMD heterostructures, revealing new quantum degrees of freedom for engineering tunable quantum systems.

Contribution

It demonstrates spin-layer locking of interlayer excitons in moiré potentials, highlighting the intrinsic locking of atomic registries in 2H-stacked TMD heterostructures.

Findings

Observation of spin-layer locking in interlayer excitons

Identification of two quantum-confined exciton species with distinct configurations

Intrinsic locking of moiré site registries due to 2H stacking

Abstract

Van der Waals heterostructures offer attractive opportunities to design quantum materials. For instance, transition metal dichalcogenides (TMDs) possess three quantum degrees of freedom: spin, valley index, and layer index. Further, twisted TMD heterobilayers can form moir\'e patterns that modulate the electronic band structure according to atomic registry, leading to spatial confinement of interlayer exciton (IXs). Here we report the observation of spin-layer locking of IXs trapped in moir\'e potentials formed in a heterostructure of bilayer 2H-MoSe$_2$ and monolayer WSe$_2$. The phenomenon of locked electron spin and layer index leads to two quantum-confined IX species with distinct spin-layer-valley configurations. Furthermore, we observe that the atomic registries of the moir\'e trapping sites in the three layers are intrinsically locked together due to the 2H-type stacking characteristic of bilayer TMDs. These results identify the layer index as a useful degree of freedom to engineer tunable few-level quantum systems in two-dimensional heterostructures.

Equations

$$\Delta \left(B_z\right)=E^{{\sigma }^{+}}\left(B_z\right)-E^{{\sigma }^{-}}\left(B_z\right)=g{\mu }_B{B}_z,$$

$$|\Delta E^{Rs}\left(B_z\right)|=2|2+{\alpha }_v-{\alpha }_c|{\mu }_B{B}_z,$$

$$|\Delta E^{Rt}\left(B_z\right)|=2|4+{\alpha }_v-{\alpha }_c|{\mu }_B{B}_z;$$

$$|\Delta E^{Hs}\left(B_z\right)|=2|2+{\alpha }_v+{\alpha }_c|{\mu }_B{B}_z,$$

$$|\Delta E^{Ht}\left(B_z\right)|=2|4+{\alpha }_v+{\alpha }_c|{\mu }_B{B}_z.$$

Full text

The electronic and optical properties of van der Waals heterostructures can be widely engineered by the diverse choice of crystal combinations geim2013van and their relative rotation bistritzer2011moire ; zhang2017interlayer ; cao2018unconventional ; jin2019observation ; alexeev2019resonantly and interlayer spacing tong2017topological ; yankowitz2018dynamic . For nearly commensurate bilayers (BLs), a slight lattice mismatch or relative rotation results in a moiré superlattice which spatially modulates the electronic band-structure. Single particle wavepackets can be trapped in the moiré-induced potential pockets with three-fold symmetry yu2017moire ; wu2018theory ; yu2018brightened . Recently, signatures of IX trapped in such moiré potentials were observed in TMD hetero-BL samples seyler2019signatures ; tran2019evidence .

Due to the potential to harness the carrier spin, valley index, and layer index xu2014spin , layered TMDs present an intriguing platform for quantum electronics and optics. The broken inversion symmetry in TMDs leads to an effective coupling between a carrier spin and the valley index of the electrons or holes at the $\pm$K corners of the hexagonal Brillouin zone xiao2012coupled , as shown for monolayer (ML) WSe2 in Fig. 1c. Like the real spin, the valley index is associated to a magnetic moment xiao2012coupled ; xu2014spin , which results in valley dependent selection rules. Light with $\sigma^{\pm}$-polarisation creates electron-hole pairs exclusively in the $\pm$K valley, enabling optical and magnetic manipulation of intralayer valley excitons mak2012control ; zeng2012valley ; aivazian2015magnetic ; srivastava2015valley . Layer index is found in 2$H$-type BL TMDs which have a $180^{\circ}$ in-plane rotation between the top- and bottom-layer and minimal interlayer electronic hopping at the K valleys xiao2012coupled ; gong2013magnetoelectric ; jones2014spin ; riley2014direct . The in-plane rotation inverts the valley alignment in the two layers, such that a unique spin-valley configuration is locked to each layer, as shown for BL MoSe2 in Fig. 1c. This gives rise to the layer index. Additionally, the atomic registries of the two layers are intrinsically locked together in 2$H$-type BL TMDs.

Owing to these quantum degrees of freedom, TMDs are ideal ingredients to realise the concept of exciton trapping in moiré potentials yu2017moire ; wu2018theory ; yu2018brightened ; seyler2019signatures ; tran2019evidence . Two different ML TMDs can be combined with an atomically sharp interface to create a hetero-BL system with Type II-band alignment chiu2015determination ; wilson2017determination , which favours spatial separation of photogenerated carriers: electrons and holes rapidly transfer to reside in the layer with the lowest energy conduction (CB) and valence band-edge (VB), respectively hong2014ultrafast . Due to strong Coulomb interaction, the electrons and holes form spatially-indirect interlayer excitons which exhibit the valley-dependent optical selection rules of the monolayer TMDs but with longer exciton lifetimes, robust spin-valley polarisation, and large electric field tunability yu2015anomalous ; rivera2015observation ; rivera2016valley ; hanbicki2018double ; ciarrocchi2019polarization . Hetero-BLs with arbitrary stacking angles can be fabricated by transfer of mechanically exfoliated flakes seyler2019signatures ; tran2019evidence ; wilson2017determination ; rivera2015observation ; ciarrocchi2019polarization or chemical vapour deposition zhang2017interlayer ; chiu2015determination ; hong2014ultrafast ; hanbicki2018double . Nearly aligned $0^{\circ}$ (R-type) or $60^{\circ}$ (H-type) stacking of the hetero-BL yields minimum displacement in momentum space for carriers at the band edges ($\pm$K), maximizing coupling to the light cone for optical transitions yu2015anomalous . As shown in Fig. 1d, IXs in an R-type stacked hetero-BL (IXR) have valley conserving ground state optical transitions, identical to monolayer TMDs. Conversely, IXs in H-type stacked materials (IXH) have valley contrasting optical transitions. We label the band-edge states at $\pm$K as $\ket{V,\uparrow/\downarrow}$, $\ket{L,\uparrow/\downarrow}$, and $\ket{U,\uparrow/\downarrow}$, where $V$ represents the WSe2 valence band, $U$ ($L$) is the upper (lower) MoSe2 layer (layer index), and $\uparrow$ ($\downarrow$) represents the electron spin $s_{z}$ = 1/2 (-1/2). In addition, nearly aligned $0^{\circ}$ or $60^{\circ}$ stacking yields a moiré potential landscape in a hetero-BL in which three trapping sites (A, B, and C) with atomic registries $R_{h}^{h}$ (A), $R_{h}^{X}$ (B) and $R_{h}^{M}$ (C) emerge (see Fig. 1b), where $R^{\mu}_{h}$ denotes an $R$-type stacking with the $\mu$ site of the electron layer (either $h$ the hexagon centre, $X$ the chalcogen site or $M$ the metal site) vertically aligned with the hexagon centre ($h$) of the hole layer yu2017moire ; tong2017topological ; yu2018brightened .

Here we explore the spin, valley index, and layer index properties of moiré-trapped IXs in an artificial trilayer (TL) heterostructure consisting of a ML WSe2 and BL 2$H$-MoSe2 (see Fig. 1a). Due to the $d_{z^{2}}$ symmetry of the orbitals at the conduction band edge, electrons in BL MoSe2 present a vanishing interlayer hopping at the $\pm$K points, which leads to a strong coupling between the electron spin, the layer and the valley degrees of freedom gong2013magnetoelectric . We exploit the spin-layer locking phenomenon of BL 2$H$-MoSe2 to probe two moiré-trapped IX species with contrasting spin-valley alignment: the holes, localised in the WSe2 monolayer, are strongly Coulomb bound to electrons localised in either the lower or upper MoSe2 layer to form IXH or IXR species, respectively. Each localised IX species has a distinct spin-layer-valley configuration: IXR (IXH) exhibit electron-hole pairs with parallel (antiparallel) spin-valley-locked magnetic moments. The emission from each IX species exhibits circular polarisation which, when combined with knowledge of the spin and valley configuration, enable determination of the atomic registry of the moiré trapping sites. We report the observation of a new moiré-trapping site for IXR excitons in the TL-heterostructure as compared to IXR excitons in WSe2/MoSe2 hetero-BLs seyler2019signatures , which we attribute to the 2$H$-type stacking characteristic of BL MoSe2 that results in the intrinsic locking of the atomic registries of the three layers. Our results present new evidence that add confidence to the moiré potential as the origin of the IX confinement.

I Trapped interlayer excitons in a trilayer heterostructure

To justify our choice of TL heterostructure for the realisation of spin-layer locked IXs, we performed ab initio calculations (see Suppl. Note 1). The artificial TL heterostructures consisted of a 2$H$-MoSe2 crystal with ML and BL terraces mechanically stacked on top of a WSe2 ML and encapsulated by hBN in an inert environment (see Suppl. Note 2). The 2$H$ stacking of ML WSe2 and the bottom ML MoSe2 was confirmed by linear-polarisation-resolved second harmonic generation measurements (see Suppl Note 3). Figure 2a shows representative low-temperature (T = 4 K) confocal photoluminescence (PL) spectra measured using continuous wave excitation at 2.33 eV and an excitation power ($P_{exc}$) of 4 $\mu$W. PL spectra corresponding to different positions of the ML MoSe2/ML WSe2 heterostructure (black and blue spectra) show emission in the energy range 1.32 - 1.42 eV (energy range I). We observe that the emission is centred around two main energy windows (1.385 - 1.405 eV and 1.345 - 1.375 eV), but with spatially dependent relative intensities. Positions A (black spectrum) and B (blue spectrum) correspond to the spatial positions with the brightest relative intensities for the two windows. To confirm that the observed emission arises from IXs, we performed PL excitation spectroscopy, scanning a continuous-wave excitation laser from 1.61 eV to 1.75 eV while monitoring the intensity of the emission peaks. Figure 2b shows a representative PL excitation spectrum, featuring two prominent resonances which correspond to the absorption of the intralayer 1$s$ exciton states in ML MoSe2 and WSe2. PL spectra in the TL part of the heterostructure is markedly different: emission in spectral region I is still observed but with reduced intensity relative to a new band of emission at lower energy (1.25 - 1.31 eV, region II), see for example the red spectrum in Fig. 2a. The spatial dependence of the PL spectra suggests that ranges I and II originate from different IX species, as expected from the stacking configuration presented in Fig. 1. This heterostructure stacking configuration is corroborated by means of DC Stark effect measurements (see Suppl. Note 4). Therefore, we label IXs with emission in ranges I and II as IXH and IXR, respectively. The PL emission energy of IXH matches well with recent reports for IX emission in MoSe2/WSe2 hetero-BLs rivera2015observation ; hanbicki2018double ; ciarrocchi2019polarization ; seyler2019signatures ; Torun2018 , while IXR emission in TL heterostructures have yet to be explored in such detail.

With reducing $P_{exc}$, the broad PL gradually disappears until the sharp peaks dominate, as shown in Suppl. Note 5. Here, high-resolution PL spectra measured with reduced $P_{exc}$ reveal that IXH (IXR) PL peaks exhibit Lorentzian lineshapes with average full-width at half maximum (FWHM) of $\sim$100 $\mu$eV ($\sim$250 $\mu$eV); the narrowest peaks observed are $\sim$70 $\mu$eV (see Suppl. Note 5). These linewidths, two orders of magnitude narrower than typical IX linewidths in WSe2/MoSe2 hetero-BLs rivera2016valley ; jiang2018microsecond ; hanbicki2018double ; ciarrocchi2019polarization , are comparable to quantum emitters in ML WSe2 srivastava2015optically ; tonndorf2015single ; brotons2019coulomb and to recently reported moiré-trapped excitons seyler2019signatures . Supplementary Figure 7 shows the full evolution of the IXH emission under increasing $P_{exc}$. For each species of IX, the intensity saturates with increasing $P_{exc}$ according to a two-level system (Suppl. Fig. 7). Additionally, we observe minimal spectral wandering ($<$ 10 $\mu$eV) at long time scales (see Suppl. Fig. 8).

II Spin-valley-layer configurations of trapped interlayer excitons

The narrow linewidths and saturation behaviour provide strong evidence of IXs trapped in a moiré confinement potential. For the low $P_{exc}$ used in the PL spectra shown in Figs. 2c-e, the IX density is not high enough to fill all the trapping sites of the moiré lattice within the diffraction limited focus of our confocal PL spot. Instead, we only observe emission from a few trapping sites (10 to 20 depending on the spatial position in the sample). Under increasing excitation power, as more trapping sites are filled, we progressively lose the ability to resolve individual spectral lines.

To confirm these peaks arise from band-edge states and disentangle the spin-layer-valley configuration of each exciton species, we perform magneto-optical spectroscopy measurements in Faraday configuration. Figure 3a shows the magnetic field ($B_{z}$) dependence of representative moiré-trapped IXR and IXH (left and right panel, respectively). A clear linear Zeeman splitting with increasing $B_{z}$ is observed for every peak, and it is immediately noticeable that the $g$-factor of IXH excitons is considerably larger than IXR excitons. To confirm these are universal features of moiré trapped IXH and IXR, a second WSe2/MoSe2 heterostructure with both ML WSe2/ML MoSe2 and ML WSe2/BL MoSe2 regions and similar stacking angle ($\sim 60^{\circ}$ between the ML WSe2/BL MoSe2) was fabricated and measured (Sample 2). Sample 2 also exhibits IXR and IXH with narrow emission peaks in the same energy ranges as Sample 1. Figure 3b summarises the measured $g$-values for each IX species in Samples 1 and 2 (black and red dots, respectively) as a function of their emission energy. Trapped IXR, which only appear in energy range II from the TL part of the samples, exhibit a $g$-factor of -7.0 $\pm$ 0.6. On the other hand, trapped IXH in energy range I are observed both in the hetero-BL and hetero-TL regions and exhibit a $g$-factor of -15.76 $\pm$ 0.13.

The striking $B_{z}$ dependence for each IX species has its origin in their corresponding spin-valley configuration seyler2019signatures (see Fig. 3c), demonstrating that IXR and IXH preserve the spin-layer locking of electrons in BL 2$H$-MoSe2. Since both carrier spin and valley index are associated to a magnetic moment xiao2012coupled ; xu2014spin , the total valley-selective splitting of the interlayer transitions ($\Delta$) amounts to nagler2017giant ; seyler2019signatures

[TABLE]

with $g$ being an effective $g$-factor, $\mu_{B}$ being the Bohr magneton, and $E^{\sigma^{\pm}}\left(B_{z}\right)$ being the $B_{z}$-dependent energies of the intervalley transitions with $\sigma^{\pm}$ polarisation. $E^{\sigma^{\pm}}$ is defined as the energy difference between the conduction ($E_{c}^{\pm}$) and valence ($E_{v}^{\pm}$) band edges associated to $\sigma^{\pm}$ transitions ($E^{\sigma^{\pm}}\left(B_{z}\right)=E_{c}^{\pm}-E_{v}^{\pm}$). The Zeeman shift of the $E_{c}^{\pm}$ ($\Delta E_{c}$) and $E_{v}^{\pm}$ ($\Delta E_{v}$) band edges can be estimated as a combination of three different magnetic moment contributions: $\Delta E_{c/v}=\Delta_{s}+\Delta_{a}+\Delta_{v}$, where $\Delta_{s}=2s_{z}\mu_{B}B_{z}$ is the spin contribution, $\Delta_{a}=l_{c/v}\mu_{B}B_{z}$ is the atomic orbital contribution, and $\Delta_{v}=\tau\alpha_{c/v}\mu_{B}B_{z}$ represents the valley contribution arising from the Berry curvature xiao2012coupled . Here, $s_{z}=\pm 1/2$ is the electron spin, $l_{c}=0$ ($l_{v}=2\tau$) is the magnetic quantum number for the atomic orbital at the conduction (valence) band edge, $\tau=\pm 1$ is the index for the $\pm$K valleys, and $\alpha_{c}$ ($\alpha_{v}$) is the magnetic moment of the conduction (valence) band edge aivazian2015magnetic . According to the leading order of a simplified k$\cdot$p approximation for the band-edge carriers xiao2012coupled ; yao2008valley , the valley magnetic moments of the conduction and valence band can be estimated as $\alpha_{c,v}=m_{0}/m^{*}_{e,h}$, with $m_{0}$ the free electron mass and $m^{*}_{e}$ ($m^{*}_{h}$) the electron (hole) effective mass at the conduction (valence) band edge. Figures 3d and 3e show the Zeeman shifts of the conduction (MoSe2) and valence (WSe2) band edges of a WSe2/MoSe2 heterostructure, respectively, calculated using $m^{*}_{h}=0.37$ $m_{0}$ kormanyos2015k and $m^{*}_{e}=0.84$ $m_{0}$ larentis2018large ; goryca2019revealing . Here we assume that the spin-split conduction bands at the $\pm$K points of ML and BL MoSe2 have similar effective masses larentis2018large , and therefore we use the same $\alpha_{c}$ for both. The colour and line style used for each band edge are consistent with the schematics of the spin-layer configuration shown in Fig. 3c. Solid (dashed) lines represent the Zeeman shifts of band edges with spin up (down). Red lines represent the Zeeman shifts of the valence band states in WSe2, whereas blue and green lines represent the Zeeman shifts of the MoSe2 conduction band edges with parallel and antiparallel valley and spin configuration, respectively.

According to Equation (1), the different spin-layer-valley configuration of IXR and IXH excitons results in different total Zeeman splittings $\Delta$. Therefore, the $g$-factor of the moiré-trapped valley excitons is representative of their spin-valley configuration, which, as a consequence of the spin-layer locking of electrons in BL MoSe2, also indicates whether the electron is localised in the bottom or top MoSe2 layer. Furthermore, two different $\Delta$ splittings are possible for both IXR and IXH excitons depending on the conduction bands involved in the optical transitions (see Methods).

The vertical arrows in Figs. 3d and 3e represent the optical transitions responsible of the Zeeman splittings for each IX exciton and spin configuration. Grey (black) arrows represent optical transitions in IXR (IXH) excitons, while solid (dashed) lines represent spin-singlet (spin-triplet) optical transitions. Figure 3f shows the $B_{z}$-dependence of the $\Delta$ value for each IX exciton and spin configuration as calculated from Equations (2)-(5). The colour and line style used for the $\Delta$ value of each IX configuration is consistent with the one employed to indicate the optical transitions of the corresponding excitons. Figure 3f also shows the $B_{z}$-dependence of the experimental $\Delta$ values of two representative trapped IXR (red dots) and IXH (blue dots) excitons, as extracted from Lorentzian fits of the experimental data. The good agreement observed between the calculated and experimental $\Delta$ values corroborates our initial identification of IXR and IXH excitons. Moreover, the magneto-optical measurements provide additional information. The results shown in Fig. 3f indicate that the observed IXR and IXH excitons arise from optical transitions involving the lowest spin-split conduction band of MoSe2 at $\pm$K. This observation leads to spin-conserved and spin-flip optical transitions for IXR and IXH excitons, respectively. Although the latter is normally forbidden in ML TMDs due to its spin-flip nature, it can be brightened due to the selection rules dictated by the resulting interlayer atomic registry of the moiré pattern in our heterostrtuctures yu2018brightened .

The spin-layer-locked nature of IXR and IXH allows us to estimate the magnetic moment contribution of the conduction and valence band edges, and therefore the corresponding carrier effective masses (see Methods).

III Local atomic registries of moiré trapping sites

The relative Zeeman shifts of the conduction and valence band edges at $\pm$K points enable further insight, based on the fact that the $B_{z}$-induced shift of the WSe2 valence band edge is larger than the corresponding shifts of the MoSe2 conduction bands (as shown in Figs. 3d and 3e). The smaller Zeeman splitting for the conduction band edges is a consequence of two factors: the smaller magnetic moment contribution from the atomic orbitals of the conduction band ($l_{c}=0$), and the higher effective mass of electrons in the conduction band of MoSe2. The larger Zeeman shift for the valence band edges leads to a striking consequence: for $B_{z}>0$, the energy of the optical transitions involving the valence band edges of WSe2 at K (-K) always shift to lower (higher) energies regardless of the spin-valley configuration of the IX. Based on this, helicity-resolved PL measurements can provide information about the nature of the moiré confinement potential. Figures 4a and 4b show circularly-polarised-resolved spectra of representative IXH and IXR, respectively, under linearly polarised ($\pi$) excitation at 2.33 eV and different applied magnetic fields. Both IXH and IXR exhibit strong circular polarisation, and application of $B_{z}$ results in a Zeeman shift of the $\sigma^{+}$-polarised ($\sigma^{-}$-polarised) PL peak towards lower (higher) energies. For zero magnetic field, energy-degenerate $\sigma^{+}$ and $\sigma^{-}$ emissions are observed with near identical intensity, indicating that the IXs are trapped in confinement potentials that preserve the rotational $C_{3}$ symmetry. The degenerate circularly-polarised emission of IXR and IXH contrasts with the emission polarisation properties of neutral excitons in quantum emitters in ML WSe2, which typically exhibit a large fine-structure splitting and strictly linear polarisation srivastava2015optically ; tonndorf2015single ; brotons2019coulomb arising from the electron-hole exchange interaction energy and asymmetry in the confinement potential. The absence of observable fine-structure splitting is only expected in cases for which rotational symmetry of the crystal lattice and confining potential is maintained.

The polarisation selection rules of the moiré-trapped excitons are dictated by the local atomic registry of the moiré trapping site yu2017moire ; yu2018brightened . Figure 4c shows the selection rules for optical transitions involving the K-point valence band for both spin-singlet and spin-triplet IXs trapped in moiré potential sites with different atomic registries yu2018brightened . Accordingly, the results in Figs. 4a and 4b indicate that IXR and IXH originate from IXs trapped in moiré potentials with interlayer atomic registries $R^{h}_{h}$ (A) and $H^{h}_{h}$ (B), respectively. Interestingly, we find that IXR excitons in the TL heterostructure present a comparable $g$-factor magnitude but opposite valley selection rules compared to IXR excitons in WSe2/MoSe2 hetero-BLs seyler2019signatures . These results indicate that localised IXR excitons in the TL heterostructure and in WSe2/MoSe2 hetero-BLs seyler2019signatures are the same IX species (same spin-valley pairing) trapped in moiré potentials with different atomic registries. We attribute the different atomic registry of the moiré trapping potentials for IXR excitons in the TL heterostructure ($R^{h}_{h}$) and the WSe2/MoSe2 hetero-BLs ($R^{X}_{h}$) to the 2$H$-type stacking of characteristic of BL MoSe2, which results in the intrinsic locking of the atomic registries of the three layers (see left panel of Fig. 4c).

IV Discussion and outlook

The magneto-optical spectroscopy experiments reveal the remarkable consequence of spin-layer locking of moiré-trapped excitons in the artificial TL heterostructures. Two IX species, IXR and IXH, with distinct spin-valley-layer configurations are observed: IXR (IXH) composed of electrons in the top (bottom) MoSe2 layer present carriers with parallel (antiparallel) spin-valley locked contributions, resulting in an effective layer-locking of the Landé g-factors of the trapped IX. At cryogenic temperatures, both trapped IX species exhibit narrow linewidths and saturate with increasing excitation power, hallmarks of a few-level quantum confined system. An unambiguous demonstration of quantum emission from the moiré-trapped excitons, for instance photon antibunching, remains an important target. Finally, the combination of magneto-optics and helicity-resolved PL measurements allows the determination of the atomic registries of the moiré trapping sites.

For quantum information applications, a basic requirement is the ability to initialise the state of the few-level quantum system, which has been achieved for valley qubits in ML TMDs via optical pumping mak2012control ; zeng2012valley . Here we show the trapped IXs retain the strong valley polarisation of the constituent ML semiconductors (see Suppl. Fig. 10).

Finally, we remark that the phenomenon of spin-layer locking provides a means to engineer few-level quantum systems in van der Waals heterostructures. For example, the selection rules arising from the $C_{3}$ symmetry for the atomic registries we observe (left panel of of Fig. 4c), create a “vee-type” three level system: a single ground state ($\ket{V,\uparrow}$) couples to two non-degenerate excited states ($\ket{L,\downarrow}$ and $\ket{U,\uparrow}$). Alternatively, a three-level system analogous to a “spin-lambda” type atom, in which two ground states couple to a common excited state, can be engineered using the layer-index degree of freedom in a TL heterostructure consisting of BL 2$H$-WSe2/ML MoSe2. This quantum state engineering opens new opportunities for advanced quantum control techniques in the van der Waals platform.

V Acknowledgements

The authors thank J. J. Finley, K. Müller, M. Kremser, and A. Högele for discussions. This work is supported by the EPSRC (grant no. EP/P029892/1 and EP/S000550/1), the ERC (grant no. 725920) and the EU Horizon 2020 research and innovation program under grant agreement no. 820423. AMS acknowledges the Juan de la Cierva (Grant IJCI-2015-25799) program (MINECO, Spain) and the Marie-Curie-COFUND program Nano TRAIN For Growth II (Grant Agreement 713640). The computations were performed on the Tirant III cluster of the Servei d’Informàtica of the University of Valencia (project vlc82). Growth of hBN crystals by K.W. and T.T. was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3). B.D.G. is supported by a Wolfson Merit Award from the Royal Society and a Chair in Emerging Technology from the Royal Academy of Engineering.

VI Author contributions

B.D.G. conceived and supervised the project. H.B. fabricated the samples. K.W. and T.T. supplied the hBN crystals. M.B.-G. and H.B. performed the experiments, assisted by A.C., C.B. and D.W. M.B.-G. analysed the data, assisted by E.S. and B.D.G. A.M.-S. performed the ab initio calculations. M.B.-G. and B.D.G. cowrote the paper with input from all authors. M.B.-G. and H.B. contributed equally to this work.

VII Competing interests

The authors declare no competing interests.

VIII Methods

VIII.1 Zeeman splitting for IXs with different spin-layer-valley configurations

Optical transitions between the bottom conduction band states and the top valence band state at K give rise to four possible IX configurations: IXHs ($\ket{V,\uparrow}\leftrightarrow\ket{L,\uparrow}$), IXHt ($\ket{V,\uparrow}\leftrightarrow\ket{L,\downarrow}$), IXRs ($\ket{V,\uparrow}\leftrightarrow\ket{U,\uparrow}$), and IXRt ($\ket{V,\uparrow}\leftrightarrow\ket{U,\downarrow}$), where $s$ and $t$ superscripts denote spin-conserving (spin-singlet) and spin-flip (spin-triplet) optical transitions, respectively.

Using Eq. (1), IXR excitons can take $\Delta$ values of:

[TABLE]

and

[TABLE]

while IXH excitons can present $\Delta$ values of:

[TABLE]

and

[TABLE]

VIII.2 Magnetic moment contributions of the band edges

From the combination of Equations (2) and (5), and the measured $g$-factors for IXH and IXR, we estimate magnetic moment contributions of $\alpha_{v}$ = 2.69 $\pm$ 0.15 and $\alpha_{c}$ = 1.19 $\pm$ 0.15. The estimated magnetic moment for the band edges yield effective masses of $m^{*}_{e}\approx 0.84\pm 0.11$ $m_{0}$ and $m^{*}_{h}\approx 0.37\pm 0.02$ $m_{0}$ for electrons and holes at the bottom conduction band of MoSe2 and top valence band of WSe2, respectively.

In the previous discussion we have considered that IXH arise from optical spin-flip transitions involving the lowest spin-split conduction band of MoSe2 at $\pm$K. However, IXH could also be tentatively attributed to spin-conserved optical transitions from the top valence band of WSe2 and the higher energy spin-split conduction band of MoSe2 at $\pm$K seyler2019signatures (see Fig. 3c). For such spin-singlet configuration (IXHs), the spin magnetic moments contribution of the electron and hole cancel each other, and the total Zeeman splitting can be calculated by Eq. (4). In this case, the combination of the measured $g$-factors with Eqs. (2) and (4) leads to effective masses of $m^{*}_{e}\approx 0.46\pm 0.03$ $m_{0}$ and $m^{*}_{h}\approx 0.27\pm 0.01$ $m_{0}$ for electrons and holes at the top conduction band of MoSe2 and top valence band of WSe2, respectively. These values differ significantly from the corresponding reported effective masses. On the other hand, assuming a spin-triplet configuration for IXH results in estimated carrier effective masses that match well previously calculated and experimental values kormanyos2015k ; larentis2018large ; goryca2019revealing , providing confidence that both trapped IXH and IXR originate from optical transitions involving the lowest split conduction band of MoSe2 at $\pm$K.

IX Data availability

Data described in this paper and presented in the Supplementary materials are available online at https://researchportal.hw.ac.uk/en/persons/brian-d-gerardot/datasets/