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K Oreszczuk, A Rodek, M Goryca, T Kazimierczuk, M Raczyński, J Howarth, [T Taniguchi](https://orcid.org/0000-0002-1467-3105), [K Watanabe](https://orcid.org/0000-0003-3701-8119), M Potemski, P Kossacki

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[Enhancement of electron magnetic susceptibility due to many-body interactions in monolayer MoSe<sub>2</sub>](https://mdr.nims.go.jp/datasets/09bdda90-df84-4a58-a940-97b6b8782178)

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Enhancement of electron magnetic susceptibility due to many-body interactions in monolayer MoSe22D MaterialsPAPER • OPEN ACCESSEnhancement of electron magnetic susceptibilitydue to many-body interactions in monolayerMoSe2To cite this article: K Oreszczuk et al 2023 2D Mater. 10 045019 View the article online for updates and enhancements.You may also likeEffects of a semiconductor matrix on theband anticrossing in dilute group II-VIoxidesM Wena, R Kudrawiec, Y Nabetani et al.-Quantum engineering of Majoranaquasiparticles in one-dimensional opticallatticesAndrzej Ptok, Agnieszka Cichy andTadeusz Domaski-Comparison of magneto-optical propertiesof various excitonic complexes in CdTeand CdSe self-assembled quantum dotsJ Kobak, T Smoleski, M Goryca et al.-This content was downloaded from IP address 144.213.253.16 on 02/09/2023 at 07:18https://doi.org/10.1088/2053-1583/acefe3/article/10.1088/0268-1242/30/8/085018/article/10.1088/0268-1242/30/8/085018/article/10.1088/0268-1242/30/8/085018/article/10.1088/1361-648X/aad659/article/10.1088/1361-648X/aad659/article/10.1088/1361-648X/aad659/article/10.1088/0953-8984/28/26/265302/article/10.1088/0953-8984/28/26/265302/article/10.1088/0953-8984/28/26/2653022D Mater. 10 (2023) 045019 https://doi.org/10.1088/2053-1583/acefe3OPEN ACCESSRECEIVED3 April 2023REVISED17 July 2023ACCEPTED FOR PUBLICATION14 August 2023PUBLISHED30 August 2023Original Content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.PAPEREnhancement of electron magnetic susceptibility due tomany-body interactions in monolayer MoSe2K Oreszczuk1,∗, A Rodek1, M Goryca1, T Kazimierczuk1, M Raczyński1, J Howarth2,T Taniguchi3, K Watanabe4, M Potemski1,5,6 and P Kossacki11 Institute of Experimental Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland2 National Graphene Institute, University of Manchester, Booth St E, M13 9PL Manchester, United Kingdom3 International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan4 Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan5 Laboratoire National des Champs Magnétiques Intenses, UPR 3228, CNRS, EMFL, Univ; Grenoble Alpes, 38042 Grenoble, France6 CENTERA Labs, Institute of High Pressure Physics, PAS, 01-142 Warszawa, Poland∗ Author to whom any correspondence should be addressed.E-mail: Kacper.Oreszczuk@fuw.edu.plKeywords: TMD, MoSe2, 2DEG, magnetic susceptibility, g-factorSupplementary material for this article is available onlineAbstractEmploying the original, all-optical method, we quantify the magnetic susceptibility of atwo-dimensional electron gas (2DEG) confined in the MoSe2 monolayer in the range of low andmoderate carrier densities. The impact of electron–electron interactions on the 2DEG magneticsusceptibility is found to be particularly strong in the limit of, studied in detail, low carrierdensities. Following the existing models, we derive the value of g0 = 2.5± 0.4 for the bare (in theabsence of the interaction effects) g-factor of the ground state electronic band in the MoSe2monolayer. The derived value of this parameter is discussed in the context of estimations fromother experimental approaches. Surprisingly, the conclusions drawn differ from theoretical abinitio studies.1. IntroductionCollective properties of the two-dimensional elec-tron gas (2DEG) and the 2D hole gas (2DHG)have been studied extensively for a wide variety ofsystems. The ease of the electrical control of car-rier concentration makes 2D systems an excellentplayground for exploring carrier–carrier interactions,facilitatingmany interesting phenomena, such as spintextures [1] or quantum Hall ferromagnetism [2].The Coulomb repulsion enhances the pseudospinsusceptibility [2–6], possibly leading to the spontan-eous creation of broken symmetry phases [7–10].Monolayers of transition metal dichalcogenides(TMDs) draw a lot of attention as semiconduct-ing materials with robust optical properties, strongCoulomb interaction [11–13] and an optically access-ible valley degree of freedom [14–17]. TMDs arean example of a system with near-ideal 2D quant-ization, where the magnetooptical measurementsreveal significant collective effects [10, 18]. Relativelylarge carrier masses and reduced dielectric screening[19, 20] promise strong electron–electron interac-tions even at large carrier concentrations.Collective behavior of the carriers in an ideal2DEG can be modeled, for example, employingthe quantum Monte Carlo (QMC) calculations [6].Theoretical methods predict a strong enhancementof the carrier gas polarizability in low carrier dens-ity regimes. The experimentally obtained values of thecarrier gas polarizability can be compared with the-oretical predictions to estimate the effective single-particle band g-factor [18].Phenomena related to the enhancement of thespin susceptibility or other collective propertiesof the 2D carrier gas in monolayer TMDs canbe experimentally observed through the Landaulevel filling processes in both Zeeman-split valleys[10, 18, 21–26]. Such experiments usually yield largeeffective g-factor (g∗) values for 2DEG in MoS2 [18,27], 2DHG in WSe2 [10, 21, 26] and 2DEG in MoSe2[18]. The g-factor values usually reach between 10© 2023 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2053-1583/acefe3https://crossmark.crossref.org/dialog/?doi=10.1088/2053-1583/acefe3&domain=pdf&date_stamp=2023-8-30https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0001-8830-0005https://orcid.org/0000-0002-0263-3122https://orcid.org/0000-0001-7582-1880https://orcid.org/0000-0001-6545-4167https://orcid.org/0000-0003-0443-1943https://orcid.org/0000-0002-0560-8985https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0001-8881-6618https://orcid.org/0000-0002-7558-1044mailto:Kacper.Oreszczuk@fuw.edu.plhttps://doi.org/10.1088/2053-1583/acefe32D Mater. 10 (2023) 045019 K Oreszczuk et aland 20 for carrier densities close to 4× 1012 cm−2.This approach, however, is viable only in the regimeof relatively high carrier densities (usually above3× 1012 cm−2). The low and moderate carrier dens-ity regimes, where the collective effects are expected tobe most pronounced, must be investigated by differ-ent approaches. In that view, the experimental tech-niques that are viable in low carrier densities are ofhigh importance.Here we present a novel experimental approachto study the polarizability of 2DEG in the MoSe2monolayer by means of all-optical electron gaspolarization measurements. We employ two comple-mentary approaches to measure the effective elec-tron g-factors in low and moderate 2DEG densit-ies. Our experimental methods are not constrainedby the Landau quantization and can be employedboth in high and low-to-moderate 2DEG densityregimes. Moreover, our approaches are more ver-satile by permitting the measurement of materialswith significant inhomogeneity or Coulomb disorder,which otherwise would prohibit the application ofmethods relying on the signatures of the Landaulevels.2. Sample and experimental setupThe electrically gated MoSe2 sample, schematicallyshown in figure 1(a), was prepared with the means ofmechanical exfoliation using the dry transfermethod.The MoSe2 monolayer was exfoliated on top of thegraphite back gate and 36 nmhexagonal boronnitride(hBN) spacer. The thickness of the hBN spacer wasmeasuredwith the atomic forcemicroscope. Next, thesecond graphene flake was then deposited at the edgeof the MoSe2 monolayer to provide electric contact.Finally, gold contacts were deposited on the graphiteback gate and on the graphene contact. The photo-graph of the sample is shown in figure 1(b). The pho-toluminescence and reflectance spectra of the MoSe2monolayer are presented in figures 1(c) and (d). Thereflectance spectra were divided by the reference spec-trum measured on the gold contact and then nor-malized. Neutral exciton (X) and negatively chargedexciton (X−) resonances can be resolved in the photo-luminescence and reflectance spectra at the zero gatebias voltage.Most magnetooptical experiments were carriedout in a cryostat equipped with a superconductingcoil providing magnetic fields up to 10 T. In thisexperimental setup, samples were placed in a heliumgas atmosphere at the temperature of 6 K or 11K orin the superfluid helium bath at 1.6 K. The temper-ature was calibrated with a thin film resistive sensorplaced on the sample holder. Unless noted otherwise,the data were acquired at 6 K. The optical signal wasfocused by a single aspheric lens (NA = 0.68) placedinside the cryostat.High magnetic field (up to 30 T) measurementswere performed with the use of a resistive magnetat the temperature of 4.2 K. The optical signal wasfocused by amicroscope objective (NA= 0.25) placedinside the cryostat.In both experimental configurations, the samplewas mounted on the x-y-z piezoelectric stage.3. ResultsThe map of the reflectance spectrum of the sampleplotted against the gate voltage is presented infigure 2(a). Three carrier concentration regimescan be distinguished. The p-doping regime emergesat strong negative gate voltages, while the mod-erate negative gate voltages result in the mid-bandgap Fermi level, yielding a neutral regime.Positive gate voltage induces n-doping of the MoSe2monolayer.The exact value of the n-doping transition voltageis important for the precise determination of theelectron densities. Figures 2(b) and (c) shows theamplitudes and positions of the excitonic peaks as afunction of the gate voltage. Qualitative change is vis-ible at the voltage of −0.5 V, indicating a transitionbetween neutral and n-doped regimes. The negativevalue of the transition voltage indicates that the stud-ied sample is in the weak 2DEG regime at zero biasvoltage. The 2DHG regime can be distinguished atgate voltages below−14V.In this work, we focus on the attractivepolaron/negatively charged exciton (X−) peak inthe 2DEG regime. The carrier concentration isapproximated with a flat capacitor formula withthickness equal to d= 36.0 nm. The estimationof the relative permeability of hexagonal boronnitride ϵ⊥ ≈ 3.5 is based on previous works [28,29]. The exact value of the threshold voltagebetween the 2DEG regime and the neutral regimewas determined from the changes in the oscil-lator strength and resonance energy of the X− peak(figures 2(b) and (c)).Using two complementary methods, we investig-ate the effective susceptibility of the electron gas at dif-ferent carrier densities.We neglect the Landau quant-ization in both experimental approaches and treatthe electron bands as continuous. The Landau levelseparation equals 1.4meV at the magnetic field of10 T. Consequently, the resulting electron density in asingle Landau level is equal to 0.24× 1012 cm−2, withboth values scaling linearly with the magnetic field.The Landau level splitting is significantly smaller thanthe Zeeman splittings analyzed in these experiments.In particular, the Landau level separation is alsosmaller than the amplitude of the electric poten-tial fluctuations within the monolayer. This prohibitsLandau-level signatures from emerging in the exper-imental data.22D Mater. 10 (2023) 045019 K Oreszczuk et alFigure 1. (a) Scheme of the MoSe2 monolayer with graphene contacts on the top and graphite gate at the bottom. (b) Photographof the sample. The positions of the MoSe2 monolayer and graphene top contacts are marked with contours. The graphite backgate is visible as a darker area in the middle of the hBN flake. (c) PL spectrum of the sample under the excitation with 600 nm,10µW femtosecond pulsed laser. (d) Reflectivity spectrum of the sample. Spectra in (c), (d) were acquired at the gate voltage of0 V in the temperature of 6 K. Neutral exciton (X) and negatively charged exciton (X−) resonances can be resolved.In the primary approach, we apply the magneticfield up to 30T and probe the X− resonance at dif-ferent 2DEG densities at σ+ polarization of detec-tion (figure 3(a)). At sufficiently highmagnetic fields,two different regimes can be distinguished. At lowcarrier densities, 2DEG is fully confined in the ener-getically favorable K− valley, while above a certaindensity threshold, both valleys are partially filled(figure 3(b)). The two regimes can be differentiatedby observing the rate of the change of the energy of theX− resonance upon increasing 2DEG density. Belowthe threshold density, the resonance energy decreaseswith increasing density due to the attractive interac-tions with the electron gas. Above the threshold dens-ity, when the K+ valley starts being filled, k-spacefilling effects induce a rapid positive shift of the X−resonance energy (figures 3(c) and (d)). We meas-ure the threshold 2DEG density in different mag-netic fields. Then we calculate the Zeeman split-ting necessary to contain 2DEG in the single valleyand, consequently, determine the effective electrong-factor. Here, we define the effective g-factor g∗ sothat the Zeeman Splitting EZ = g∗µBB, in line withthe definition used in [10, 26] (note, that the defin-ition used in [18, 21, 27] differs by a factor of 2). Theeffective mass of the electron in monolayer MoSe2is assumed equal to me = 0.84 (Goryca et al [30]),from which follows the single-valley density of statesρ= m0m∗2π h̄2. The values of the effective electron g-factor at different carrier densities are presented infigure 3(e).To complete the determination of the electrong-factor in a broader range of carrier densities, weemploy a supplementary approach. We focus on thecircular polarization resolved oscillator strength ofthe X− resonance in the MoSe2 monolayer in the2DEG regime. Figure 2(a) shows the reflectance spec-trum of the sample at different gate voltages.The reflectance of the sample is probed withthe circular polarization of detection at oppositemagnetic fields, corresponding to the σ+ and σ−polarizations (figures 4(a) and (b)). The reflect-ance measurements are performed at differentmagnetic fields and gate voltages. We analyze theoscillator strengths of transitions related to X−formation in two circular polarizations (oscillatorstrengths are denoted as I+ and I− in σ+ and σ−polarizations, respectively). Figures 4(c) and (d)show the magnetic field dependence of the circu-lar polarization degree (P= (I+ − I−)/(I+ + I−))of the X− resonance at two different carrierconcentrations.We describe the magnetic field evolution of theobserved circular polarization degree of the X−peak with a simple model based on the followingassumptions:(i) The total carrier density is obtained from theflat capacitor formula, which means that theZeeman shifts are negligible with respect to elec-trostatic potential.(ii) The effective mass of the electron in monolayerMoSe2 is me = 0.84 (Goryca et al [30]), fromwhich follows the single-valley density of statesρ= m0m∗2π h̄2.(iii) The electron gas follows the Fermi–Diracdistribution with the effective temperature Teff.(iv) The polarization degree P of the 2DEG is equalto the polarization degree of the X− resonanceobserved in the reflectance spectrum.32D Mater. 10 (2023) 045019 K Oreszczuk et alFigure 2. (a) Reflectance spectrum of the MoSe2 monolayer measured at different gate voltages in the temperature of 6 K. Spectraare composed of neutral exciton (X), negatively charged exciton (X−) and positively charged exciton (X+) resonances.(b) Oscillator strengths of the neutral and charged exciton peaks normalized to their maximal value. (c) Energy shift of the X andX− peaks relative to their positions in the neutral regime. Vertical dashed line in (b) and (c) marks the voltage of−0.5 V, wherethe Fermi level crosses the bottom of the conduction band.In assumption (iii), the effective temperature para-meter Teff describes both the distribution related tothe nonzero temperature of the electron gas as wellas the approximation of the in-plane Coulomb fluc-tuations. The latter effect is dominant in this workdue to the low temperatures. One should note thatthe electric potential fluctuations in the conduct-ance band may be comparable but not necessar-ily equal to the inhomogeneous broadening of theexcitonic peaks. The effective temperature parameterTeff is derived from the sample temperature T andconductance band disorder parameter Tdis as a rootsum of squares: T2eff = T2 +T2dis. The estimated valueof the disorder parameter is equal Tdis = (50± 15)K.The estimation was performed in a way to ensure thequality of fit in figure 4(e) and to match the values ofthe effective g-factor obtained with the highmagneticfield approach. Thus, the results—which rely stronglyon the value of theTdis parameter—must be treated asan extrapolation of the high magnetic field approach.As such, the uncertainties of both are strongly correl-ated. This is relevant mainly in the low carrier dens-ity regime (below 2× 1012 cm−2), and has no impacton the results obtained in carrier densities above 4×1012 cm−2. See supplementary information, figures 1and 2 for more information on the impact of the Tdisparameter on the fit quality and resulting values of theeffective g-factor.Assumption (iv) may require additional justi-fication, as the oscillator strength of the X− res-onance is directly proportional to the 2DEG dens-ity only in the part of the gate voltages range(figure 2(b)). However, previous works on the 2DEGin quantum wells [31] indicate that the observed42D Mater. 10 (2023) 045019 K Oreszczuk et alFigure 3. (a) Reflectance spectrum of the MoSe2 monolayer at different carrier densities in the 2DEG regime in the magnetic fieldof 30 T. (b) Schematic presentation of the valley filling at three different carrier densities marked in panel (a). (c), (d) Dependenceof the X− resonance energy on the carrier density. Vertical lines mark the threshold carrier density for filling the secondZeeman-split valley. (e) Effective electron g-factors are calculated from threshold carrier densities measured at different magneticfields.sublinearity of the oscillator strength of the X− peakin high carrier density can be described in terms ofthe reduction factor ξ(n) common for both polariz-ations of detection and dependent on the total car-rier density n, rather than in terms of separate reduc-tion factors dependent on the carrier densities nK+(−)attributed to each valley. In this description, the oscil-lator strength at σ+(σ−) polarization of detection isdescribed by formula I+(−) = nK+(−) · ξ(n), leadingto the equivalence between optically observed polar-ization degree and the distribution of the carriersin Zeeman-split valleys: P= (I+ − I−)/(I+ + I−) =(nK+ − nK−)/(nK+ + nK−).Such assumptions are further supported bythe observation that the total oscillator strengthof the X− resonance remains constant for 2DEGpolarizations induced by different magnetic fields(figures 4(a) and (b)). In particular, we find theoscillator strength at B= 0T to be equal to halfthe oscillator strength at the saturation magneticfield. Reduction factor—if common for both cir-cular polarizations—does not perturb the observedpolarization degree of the X− resonance, assuring thevalidity of the assumption (iv).Carrier densities in K+ and K− valleys can bedescribed with the integral of the Fermi–Dirac distri-bution over the single-band density of states ρ:nK+(−) =ˆ ∞± EZ2ρeE−µkTeff + 1dE= ρkTeff log(e± EZ2kTeff + eµkTeff)∓ ρEZ2. (1)There is exactly one solution for the Fermilevel µ and Zeeman splitting EZ that satis-fies the observed magnetic polarization degreeP= (nK+ − nK−)/(nK+ + nK−) and the total carrierdensity n= nK+ + nK− obtained from the flatcapacitor formula. Similarly, the effective electrong-factor g∗ (from which follows the Zeeman split-ting EZ) can be treated as a fit parameter describ-ing the 2DEG polarization degrees observed in theexperiment.Figures 4(c) and (d) show the polarization degreeof the X− reflectance peak plotted against the mag-netic field at two different 2DEG densities. The effect-ive electron g-factor was calculated for each carrierdensity to reproduce the observed polarization degree52D Mater. 10 (2023) 045019 K Oreszczuk et alFigure 4. (a), (b) Reflectance spectra of the MoSe2 monolayer measured with the circular polarizations of detection at differentmagnetic fields in the temperature of 6 K. Voltages applied to the gated structure are equal to 1V (a) and 6V (b), resulting in2DEG density equal to 0.84× 1012 cm−2 and 3.6× 1012 cm−2, respectively. (c), (d) Magnetic field dependencies of circularpolarization degree of the X− peak at corresponding 2DEG densities. Red solid lines: fits to the experimental data with theeffective g-factor value as a fitting parameter. Red dashed lines: polarization degrees expected under conditions of no disorder andvery low temperature. (e), (f) Visualizations of the Zeeman-split valleys at different magnetic fields at corresponding 2DEGdensities. Red lines visualize the Fermi–Dirac distribution at the temperature of 6 K. Carrier density at each valley is proportionalto the area of the shape filled with gray color. Horizontal dashed lines correspond to the uncertainty of the g∗-induced Zeemansplitting. Blue dashes on panel (f) visualize the energy separation of the Landau Levels at the magnetic field of 9 T.dependency on the magnetic field. Figures 4(e) and(f) show the visualizations of the Zeeman Splittingand carrier distribution between K+ and K− valleysfor different 2DEG densities and magnetic fields. Redsolid lines on figures 4(e) and (f) represent the expec-ted polarization degree evolution according to thebest fit of the effective g-factor to the experimentaldata.The effective g-factor was calculated for severalgate voltages at three different temperatures. Theresults are presented in figure 5 with blue, yellow,and red data points. Regardless of the temperat-ure, the effective g-factor exhibits a value of morethan 30 at concentrations below 2× 1012 cm−2 anddeclines pronouncedly reaching values close to 10 atthe 2DEG densities above 5× 1012 cm−2. The valueof the effective g-factor seemingly rebounds in carrierdensities above 7× 1012 cm−2. However, this prob-ably is an artifact related to the filling of the secondspin-split valley. The spin–orbit splitting in the con-duction band of the MoSe2 monolayer is equal to∆C = 21meV [32], which corresponds to the carrierdensity of 7× 1012 cm−2 distributed between the twovalleys.Recent work [33] suggests that resonant excita-tion of neutral exciton peak can induce significantdepolarization of the 2DEG, even under the weakexcitation induced by white light. To verify the influ-ence of that effect in our experimental conditions, weperformed an additionalmeasurement with the white62D Mater. 10 (2023) 045019 K Oreszczuk et alFigure 5. Effective g-factor value as a function of the electron gas density measured with different approaches and in differenttemperatures.Figure 6. Circles: values of the effective electron g-factor in monolayer MoSe2 averaged over different approaches and differenttemperatures presented in figure 5. Dashed line: fit of the QMC calculations [6] to the experimental data, resulting in the value ofthe electron g-factor in the absence of interaction effects g0 = 2.5± 0.2. Squares: values obtained in Landau Level studies byLarentis et al [18] (resulting in g0 = 2.2).light spectral range limited to the nearest proximityof the X− peak, that is, to 1560–1633meV. The spec-tral range was fine-tuned during the measurementto follow the energy shifts of the X and X− peaks,present when themagnetic field and gate voltage werenot equal to zero. The results of this experiment arepresented in figure 5 with filled yellow circles. We doobserve an increase in polarizability after filtering outthe resonant excitation, however, the effect is incre-mental and does not fundamentally alter our experi-mental results.The results of all our experiments performed indifferent temperatures and with different approacheshave been averaged and presented in figure 6.Wherever the g-factor value at given carrier densitywas missing in some of the averaged datasets, linearinterpolation between nearest data points was used.We fit the QMC calculations [6] and obtain the valueof the lowest conduction band g-factor in the absenceof the interaction effects equal to g0 = 2.5± 0.4.The interparticle distance parameter rs was calcu-lated with the effective dielectric constant of thehBN environment equal to κ=√ϵ⊥ϵ∥, assumingϵ∥ = 6.9 [29].Our results are in agreement with Landau Levelstudies in monolayer MoSe2 [18] (g0 = 2.2). Ourapproaches, however, allow for probing deeper intothe low carrier density regime, where the collect-ive effects are most pronounced. The value of theconduction band g-factor obtained in our work isalso in line with the experimental estimations madefor monolayer MoSe2 in the neutral regime [34]72D Mater. 10 (2023) 045019 K Oreszczuk et al(g0 ≈ 2.2). Here, however, one should note thatthe g-factor describing magnetic susceptibility differsfrom the electron factor used (together with the holeone) to calculate the Zeeman splitting of the opticaltransition. In particular, the Kohn theorem states thatoptical transitions are not sensitive to carrier–carrierinteractions when the carriers have the same effectivemass [35, 36].Our results, supported by experimentalapproaches from other works, create a solid imageof the issue of the conductance band g-factor inmonolayer MoSe2. These results, however, are indisagreement with the results of the ab initio cal-culations, which predict up to twofold greater val-ues (g0 = 3.6 [37], g0 = 3.8 [38], g0 = 4.1 [39],g0 = 5.5 [40]). The observed discrepancy suggestsroom for improvement in the theoretical models orassumptions of the ab initio calculations. This mayrelate either to the predictions on the band g-factorvalue or to the validity of the assumptions on the2DEG interactions.Some degree of uncertainty may arrive from thedetermination of the rs parameter, which is derivedfrom the Bohr radius of the electron, which con-sequently depends on the assumptions taken on thedielectric environment of the electrons. In particular,the dielectric constant of hBN exhibits strong bound-ary effects resulting in significant thickness depend-ence of its dielectric constant [29]. Although signific-ant for the quality of fit, uncertainties regarding the rsparameter scale (see figure 6) remain unlikely to influ-ence the resulting g0 value significantly.4. ConclusionsWe determined the effective electron magnetic sus-ceptibility in low and moderate 2DEG densities inthe monolayer MoSe2. Our measurements were per-formed with two different approaches and at dif-ferent temperatures between 1.6 K and 11K. Allobtained results are quantitatively consistent. Theexploration deep into the low carrier density regimereveals strong collective effects. The shape of thesusceptibility variation with electron density agreeswith the QMC calculations [6] and leads to thevalue of the lower electron band g-factor in theabsence of the interaction effects: g0 = 2.5± 0.4.This value, while coherent with other experimentalapproaches [18, 34], contests the results of to-dateab initio calculations [37–40], opening perspectivesfor improvement in assumptions and theoreticalmodels.Data availability statementThe data that support the findings of this study areopenly available at the following URL/DOI: https://doi.org/10.18150/FOOPUD [41].AcknowledgmentsThis work was supported by National Science Centre,Poland under Projects 2021/41/N/ST3/04240 and2020/39/B/ST3/03251. The research leading to theseresults has also received funding from the NorwegianFinancial Mechanism 2014–2021 within Project No.2020/37/K/ST3/03656 and from the Polish NationalAgency for Academic Exchange within Polish Returnsprogram under Grant No. PPN/PPO/2020/1/00030.We acknowledge the support of the LNCMI-CNRS,member of the European Magnetic Field Laboratory(EMFL) and of the CNRS via the IRP ‘2DM’ Project.The Polish participation in EMFL is supported by theDIR/WK/20218/07 Grant from the PolishMinistry ofEducation and Science. M P acknowledges the sup-port from the EU Graphene Flagship and from FNP-Poland (IRA—MAB/2018/9Grant, SG 0P Programofthe EU).ORCID iDsK Oreszczuk https://orcid.org/0000-0001-8830-0005A Rodek https://orcid.org/0000-0002-0263-3122M Goryca https://orcid.org/0000-0001-7582-1880T Kazimierczuk https://orcid.org/0000-0001-6545-4167M Raczyński https://orcid.org/0000-0003-0443-1943J Howarth https://orcid.org/0000-0002-0560-8985K Watanabe https://orcid.org/0000-0003-3701-8119M Potemski https://orcid.org/0000-0001-8881-6618P Kossacki https://orcid.org/0000-0002-7558-1044References[1] Sondhi S L, Karlhede A, Kivelson S A and Rezayi E H 1993Phys. Rev. B 47 16419–16426[2] Girvin SM 2000 Phys. Today 53 39–45[3] Jungwirth T and MacDonald AH 2000 Phys. Rev. B63 035305[4] Ando T and Uemura Y 1974 J. Phys. Soc. Japan 37 1044–1052[5] Das Sarma S, Hwang E H and Li Q 2009 Phys. Rev. B80 121303[6] Attaccalite C, Moroni S, Gori-Giorgi P and Bachelet G B2002 Phys. Rev. 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Introduction 2. Sample and experimental setup 3. Results 4. Conclusions References