Electrical Control of Excitons in Bare-MoSe2 and MoSe2/NbSe2 Heterostructure

TL;DR

This study demonstrates reversible electrical control of photoluminescence in monolayer MoSe2 and MoSe2/NbSe2 heterostructures, enabling tunable light emission for advanced nanoscale optoelectronic devices.

Contribution

It reveals that electric fields can modulate PL intensity significantly and induce a direct-indirect bandgap transition, advancing electrical control in TMDC-based optoelectronics.

Findings

Electric fields recover up to 80% of PL in heterostructures.

PL intensity can be tuned by nearly three orders of magnitude.

Electric-field-induced bandgap transition from direct to indirect.

Abstract

Monolayer transition metal dichalcogenides (TMDCs) are promising materials for next-generation optoelectronic devices, owing to their strong excitonic responses and atomic thickness. Controlling their light emission electrically is a crucial step towards realizing practical nanoscale optoelectronic devices such as light-emitting diodes and optical modulators. However, photoluminescence (PL) quenching in van der Waals TMDC/metal heterostructures, caused by ultrafast interlayer charge or energy transfer, impedes such electrical modulation. Here, we investigate monolayer-MoSe2/bulk-NbSe2 heterostructures and demonstrate that a vertical electric field can effectively recover the PL intensity up to ~ 80% of bare-MoSe2. Furthermore, our analysis reveals that the room temperature PL intensity can be tuned by nearly three orders of magnitude in bare-MoSe2 and by about one order of magnitude in MoSe2/NbSe2 heterostructures. First-principles calculations incorporating spin-orbit coupling reveal that the perpendicular electric fields drive a transition from a direct to an indirect bandgap, fundamentally altering the optical response in the heterostructure. Unlike bare-MoSe2, the heterostructure exhibits a pronounced thermal dependence of the enhancement factor, implying that exciton lifetime dominates over interfacial transfer processes. Our findings demonstrate reversible, electric-field-driven PL control at a TMDC/metal interface, providing a pathway to electrically tunable light emission and improved contact engineering in two-dimensional optoelectronic devices.

Equations

$$\Delta A(F)\propto \frac{dA}{dE}\left[-\Delta \vec{\mu }\cdot \vec{F}-\frac{1}{2}\alpha F^2\right]$$

$$F=\frac{V}{d_{Mo}+d_h\left(\frac{{\epsilon }_{\perp ,0,Mo}}{{\epsilon }_{\perp ,0,h}}\right)}$$

$$\begin{array}[]{c}d_{air}=\infty,\quad n_{air}=1.0\\ d_{Si}=\infty,\quad n_{Si}=3.7\\ d_{hBN}=12\text{ nm},\quad n_{hBN}=2.12\\ d_{Gr}=3.5\text{ nm},\quad n_{Gr}=3+2.5\textit{i}\\ d_{SiO_{2}}=100\text{ nm},\quad n_{SiO_{2}}=1.45\\ \end{array}$$

Full text

††preprint: APS

Keywords: MoSe2/NbSe2, vdW heterostructure, photoluminescence, electrical control, temperature dependence

I Introduction

Van der Waals (vdW) heterostructures of transition metal dichalcogenides (TMDCs) materials have enabled the creation of artificial systems with novel functionalities that do not exist in nature. These include Moiré superlattices arising from controlled twisting or lattice mismatch, allowing for the exploration of emergent, strongly correlated electronic phases [1, 2, 3, 4, 5]. Furthermore, vdW stacking enables tunable type-I and type-II band alignment through the selection of material combination, stacking angle, and interlayer coupling [6, 7]. They also facilitate the realization of long-lived interlayer excitons [8] with spatially separate charge carriers, distinct from the ultrafast recombination seen in monolayers [9, 10]. Such features are promising for advanced optoelectronic and excitonic device platforms [11, 12, 13].

However, the integration of TMDCs into devices remains challenging due to the high contact resistance at the TMDC/metal interface. Although graphene is widely used as a transparent electrode, its strong interlayer coupling with TMDCs induces significant interfacial charge and energy transfer, resulting in severe photoluminescence (PL) quenching [14, 15]. Moreover, work function mismatch between metal contacts and semiconducting TMDCs further contributes to high contact resistance [16], thereby constraining device performance. These limitations necessitate the exploration of alternative layered metals that offer better electronic compatibility. A highly interesting candidate is the layered two-dimensional (2D) metal NbSe2, which is a type-II superconductor at temperatures below 8 K and metallic at higher temperatures with coexisting charge density wave order around 32 K [17]. Recent studies have shown the integration of 2D semiconducting layers into heterostructures with 2D NbSe2 providing a platform for the manipulation of electronic and excitonic properties [18], and for the development of device applications, such as self-powered photodetectors [19]. In these devices, the dynamic tuning of optical properties is essential, enabling real-time control over excitonic behavior and light–matter interactions, which is critical for developing next-generation programmable and tunable optoelectronic functionalities using 2D materials [20].

In recent years, electrostatic gating offers a non-invasive approach to precisely tune optical properties in TMDCs [6]. This control enables modulation of quasiparticle bandgaps [21], phase transitions [22, 23], and symmetry-breaking phenomena [24, 25], as well as excitonic states [26, 27, 28], all without introducing structural disorder, unlike chemical doping. Vertical electric fields also alter hybrid excitons with strong dipolar interactions in TMDC bilayers [29, 30, 31]. Moreover, a recent study predicts that electric fields can modulate band alignment and Schottky barrier heights at TMDC/metal interfaces [32], a key factor in minimizing contact resistance and enhancing device performance. Building on these studies, understanding how vertical electric fields govern excitonic behavior and interfacial charge dynamics in TMDC/2D-metal heterostructures, especially under varying thermal conditions, remains largely unexplored.

In this work, we leverage vertical electric field modulation to investigate the PL properties in monolayer (ML)-MoSe2/bulk-NbSe2 (TMDC/metal) heterostructure. Measurements were performed at two positions, namely, bare-MoSe2 (‘off’ position) and the MoSe2/NbSe2 heterostructure (‘on’ position). At room temperature ($T=$ 295 K), the PL emission at the ‘on’ position is reduced by more than an order of magnitude compared to the ‘off’ position. Our results reveal that the direction of the electric field determines the PL enhancement in bare-MoSe2 and MoSe2/NbSe2 heterostructure with a different degree of enhancement. Notably, at the ‘on’ position, the PL enhancement factor decreases with lowering temperature, while it remains nearly constant at the ‘off’ position. All measurements in this work were carried out down to $T=20$ K, with a specific focus on the normal (non-superconducting) metallic regime of NbSe2. Analytical calculations estimate that the electric field modifies the excitonic oscillator strength by altering the electron-hole (e-h) wavefunction overlap for the ‘off’ position. However, first-principle calculations on the MoSe2/NbSe2 heterostructure, representing the ‘on’ position, demonstrate that the field modifies the nature of the bandgap. Consequently, controlling the electric field allows modulation of the PL intensity and can recover emission at the ‘on’ position by up to $\sim$ 80$\%$ of the ‘off’ position.

II Results

**PL quenching in MoSe2/NbSe2 heterostructure

**A schematic and optical micrograph of a typical MoSe2/NbSe2 stacked heterostructure, comprising ML-MoSe2 interfaced with bulk NbSe2, are shown in Fig. 1a and b, respectively. The thicknesses of MoSe2 and NbSe2 layers are determined by the optical contrast and Raman measurement, as shown in Supplementary Fig. S1. The heterostructure, marked by a white contour in Fig. 1b, is formed in the overlapping region of the two constituent materials. Note that the layers were not rotationally aligned, implying weak electronic hybridization between the incommensurate semiconducting and metallic layers. To study the effect of electric fields in the heterostructure, a capacitive structure is assembled on a pre-patterned gold electrode (details given in Supplementary section) using a layer-by-layer dry transfer stacking technique with hexagonal boron nitride (hBN) as the dielectric layer. The stack consists of few-layer-graphene/hBN/NbSe2/MoSe2/hBN/few-layer-graphene, with both the top and bottom hBN layers measuring approximately 12 $\pm$ 3 nm in thickness. The spatial PL intensity map, as shown in Fig. 1c, predominantly displays two colors. The blue colored area corresponds to bare-MoSe2, while the region outlined by the white contour, representing the MoSe2/NbSe2 heterostructure, appears similar in color to the background. This indicates substantial PL quenching of MoSe2 across the entire heterostructure area involving NbSe2.

For simplicity, further analysis focuses on two representative positions, denoted as ‘off’ and ‘on’ in Fig. 1a by blue and red points, respectively. At $T=$ 295 K, PL spectra in the absence of a vertical electric field (i.e., voltage, $V$ = 0 V) at these two positions are presented in Fig. 2a and b, respectively. The spectra were fitted with two Gaussian functions representing the A-exciton and trion at 1.57 $\pm$ 0.05 eV and 1.53 $\pm$ 0.05 eV, respectively. The reflectance contrast spectra, $\Delta R/R=\frac{R-R_{0}}{R_{0}}$, where $R$ and $R_{0}$ are the reflectance signal of the stack, with and without MoSe2, respectively, for both ‘off’ and ‘on’ positions, are shown in Fig. 2c and d, respectively. The ‘off’-position spectrum predominantly indicates the real component of the dielectric function, while the ‘on’-position is governed by both real and imaginary parts [33]. The transition energies for the respective positions are marked by dotted lines in the figure. Although excitons in ML-MoSe2 are spatially confined within the layer, the associated dipolar electric fields naturally extend beyond the layer due to the reduced dimensionality. As a result, forming a heterostructure of MoSe2 with metallic NbSe2 inherently influences the excitonic behavior by enhancing environmental screening and modifying the local dielectric landscape. This interaction significantly alters the optical response, manifesting as distinct variations in $\Delta R/R$ at these two positions.

The most striking feature is the PL intensity suppression of around one order of magnitude ($\sim$ 11) between ‘off’ and ‘on’ positions. We conducted the measurements using a 532 nm laser at $\sim$ 15 $\mu$W power to ensure operation within the linear excitonic regime, as illustrated in Fig. S2a. Notably, the quenching factor remains consistent across the experimental power range as depicted in Fig. S2b. This quenching phenomenon is consistent with observations at semiconductor/metal interfaces, such as TMDC/graphene heterostructures, where PL intensity is suppressed due to photoinduced charge or energy transfer via Dexter or Förster processes [34]. This indicates substantial PL quenching of MoSe2 across the entire heterostructure area involving NbSe2. These processes occur on sub-picosecond timescales, significantly faster than the nanosecond-scale exciton lifetime at $T=$ 295 K. The extent of PL quenching is strongly influenced by interlayer coupling, including factors such as interlayer distance, stacking sequence, and dielectric screening [14]. Since this quenching reflects a reduction in the exciton density, external electric fields that modulate exciton formation and recombination dynamics provide a promising route to restore or enhance PL emission in vdW heterostructures.

**Electric field-dependent PL enhancement at room temperature

**We next investigated the influence of an applied electric field (F) on the excitonic behavior, particularly, its effect on spectral intensity, as a proof-of-concept for implementing field-driven tunability in 2D materials-based heterostructures. A positive voltage ($V>0$) corresponds to the top electrode near the MoSe2 being positively biased while the bottom electrode remains grounded, resulting in a downward-pointing electric field, as illustrated in Fig. 1a. In contrast, applying a negative voltage ($V<0$) reverses the field direction. Contour color plots of the PL spectra for the ‘off’ and ‘on’ positions are presented in Fig. 3a and b, respectively.

The integrated intensities at both positions are displayed in Fig. 3c, with blue circles and red triangles representing the ‘off’ and ‘on’ positions, respectively. The integrated intensity exhibits a step-like variation: the ‘off’ position shows a two-step change, while the ‘on’ position demonstrates a single-step behavior. For the ‘off’ position, the PL intensity increases slightly at $V$ $\sim$ +0.8 V, reaching a maximum before rapidly decreasing at higher voltages. Similarly, a sharp decrease is observed below $V$ $\sim$ -0.6 V. For the ‘on’ position, a notable enhancement in PL intensity occurs at $V$ $\sim$ -1.8 V. The PL enhancement factor, defined as $\frac{I_{V}}{I_{0}}$, where $I_{V}$ is the PL intensity integrated over energy at a given voltage and $I_{0}$ is the integrated intensity at zero voltage, is illustrated in Fig. 3d. A modest increase of a factor of $\sim$ 1.1$\times$ is observed for the ‘off’ position, while the ‘on’ position shows a maximum of $\sim$ 4.0$\times$ enhancement. However, at a fixed position, the absolute change in intensity over the applied voltage sweep is much more pronounced, with nearly three orders of magnitude for the ‘off’ position and one order of magnitude for the ‘on’ position, respectively.

In a previous study, a thin hBN layer was used to achieve resonant tunneling of energetic electrons from graphene to MoSe2 [35]. However, the structural differences in the present work, particularly the use of a thicker hBN layer, rule out this mechanism as the source of the observed PL enhancement. Moreover, the enhancement achieved at different polarities differs between the two positions: $V>0$ for the bare-MoSe2 and $V<0$ for the MoSe2/NbSe2 heterostructure. A direct comparison of the PL intensity between the ‘on’ and ‘off’ positions at $V$=0, is shown as an intensity ratio in the inset of Fig. 3d. This reveals that the electrostatic field revives the optical intensity of the heterostructure to $\sim$40$\%$ of the bare-MoSe2 PL intensity, as shown in the inset of Fig. 3d. The maximum enhancement factor, although, is different for another similarly structured device (D2) studied, achieving up to 12× enhancement, $\sim$ 80$\%$ of the bare-MoSe2 intensity, as illustrated in Fig. S3. Interlayer coupling between MoSe2 and NbSe2, as well as the overall sample quality, plays a crucial role in this behavior.

Notably, different polarities of $V$ are required to achieve enhancement at the two positions. To further substantiate this finding, we replaced NbSe2 with a few-layer graphene atop MoSe2 in third device D3. In this configuration, PL enhancement was observed for both bare-MoSe2 and graphene/MoSe2 heterostructure at $V>0$, as shown in Fig. S4. The maximum enhancement factors are $\sim 1.2\times$ for bare-MoSe2 and $\sim 3.8\times$ for graphene/MoSe2 heterostructure, respectively. The result suggests a PL recovery of $\sim$ 23 $\%$ for ‘on-graphene’ heterostructure position compared to the bare-MoSe2. Therefore, regardless of the metal used, the observed enhancement and its polarity-dependent behavior are governed by the metal’s position relative to ML-TMDCs and the direction of the applied voltage, respectively.

Temperature dependence

The exciton lifetime of bare-MoSe2 is a few-nanoseconds at $T=$ 295 K and a few-picoseconds at low temperatures ($T=$ 20 K), as presented in Fig. S5a and b, respectively, and also reported earlier [9, 36]. This results in significant changes in exciton luminescence with varying temperature.

To investigate the impact of radiative lifetime of exciton on PL quenching and their modification under an applied electric field in MoSe2/NbSe2 heterostructure under different thermal conditions, we conducted voltage-dependent studies at various temperatures. For comparison, contour plots for both the positions at $T=$ 20 K are presented in Fig. 4a and b. Both the plots reveal two prominent peaks corresponding to excitons at $\sim$1.65 eV and trions at $\sim$1.62 eV. Although the mass action law predicts a constant trion-to-exciton intensity ratio in the absence of intentional doping, we observe a strong voltage dependence, likely due to photo-induced doping effects [37, 38, 39, 40]. To maintain consistency with the present study’s theme, we focus on the exciton behavior. In contrast to $T=$ 295 K, the PL-enhancement factor of the exciton for the ‘on’ position reduces at $T=$ 20 K, while maintaining a qualitatively similar voltage-dependence. The maximum enhancements at specific temperatures for both positions are shown in Fig. 4c, with circles and triangles representing ‘off’ and ‘on’ positions, respectively. Fig. 4d demonstrates that the maximum enhancement factor depends on temperature. Notably, the maximum enhancement factor at the ‘off’ position remains $(\sim 1.1\pm 0.1)$, independent of temperature. In contrast, the maximum enhancement factor for the ‘on’ position decreases continuously from $\sim$ 4.0 to 1.2 as the temperature is lowered from 295 K to 20 K.

III Discussion

To explain the field dependence of PL at the ‘off’ and ‘on’ positions we carried out a detailed analysis of $\Delta R/R$ spectra at these two points as shown in Fig. 5a and b, respectively, at $T=$ 295 K. A clear vertical electric field dependence in $\Delta R/R$ spectra at ‘off’ position can be seen.

For a more quantitative understanding, we have fitted each experimental spectrum using the Faddeeva function [41] (see Fig. S6) to extract the exciton peak position and oscillator strength ($f$). For ML TMDC, due to the lack of inversion symmetry and the absence of a net exciton dipole moment ($\Delta\mu=0$), the field dependence of excitons exhibits a quadratic behavior, as shown in Fig. S7. This yields an exciton polarizability ($\alpha$) of $(1.3\pm 0.07)\times$ $10^{-18}$ eV$\cdot$ (m/V)2. The estimated $\alpha$ is consistent with previously reported values [42], however, lower than the theoretically calculated value of 2$\times$ $10^{-20}$ eV$\cdot$ (m/V)2 [43]. The variation of the normalized oscillator strength ($\Delta f$= $\frac{f_{V}-f_{0}}{f_{0}}$) for bare-MoSe2, extracted from the fitting, is shown in Fig. 5c, where $f_{0}$ corresponds to zero applied voltage. Based on the $\alpha$ value from Fig. S7, the variation of absorption ($A$) is calculated with respect to electric field F. This calculation follows [44]

[TABLE]

For bare-MoSe2, $\frac{dA}{dE}$ at 1.57 eV is assumed to be proportional to $\frac{d(\Delta R)}{dE}$ at the same energy. The resulting $\Delta A$, calculated using Eq.1 with $\Delta\mu=0$, is shown by the solid line in Fig. 5c. It closely matches the experimental data and highlights key trends. Therefore, this change in the oscillator strength explains the variation of PL at the ‘off’ position. A slight positive voltage is required to achieve the maximum PL intensity by countering the intrinsic $n$-type doping caused by selenium (Se) vacancies in MoSe2.

To further corroborate the experimental observation at the ‘off’ position, we performed a model calculation using the transfer matrix method. The differential reflectance was obtained by considering a stack comprising the following sequence of layers: Air/few-layer-graphene/hBN/MoSe2/hBN/few-layer-graphene/SiO2/Si. The resulting $\Delta R/R$ values, shown in Fig. S8b, exhibit a variation similar to that observed in the experiment in Fig. 3c, thereby validating the optical modeling. In addition, a perturbative analysis is employed to quantify the influence of the electric field on exciton properties. In particular, the exciton oscillator strength is approximately proportional to the square of the electron-hole e–h overlap. The electric field pulls electrons and holes in opposite directions, thereby reducing their overlap. The calculation reveals that the e–h overlap decreases with increasing field strength by a factor of $\frac{1}{1+(F/F_{0})^{2}}$, where the characteristic field is $F_{0}$ = 2450 kV/cm, as shown in Fig. S8c. This reduction in e–h overlap directly contributes to a suppression of exciton recombination, and hence, the modulation of PL intensity observed at the ‘off’ position in Fig. 4c.

Fig. 5c shows that, unlike the ‘off’ position, the $\Delta R/R$ signal at the ‘on’ position exhibits negligible variation with $V$, indicating that changes in PL intensity are not due to absorption variations as seen in bare-MoSe2. Therefore, to uncover the origin of the PL behavior at the ‘on’ position, we performed density functional theory (DFT) calculations, investigating the electronic band structures and analyzing their impact on the intensity of bandgap transitions. An intense optical transition requires a direct band gap with significant contributions from MoSe2 states in both valence and conduction bands. Conversely, an indirect band gap is associated with weak band-gap emission. Hence, to address this question, bands in the vicinity of the band gap must be projected onto the parent MoSe2 and NbSe2 layers to ascertain the direct/indirect nature of the transition.

Our DFT-based calculations of MoSe2/NbSe2 heterostructures (assuming a single ML of each material) include spin–orbit coupling (SOC) and employ a localized basis set, enabling accurate treatment of strong perpendicular electric fields (see Methods). Specifically, standard plane-wave bases with supercells extended perpendicular to the layers are avoided, as they produce spurious field-induced states at the supercell boundaries. We assume AB stacking corresponding to a single MoSe2/NbSe2 structural unit in the unit cell. This necessarily implies that individual layers are strained relative to their free-standing structures. Importantly, such commensurate geometries mean that MoSe2 and NbSe2 layers are strongly coupled electronically. Effectively, metal- and semiconductor-derived states become interlocked and, thereby, less susceptible to electric fields. Conversely, decoupled layers are highly susceptible to electric fields since the dipole moment $F\times d$, where $d$ is the center-to-center distance between the Se atoms of the two layers, will cause significant vertical shifts in the band structure.

The calculated band structures are shown in Fig. 6a-c. In particular, the band structure in the absence of an electric field verifies that MoSe2/NbSe2 has a direct band gap between semiconductor-derived bands (Fig. 6b). However, in the presence of electric fields, the indirect band gap shrinks in proportion to the field in the positive direction, while negative fields enlarge the indirect gap, c.f. Fig. 6a and Fig. 6c. This is in agreement with experimental spectra in Fig. 3d. However, the field required for indirect and direct band gaps to cross is $\sim$ $1.0\times 10^{5}$ kV/cm, as shown in Fig. 6d, far greater than the experimentally observed range. We suggest that the discrepancy arises from the fact that the experimental MoSe2/NbSe2 heterojunctions are not commensurate but, rather, rotated relative to each other. Thereby, the electronic coupling is significantly weakened, leading to a reduction of the field required for a transition to an indirect band gap. Furthermore, the temperature variation in the maximum PL enhancement factor at the ‘on’ position can be attributed to radiative recombination competing with ultrafast charge and energy transfer processes in the TMDC/metal heterostructure. At low temperatures, the reduced exciton lifetime down to a few picoseconds means that radiative recombination dominates. In contrast, at $T=$ 295 K, non-radiative channels contribute significantly, leading to a decreased PL enhancement.

IV Conclusion

In summary, our findings reveal a significant enhancement of emission in TMDC/metal vdW heterostructures, enabled by electric field control. By applying a vertical electric field, we demonstrate the ability to tune the absolute PL intensity–by up to three orders of magnitude at the ‘off’ position and one order at the ‘on’ position. Such large modulation is promising for applications in electrically controlled switches and modulators, as suggested by previous studies [45, 46]. The variation at the ‘off’ position is linked to the modification of the excitonic oscillator strength, while calculated band structures demonstrate field-dependent modifications of the bandgap at the ‘on’ position. Temperature-dependent measurements reveal the impact of radiative recombination in PL enhancement factor. This work underscores the potential of utilizing vertical electric fields as a precise and effective method to tailor excitonic and electronic properties in TMDC-based heterostructures. Unlike conventional tuning methods based on chemical doping or strain, our electric-field approach offers clean, reversible, and disorder-free control of exciton behavior. Moreover, our findings act as a guiding light for further exploration of 2D superconductors based TMDCs heterostructures below the superconducting critical transition temperatures. This can open interesting avenues to investigate the emergent quantum states influencing superconducting pairing mechanism and the excitonic physics.

Methods

Device fabrication: The devices were fabricated via mechanical exfoliation of bulk crystals, followed by dry transfer using a polyDimethylSiloxane (PDMS) film onto the prepatterned electrodes. Details of the electron beam lithography (EBL) process for electrode patterning are provided in the Supplementary section. Monolayer MoSe2 was obtained by exfoliation of a bulk crystal grown via chemical vapor deposition, while all other bulk crystals were purchased from HQ Graphene. The thickness of the hBN flakes was measured by an atomic force microscope.

Optical spectroscopy: Photoluminescence (PL) measurements were carried out using a continuous-wave 532 nm laser, focused to a $\sim$ 1 $\mu$m spot with a Mitutoyo objective (×50, 0.65 NA ). The incident pump power was controlled using adjustable optical density filters in the excitation path. For reflection measurements, a white light laser (SuperK Extreme, NKT Photonics) was used.

Computational details: Density-functional calculations were performed using the GPAW software package [47]. A localized dzp-zeta basis combined with a 15$\times$15$\times$1 k-space grid was employed, and all results are based on the PBE exchange-correlation functional including d3 van der Waals corrections. Spin-orbit interactions are included, and the AB-stacking unit cell was relaxed, yielding residual forces below 0.05 eV/Å. The application of an electric field has a minor but significant effect on the atomic positions in the unit cell. Therefore, the structure was relaxed for all applied electric fields. The indirect bandgap is defined as the difference between the $\mathrm{K}$-point energy of the first conduction band, where MoSe2 contributes most strongly, and the average $\Gamma$-point energy of the six bands immediately below the Fermi level. There are a total of six bands due to spin-orbit coupling (SOC)-induced splittings, but the resulting SOC-induced splittings at the $\Gamma$-point are negligible. We use their average energy since all six bands exhibit some degree of hybridization, and the extent of this hybridization varies with the applied field strength.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgements.

We gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the projects Ho5194/16-1 and INST 93/1025-1 FUGG. S.H and A.P. acknowledge the funding from the lighthouse project IQ-Sense of the Bavarian State Ministry of Science and the Arts as part of the Bavarian Quantum Initiative Munich Quantum Valley (15 02 TG 86). S.H., S.K. and C.G.M acknowledge financial support from the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, DFG project ID 390858490). T.G.P. was supported by the DNRF Centre CLASSIQUE sponsored by the Danish National Research Foundation, grant nr. 187. S.A.T acknowledges primary support from DOE-SC0020653 (excitonic tests on crystals). Partial support comes from NSF CBET 2330110 (environmental stability tests). S.A.T. also acknowledges partial support from Applied Materials Inc. and Lawrence Semiconductor Labs for growth systems. We are grateful for enabling us to have used the Raman measurement facility at the Julius-Maximilians-Universität Würzburg, Experimental Physics 6.

Conflict of interest

The authors declare no competing interests.