Letter | Published:

# Far out-of-equilibrium spin populations trigger giant spin injection into atomically thin MoS2

## Abstract

Injecting spins from ferromagnetic metals into semiconductors efficiently is a crucial step towards the seamless integration of charge- and spin-information processing in a single device1,2. However, efficient spin injection into semiconductors has remained an elusive challenge even after almost three decades of major scientific effort3,4,5, due to, for example, the extremely low injection efficiencies originating from impedance mismatch1,2,5,6, or technological challenges originating from stability and the costs of the approaches7,8,9,10,11,12. We show here that, by utilizing the strongly out-of-equilibrium nature of subpicosecond spin-current pulses, we can obtain a massive spin transfer even across a bare ferromagnet/semiconductor interface. We demonstrate this by producing ultrashort spin-polarized current pulses in Co and injecting them into monolayer MoS2, a two-dimensional semiconductor. The MoS2 layer acts both as the receiver of the spin injection and as a selective converter of the spin current into a charge current, whose terahertz emission is then measured. Strikingly, we measure a giant spin current, orders of magnitude larger than typical injected spin-current densities using currently available techniques. Our result demonstrates that technologically relevant spin currents do not require the very strong excitations typically associated with femtosecond lasers. Rather, they can be driven by ultralow-intensity laser pulses, finally enabling ultrashort spin-current pulses to be a technologically viable information carrier for terahertz spintronics.

## Main

Recently the discovery of ultrashort spin currents brought to the fore a very promising carrier of information13,14,15,16,17. Subpicosecond spin-polarized current pulses (which, from now on, we will call simply spin currents) can be created in a ferromagnet after fs laser excitation13. Their appeal arises from their intrinsic extreme time compression of signal, with a maximal overlap-free information processing and transfer frequency up to several THz. They have already been successfully injected into other metals18,19. However, it is an open question whether they could provide any advantage in tackling the issue of spin injection into semiconductors, as has been recently proposed20. We here set out to experimentally demonstrate that such out-of-equilibrium spin-current pulses possess the remarkable characteristic of an extremely highly efficient injection in semiconductors across the simplest of contacts—the bare metal/semiconductor interface. We will also illustrate how this arises from strong out-of-equilibrium effects, empirically demonstrating how far-from-equilibrium distributions, with their increased number of degrees of freedom, allow for the appearance of a number of exciting emergent phenomena.

The strategy is as follows: a strongly out-of-equilibrium carrier distribution is generated in the ferromagnetic layer by a fs laser excitation (Fig. 1b). As the out-of-equilibrium excited carriers diffuse, they relax in energy13 (schematically depicted in Fig. 1a). Due to the strong spin asymmetry of the high-energy electron–electron scattering lifetimes21, minority-spin electrons are expected to thermalize very quickly towards a hot Fermi–Dirac distribution, while a significant number of majority-spin electrons will persist for a longer time at high energies (Fig. 1c). As theoretically proposed in ref. 20, of those electrons that reach the ferromagnet/semiconductor interface, only those with excitation energy higher than the semiconductor conduction-band minimum can cross into the semiconducting layer. The semiconductor’s bandgap will hence filter only the high-energy carriers where the population is almost fully spin polarized;20 this is expected to lead to an extremely high spin polarization of the current injected into the semiconductor, as depicted in Fig. 1d.

However, realizing the above spin-injection concept experimentally is a formidable challenge. While measuring spin currents is already problematic in general, in this case it is even more complicated since such spin currents exists for just a few hundred fs. Even more importantly, it is imperative to prove that the measurement implies a spin current flowing within the semiconductor, and not a spurious signal generated within the metallic regions of the sample.

To address the first problem, we focus on semiconductors with high spin–orbit interaction. In these, the spin current flowing through the semiconductor can be converted, via the spin–orbit-mediated effects3,12, into a charge current flowing in a direction orthogonal to both the current propagation direction and the spin axis. Such charge current pulses (flowing parallel to the surface) will produce THz radiation that can be collected at a detector and used to reconstruct the temporal shape of the current itself14,15,16,17.

Unfortunately, not all high-spin–orbit semiconductors are suitable. First, the semiconductor needs to possess a finite bandgap everywhere. Moreover, the ferromagnet/semiconductor interface has to remain chemically and structurally stable. MoS2 (in a Co/MoS2 heterostructure) proved to be an ideal environment. Its high spin–orbit interaction allows for a high spin-to-charge conversion efficiency22, which is essential to selectively pinpoint the semiconducting layer as the source of the THz radiation. Furthermore, the two-dimensional semiconducting character of MoS2—the exposed gapped surface states together with the smooth and atomically thin Co/MoS2 interface—guarantees that no metallic character is expected anywhere on the MoS2 layer, and therefore that any signal from MoS2 implies that spin has been injected across its bandgap.

To this end, we fabricated Co/MoS2 heterostructures, with care to ensure that the MoS2 film (1) is pure, (2) is continuous, (3) is truly monolayer and (4) contains no intrinsic free carriers. Large-area monolayer MoS2 films (>7 mm diameter) were grown by physical vapour deposition23 on c-plane sapphire substrates; Raman and photoluminescence data confirm its good quality and monolayer thickness23. A ferromagnetic layer (5 nm Co) and a protection layer against oxidation (3 nm SiO2) were then grown by magnetron sputtering, giving rise to a SiO2/Co/MoS2/sapphire heterostructure, and the Raman data of this heterostructure show that the damage of sputtering on MoS2 is insignificant. X-ray photoelectron spectroscopy data show that the MoS2 film contains only Mo and S atoms, while atomic force microscopy data show that the MoS2 film is contiguous, and the roughness of both the Co/MoS2 and pure MoS2 are small (0.3–0.4 nm; for a full account of the sample growth and characterization, see Supplementary Information). The quality of the sample ensures that the MoS2 layer is indeed a two-dimensional semiconductor. This is confirmed by THz transmittance measurements (Fig. 2a), which show that the MoS2 film has 0 THz absorption within our sensitivity. Indeed, the THz absorption of the Co/MoS2 heterostructure and pure Co film are virtually identical. This indicates that MoS2 acquires no Drude weight after Co deposition, and hence possesses no intrinsic free carriers or metallic character.

We irradiated the sample (Fig. 2b) with 50 fs linearly polarized optical laser pulses (800 nm wavelength, 1 kHz repetition rate, diameter 7 mm, 0.78 mJ cm−2). The magnetization direction of Co is controlled by an external magnetic field (~80 Oe). The emitted THz radiation impinges on a THz polarizer and is then detected by electro-optic sampling using a ZnTe detector crystal. A strong THz emission is detected from the Co/MoS2 (Fig. 2c). Interestingly, the THz emission has an amplitude approximately 2% of that generated by the commonly used 1 mm thick THz generating crystal ZnTe at the same pump fluence.

In the following we pinpoint the origin of our emitted THz signal, by providing a full parameter-space characterization of the phenomenon. In particular we will show that the emitted THz amplitude (1) originates from the heterostructure itself, rather than from the Co or MoS2 layers independently, (2) rotates with the magnetic field direction, indicating its spin-based origin, and (3) switches sign upon sample flip, indicating a spin-current-based origin24.

Previous research reported that a pure Co thin film can emit THz radiation originating from a fs laser-induced demagnetization process25,26. Fig. 2c shows that the THz amplitude emitted from the Co/MoS2 heterostructure is about 10 times that from pure Co film of the same thickness. While some THz emission is expected to originate in MoS2 due to nonlinear optical effects27,28,29, which depend on the relative orientation between lattice and light polarization, we measure a negligible THz emission from pure monolayer MoS2 (magenta line, Fig. 2c). This is consistent with the polycrystalline nature of our physical vapour deposition-grown MoS2 thin films. Further, we find that the emitted THz amplitude is independent of pump polarization θP (the angle between the laser polarization and the THz polarizer axis; see the red squares in Fig. 3a). These, together, establish that the THz generation in the Co/MoS2 heterostructure does not depend on the nonlinear optical response that is related to the crystalline structure of the samples and its relative orientation with respect to the laser polarization axis.

Second, to confirm the spin origin of our signal, the THz amplitude was measured as a function of the direction of the applied magnetic field (θM), as shown in Fig. 3a,b. These show the strong Co magnetization tuning of the THz peak. In particular, three features of the θM dependence stand out: (1) the THz-peak amplitude exhibits a 360° symmetry, which can be fitted to a sinusoidal function (Fig. 3a), (2) the maximum (minimum) of the THz peak is at θM = 180° (0°), establishing that the polarization of emitted THz pulses is always perpendicular to the magnetic field, and (3) the THz time-domain normalized waveforms (and their corresponding frequency-domain spectra after Fourier transform) at different θM values are similar, (excluding important contributions from nonlinear effects, which should rotate following the crystal symmetry axis27,28,29). These features are fully consistent with the spin-to-charge conversion mechanism in MoS2 that obeys $${\bf{j}}_{\rm{C}} \propto {\bf{j}}_{\rm{S}} \times {\bf{M}}/\left|{\bf{M}}\right|$$, where jC is the charge current, jS is the spin-injection current and M is the magnetization of the Co layer (M/|M| represents the spin polarization direction of injected spin current).

Finally, to confirm the spin-current-based origin of our signal, we flip the sample (to change the sign of $${\bf{j}}_{\rm{S}}$$ in the laboratory frame); Fig. 3b shows that the polarities of the emitted THz pulses from Co/MoS2 with front- and back-incident pumps are opposite. This eliminates Co demagnetization as a source of the measured THz radiation (as this would give the same polarity for both configurations26). Note that the observed time difference between THz signals from front and back pumps is due to the different refractive indices of the substrate (c-cut sapphire) for 800 nm and THz pulses.

All three of the above experimental observations, as illustrated by Fig. 3a,b, collectively confirm the spin-current origin of the giant THz emission from the Co/MoS2 interface. Indeed, this picture finds further corroboration in our photocurrent measurements, which directly measures the charge current induced by the spin injection. Fig. 3a shows the simultaneous measurements of photocurrent and THz emission on Co/MoS2 (see Supplementary Information). The same θM dependence of the THz peak and photocurrent indicate that the two signals arise from the same origin: the spin-to-charge conversion of large spin currents injected from the Co/MoS2 interface discussed above.

The above results establish that we have generated and directly probed ultrafast spin injection across a ferromagnet/semiconductor interface. Even more striking, however, is the strong dependence of the emitted THz amplitude on laser wavelength in Fig. 4a,d at constant absorbed fluence (the absorbed fluence is obtained by measuring the incident, reflected and transmitted powers of the device and the beam diameter). As we explain below, these provide clear empirical evidence/demonstration of the strongly out-of-equilibrium nature of spin injection in our devices, and its dependence on MoS2 material parameters.

We first clarify that these results (Fig. 4a,d) are incompatible with a close-to-equilibrium (hot) electron distribution. If the spin diffusion after a fs laser excitation were to occur when the electrons have already attained internal thermalization30,31 as shown in Fig. 4b, the spin polarization and the amount of injection would depend only on the total deposited energy (number of absorbed pump photons × pump photon energy), displaying insensitivity to photon energy/wavelength; the total deposited energy, in turn, defines the temperature of the thermalized hot Fermi–Dirac distribution of carriers. Remarkably, our observation in Fig. 4a,d shows that the THz-peak amplitude increases with increasing pump photon energy for the same amount of absorbed energy. As a result, we conclude that a non-thermalized and far out-of-equilibrium spin population dominates our THz signal (Fig. 4c).

The detailed photon-energy-resolved map (from 0.5 to 2.5 eV) in Fig. 4d enables us to sensitively track the energy dependence of the out-of-equilibrium spin-current-injection process. While the THz emission of Co by itself is photon-energy independent (grey region in Fig. 4d), THz emission from the Co/MoS2 heterostructure rapidly rises for photon energies above 0.5 eV, achieving signals about 10 times larger when photons of 2.5 eV are incident. To understand this rapid increase, we note that the out-of-equilibrium distribution of laser-excited electrons (holes) in the ferromagnet is continuous and extends from the Fermi energy to energies that are up to (dip below) the laser frequency above (below) the Fermi energy. At very low excitation energies (<0.55 eV, see the red region of Fig. 4d, and Fig. 4e) none of the excited electrons or holes have sufficient energy to overcome the Co/MoS2 Schottky barrier. Indeed, in this regime, our measured Co/MoS2 THz signal coincides with that of Co by itself—see the grey shaded region in Fig. 4d. As a result, we conclude that the dominant THz emission observed in Co/MoS2 is dominated by processes within the Co layer (for example, via ultrafast demagnetization).

However, above the approximately 0.55 eV threshold (see the white region of Fig. 4d, and Fig. 4f), a fraction of the laser-excited (spin-polarized) electrons in the Co have enough energy to enter the semiconductor above the bottom of the conduction band of MoS2 and produce spin current within it (for a more detailed discussion, see Supplementary Information and ref. 20). This fraction of electrons increases (roughly linearly) with the photon energy. Under a higher-energy photon pump (>1.20 eV, see the purple region of Fig. 4d, and Fig. 4g), the hole population (whose currents’ spin polarization is opposite to and smaller than that from the electrons) reaches the top of the valance band of MoS2, adding a further contribution to the net spin current, and causes a kink in Fig. 4d, and a slight decrease in the slope.

The two thresholds correspond to the electron and hole Schottky barrier heights in the Co/MoS2 heterostructure; from our data, we can estimate these to be (0.55 ± 0.06) eV and (1.20 ± 0.11) eV respectively. (The error in our extractions for the Schottky barrier heights can be estimated by considering the bandwidth of the pulse from our optical parametric amplifier (bandwidth ~80 nm at centre wavelength 1,000 nm and ~250 nm at 2,300 nm), which broadens the excitation profile.) Their sum (1.75 ± 0.17) eV should be equal to the bandgap of MoS2. This value agrees well with the expected value for the MoS2 bandgap (~1.9 eV) found in the literature (see, for example, ref. 32).

Finally, we estimate33 the magnitude of the peak spin-current density $$J_{\rm{S}}^{\rm{peak}}$$ directly from the measured THz electric field: $$J_{\rm{S}}^{\rm{peak}} = J_{\uparrow}^{\rm{peak}} - J_{\downarrow}^{\rm{peak}} \approx 4 \, \times$$ (106–108) A cm−2 , which is the difference between peak majority $$J_{\uparrow}^{\rm{peak}}$$ and peak minority $$J_{\downarrow}^{\rm{peak}}$$ spin current (the detailed calculations and the discussion of spin-to-charge conversion in MoS2 are in the Supplementary Information). Even in the most conservative estimation this enormous injected spin-current density is orders of magnitude larger than amplitudes of typical spin-current injection into semiconductors (for example, 102–103 A cm−2 using spin pumping34, 10−1–10 0A cm−2 via tunnel junction8,35). Its efficiency is a direct result of the far out-of-equilibrium nature of spin-current injection in our devices. It moreover works across a bare metal/semiconductor interface, circumventing the problem of impedance mismatch, which close-to-equilibrium spin currents face. Interestingly, we obtain our record spin injection without any attempt at optimizing the device. Our work sets the bedrock for ultrafast spin currents as technologically viable carriers of information, and provides fundamental science with a simple method to inject massive spin currents into gapped materials.

## Methods

### Sample fabrication

High-quality monolayer MoS2 films were grown by physical vapour deposition on c-plane sapphire substrates at 800 °C by reactively sputtering of an Mo target in a sulfur vapour ambient. During the deposition process, the chamber pressure was kept at 3.2 × 10−4 mbar and the sputtering power was kept at 10 W. Prior to the growth, the Mo target was presputtered for 15 min to remove the contaminants on its surface. A ferromagnetic layer (5 nm Co) and a protection layer (3 nm SiO2) were then grown by magnetron sputtering. The protection layer is to prevent oxidation of the magnetic layer. The monolayer nature of MoS2 was confirmed by Raman spectroscopy and the thickness of the Co/MoS2 device was measured by atomic force microscopy (see the sample characterization in Supplementary Information for details).

### THz emission set-up

As shown in Supplementary Fig. 1, THz emission spectroscopy is caried out in a typical time-resolved THz spectroscopy set-up36. Femtosecond laser pulses (Coherent Legend-Elite, 50 fs pulse duration, 1 kHz repetition rate, 800 nm wavelength, 7 mm diameter) are incident on the device (or ZnTe THz emitter), then the generated THz pulses are projected onto the x-axis (vertical) using a wire-grid THz polarizer and collected and focused by two parabolic mirrors onto a 1 mm thick 〈110〉 ZnTe crystal for electro-optic sampling. The magnetic field at the sample position is about 800 Oe, and is provided by permanent magnets. The polarization angle and magnetic field direction are controlled by motorized rotational stages (Thorlabs PRM1/MZ8). Low-temperature measurements were performed in a Cryo Industries cryostat.

The photocurrent measurement was performed on a Co/MoS2 heterostructure with THz emission spectroscopy simultaneously. Two electrodes were made at opposite ends of the device, and the distance between them is larger than the laser diameter (~7 mm) to make sure the electrodes are not excited by the pump pulses. In the measurement, the sample with electrodes was rotated to make sure the direction of the measured photocurrent (the direction from one electrode to another) is the same as that of the THz polarizer, which leads to the similar phase of the two measurements (Fig. 3a).

## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

We acknowledge funding from the A*STAR PHAROS Programme on Topological Insulators (SERC Grant No. 152 74 00026) and 2D Materials (SERC Grant No. 152 70 00012 and 152 70 00016), and Singapore Ministry of Education AcRF Tier 1 (MOE2018-T1-001-97) and Tier 2 (MOE2015-T2-2-065, MOE2016-T2-1-054) grants. J.C.W.S. acknowledges the support of the Singapore National Research Foundation under fellowship award NRF-NRFF2016-05. M.B. gratefully acknowledges Nanyang Technological University, NAP-SUG and the Austrian Science Fund (FWF) through Lise Meitner position M1925-N28 for the funding of this research. The work was supported in part by the Center for Integrated Nanotechnologies, a US DOE BES user facility. We acknowledge B. Tang from the National University of Singapore and D. Seng from the Institute of Materials Research and Engineering, A*STAR, for Raman and X-ray photoelectron spectroscopy data.

## Author information

### Author notes

1. These authors contributed equally: Liang Cheng, Xinbo Wang.

### Affiliations

1. #### Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

• Liang Cheng
• , Xinbo Wang
• , Xiaoxuan Chen
• , Handong Sun
• , Justin C. W. Song
• , Marco Battiato
•  & Elbert E. M. Chia

• Xinbo Wang
3. #### Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), Singapore, Singapore

• Weifeng Yang
• , Jianwei Chai
• , Ming Yang
• , Dongzhi Chi
• , Kuan Eng Johnson Goh
•  & Shijie Wang
4. #### Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

• Mengji Chen
• , Yang Wu
•  & Hyunsoo Yang
5. #### Theoretical Division and Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, NM, USA

• Jian-Xin Zhu
6. #### Institute of High Performance Computing, A*STAR (Agency for Science, Technology and Research), Singapore, Singapore

• Justin C. W. Song
7. #### Institute of Solid State Physics, Vienna University of Technology, Vienna, Austria

• Marco Battiato

### Contributions

E.E.M.C. and H.Y. conceived the experiments. W.Y., Y.W. and M.C. fabricated the heterostructures. L.C. and X.W. carried out the THz measurements and data analysis with the help and guidance of E.E.M.C. and H.Y. M.B., J.C.W.S. and J.X.Z. provided theoretical inputs. W.Y. and S.W. performed and analysed the X-ray photoelectron spectroscopy and Raman measurements. L.C., X.W., J.C.W.S, M.B. and E.E.M.C wrote the manuscript together. All authors discussed the results and commented on the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding authors

Correspondence to Justin C. W. Song or Marco Battiato or Hyunsoo Yang or Elbert E. M. Chia.

## Supplementary information

1. ### Supplementary Information

Supplementary Chapters 1–8, Supplementary Figures 1–7 and Supplementary References 1–12