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Shuichi Iwakiri, Jakob Miller, Florian Lang, Jakob Prettenthaler, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Sung Sik Lee, Pascal Becker, Detlef Günther, Thomas Ihn, Klaus Ensslin

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[High-mobility transport in isotopically enriched <math>  </math> and <math>  </math> exfoliated graphene](https://mdr.nims.go.jp/datasets/fc7c92de-dcdc-4d9d-b020-723e879a049a)

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High-mobility transport in isotopically enriched $\sideset{^{12}}{}{\mathop {\rm C}}$ and $\sideset{^{13}}{}{\mathop {\rm C}}$ exfoliated graphenePHYSICAL REVIEW RESEARCH 5, 043212 (2023)High-mobility transport in isotopically enriched 12C and 13C exfoliated grapheneShuichi Iwakiri ,1,* Jakob Miller,1 Florian Lang ,1 Jakob Prettenthaler ,1 Takashi Taniguchi ,2 Kenji Watanabe ,3Sung Sik Lee ,4 Pascal Becker ,5 Detlef Günther ,5 Thomas Ihn,1,6 and Klaus Ensslin 1,61Solid State Physics Laboratory, ETH Zurich, CH-8093 Zurich, Switzerland2Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan3Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan4ScopeM, ETH Zurich, CH-8093 Zurich, Switzerland5Department of Chemistry and Applied Biosciences, ETH Zurich, CH-8093 Zurich, Switzerland6Quantum Center, ETH Zurich, CH-8093 Zurich, Switzerland(Received 16 August 2023; accepted 6 November 2023; published 7 December 2023)Graphene quantum dots are promising candidates for qubits due to weak spin-orbit and hyperfine interactions.The hyperfine interaction, controllable via isotopic purification, could be the key to further improving thecoherence. Here, we use isotopically enriched graphite crystals of both 12C and 13C grown by a high-pressure-high-temperature method to exfoliate graphene layers. We fabricated Hall bar devices and performed quantumtransport measurements, revealing mobilities exceeding 105 cm2/V s and a long mean free path of microns,which are as high as natural graphene. Shubnikov–de Haas oscillations, quantum Hall effect up to the fillingfactor of one, and Brown-Zak oscillations due to the alignment of hBN and graphene are observed thanks to thehigh mobility. These results constitute a material platform for physics and engineering of isotopically enrichedgraphene qubits.DOI: 10.1103/PhysRevResearch.5.043212I. INTRODUCTIONGraphene quantum dots are among the most promisingcandidates as platforms for spin qubits [1–3] thanks to theweak spin-orbit coupling and hyperfine interactions. Under-standing the hyperfine interaction is a strategy to improve thequbit coherence in several systems such as GaAs [4–7] andSi-based systems [8–10]. The hyperfine interaction has alsobeen investigated in 13C-enriched carbon nanotube quantumdots [11] and it was theoretically proposed that graphenequantum dots could benefit from isotope purification [1,12–14], modulating the ratio of 12C (nuclear spin 0) and 13C(nuclear spin 1/2) (see Appendix A). Comparing the results of12C and 13C enrichment would enable the direct investigationof the effect of hyperfine interaction. Isotopically enrichedgraphene has been realized by the chemical vapor deposition(CVD) method [15,16]. High-quality single layer graphenehas been fabricated by the same method [17], while it remainsdifficult to produce bilayer graphene by CVD growth.In this work, we investigate high-quality exfoliatedgraphene devices out of 12C-enriched (99.7%) and 13C-enriched (91.4%) graphites. We synthesize enriched graphiteby the high-pressure-high-temperature method [18,19]. Wethen establish a recipe to exfoliate the layered crystals to*siwakiri@phys.ethz.chPublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.obtain monolayer and bilayer graphene. The isotope effect ischaracterized by mass spectroscopy and Raman spectroscopy,showing a clear difference between 12C and 13C graphene.After confirming the enrichment, we fabricate a Hall bardevice from each kind of graphite and perform quantumtransport measurements. For both graphene samples, highmobility (μ � 1 × 105 cm2/V s) and long mean free path(lmfp � 1 µm) are demonstrated. These values demonstratethat the electronic quality of graphene remains as high asnatural graphene after isotopic enrichment. We also observethe Shubnikov–de Haas oscillations, quantum Hall effect, andBrown-Zak oscillations, which confirm the quality of the sam-ple. While all of these observations constitute well-knownproperties of graphene their appearance in samples derived byisotopically purified carbon crystals is by no means obvious.This result forms the basis for building isotopically en-riched graphene qubits and investigating the role of hyperfineinteractions.II. CHARACTERIZATION RESULTSA. Enriched graphite and exfoliationFigure 1(a) shows the optical picture of the crystal of12C-enriched and 13C-enriched graphite. Hereafter, we callthem 12C graphite/graphene and 13C graphite/graphene forconvenience. For 12C and 13C isotope-enriched graphite, theconditions for diamond single-crystal growth and synthesiswere carried out in the pressure and temperature range wheregraphite is stable [20]. Namely, at 4 GPa and 1600 ◦C, Co-Ti alloy was used as a solvent and carbon isotope-enrichedcarbon source as a starting material; 12C-enriched carbon was2643-1564/2023/5(4)/043212(7) 043212-1 Published by the American Physical Societyhttps://orcid.org/0000-0003-2668-8328https://orcid.org/0009-0001-5330-5137https://orcid.org/0009-0001-6170-7873https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0001-9267-232Xhttps://orcid.org/0000-0002-9480-9681https://orcid.org/0000-0001-7867-4310https://orcid.org/0000-0001-7007-6949http://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevResearch.5.043212&domain=pdf&date_stamp=2023-12-07https://doi.org/10.1103/PhysRevResearch.5.043212https://creativecommons.org/licenses/by/4.0/SHUICHI IWAKIRI et al. PHYSICAL REVIEW RESEARCH 5, 043212 (2023)(a) (d)(c)(b)MonolayerBilayer1 μm2.5 μm4 μmVxxVxyG2D2D’D+D’’G2D2D’D+D’’I12C 13CGraphiteHall barshBNFIG. 1. (a) Optical picture of 12C and 13C graphite crystals. The minimum grid size in the background is 1 mm. (b) Histogram of 12Cgraphene flake size. Inset shows a picture of the example bilayer flake. The scale bar is 50 µm. (c) Raman spectrum of 12C and 13C graphene.Top: monolayer graphene. Bottom: bilayer graphene. (d) Top panel: optical picture of the fabricated Hall bar. The scale bar is 10 µm. Bottompanel: schematic of the fabricated Hall bar.thermal CVD diamond from Tomei Diamond, using methanegas with 99.998% 12C as a starting material; 13C enriched wascommercial amorphous graphite powder with purity of 99%(Cambridge Isotope Laboratories, Inc). After HP-HT synthe-sis, recovered graphite single crystals with metal solvent weretreated with hot aqua regia for purification.Note that the crystal size (∼5 mm) is relatively smallcompared to the natural graphite crystals, which can be upto the order of cm. The relative isotope ratio found in thecrystals is determined using inductively coupled plasma time-of-flight mass spectrometry (ICP-TOFMS). The ICP-TOFMS(icp-TOF2R, TOFWERK AG, Thun, Switzerland) is operatedin low-mass mode and was coupled to an ArF excimer laser(193 nm, GeoLas C, Lambda Physik, Göttingen), equippedwith a low dispersion ablation cell for minimally invasivesampling of the small crystals. The ratios of isotopes are de-termined for natural graphite, 12C graphite, and 13C graphite.The results of the natural graphite are used to calibrate theratio for the other samples, assuming the natural abundanceof 12C : 13C = 98.9 : 1.1. The result of the mass spectroscopyyields 12C : 13C = 99.7 : 0.3 for the 12C sample and 8.6 : 91.4for the 13C sample, confirming the effect of enrichment. Therelative concentrations of the isotopes determined by massspectroscopy have a relatively large error because of the smallamount of the sample available.In spite of the relatively small size of the graphite crystals,exfoliation is possible for both 12C and 13C. We performexfoliation by using the standard scotch tape method, wherewe deposit graphite onto the scotch tape and fold and peelapart the tape a certain number of times before the flakes aretransferred onto a Si/SiO2 substrate (with an oxide thicknessof 285 nm). We compare exfoliation for folding and peelingapart the tape 4–6 times with 10–15 times. We analyze thechips under a microscope and record the size of the flakes.The statistics of the flake size (mono-, bi-, and trilayer 12Cgraphene) is shown in Fig. 1(b), together with an image ofan example of a large bilayer flake. It turns out that after4–6 times of exfoliation, it is possible to obtain 50 µm scalegraphene flakes of mono-, bi-, and trilayers. The same result isobtained for the 13C graphene. These results demonstrate thatthe enriched 12C and 13C exfoliation is possible and that theflakes are available for fabricating devices.B. Raman spectroscopyThe exfoliated graphene is further characterized by Ramanspectroscopy (Horiba LabRAM HR Evolution UV-VIS-NIR).The laser energy and wavelength are 1 mW and 532 nm, re-spectively. We choose a flake larger than 10 µm and performa Raman spectrum measurement by changing the laser po-sition. The data shown in Fig. 1(c) is from the part of thegraphene that is a few µm inside from the edge of the flake.The measurements are done on mono- and bilayer flakes. Asshown in Fig. 1(c), both 12C and 13C graphene show promi-nent G (∼1520–1580 cm−1), D+D′′ (∼2360–2490 cm−1), 2D(∼2540–2710 cm−1), and 2D′ (∼3120–3250 cm−1) peaks.The numbers in the parentheses are typical ranges of the ob-served peak wave numbers. We see a clear peak wave numbershift between 12C and 13C. These differences are one of themost prominent signatures of the isotope effect because thenuclear mass difference results in a phonon frequency andRaman shift difference. We do not observe a shift between12C and natural graphene within the experimental resolution.After subtracting a linear background from the data, we fit allthe peaks with Lorentzian functions. The fit parameters are inTable I in Appendix B.The obtained parameters are consistent with the onesreported in exfoliated natural graphene and isotopically en-riched CVD graphene [21–27]. The measured wave numberof the G peak, ωG, for 12C or natural graphene reported inRefs. [21–25] are between −2 cm−1 and +10 cm−1 of ourmeasured values for 12C graphene (for mono- and bilayer).The ωG for 13C graphene reported in [23,25] is in the rangeof −5 cm−1 to +8 cm−1 of the values we measure for mono-or bilayer. Comparing the wave number of the 2D peak, ω2D,to literature values, it turns out that the values reported are043212-2HIGH-MOBILITY TRANSPORT IN ISOTOPICALLY … PHYSICAL REVIEW RESEARCH 5, 043212 (2023)TABLE I. Fit parameters for the Raman peaks. We fit the data with the sum of one to three Lorentzian functions (in the case we usemultiple Lorentzian to fit, all fit parameters are shown in order and separated by comma).Layers 1 1 2 2Material 12C 13C 12C 13CωG (cm−1) 1584 1530 1581 1522�G (cm−1) 8.143 5.316 11.14 9.983ω2D (cm−1) 2678 2580 2646, 2681, 2704 2546, 2580, 2602�2D (cm−1) 21.431 22.296 14.98, 21.76, 31.32 13.49, 21.47, 29.96ω2D′ (cm−1) 3247 3128 3248 3125�2D′ (cm−1) 8.455 11.274 8.709 10.61ωD+D′′ (cm−1) 2479, 2457 2366, 2388 2458, 2489 2365, 2394�D+D′′ (cm−1) 41.27, 15.29 14.41, 36.46 26.04, 48.69 21.82, 41.55generally slightly higher (up to 1.5%) than the values we mea-sure. For the monolayer 12C graphene ω2D, we find that ourmeasurement aligns very well (within 1 cm−1) with the naturalgraphene measurement in [21]. However, the measurementsin Refs. [23–25] find values 15–35 cm−1 higher than whatwe measure for 12C monolayer graphene as well as for 13Cmonolayer graphene. Looking at the bilayer measurements forω2D peaks [21], we find two peaks that are 2 cm−1 and 3 cm−1apart. For ω2D′ Ref. [28] reports 3250 cm−1 for 12C grapheneand 3130 cm−1 for 13C graphene. These values are consistentwith what we measure.We also estimate the isotopic concentration of 13Cgraphene from the Raman shift using the relation ω =ω12C√mm+x�m [29]. Here, ω12C is the Raman shift of pure 12Cgraphene, m is the atomic mass of 12C, x is the concentrationof 13C, and �m is the atomic mass difference of 12C and 13C.For 13C graphene, we obtain a 13C enrichment x = 92.9%using the 2D and 2D′ peaks and x = 86.2% using the G peak.Since the G peak is sensitive to the distortion and carrierdensity [30], it can be affected by unintentional doping dueto the charged impurity in the silicon substrate, making thepeak shift. The estimation from 2D and 2D′ peaks is closerto the value obtained by the mass spectroscopy with a slightoverestimation (±1.5%). At around 93% of 13C, the deviationof Raman shifts by one cm−1 modulates the concentrationestimation by ∼1.7%. Therefore, considering the resolution ofthe measurement, the estimation from the 2D and 2D′ peaksis consistent with the one from the mass spectroscopy.C. Device fabricationTo characterize the transport quality of the isotopicallyenriched graphene, we fabricate Hall bars of 12C and13C bilayer graphene as shown in Fig. 1(d). A stack ofhexagonal boron-nitride (top hBN)/bilayer graphene/hBN(bottom hBN)/graphite (back gate) is made by thepolydimethylsiloxane/polycarbonates dry transfer method.Thicknesses of top and bottom hBN are 12 nm and 18 nm forthe 12C sample and 20 nm and 30 nm for the 13C one. Electriccontacts to the edge of the bilayer graphene are fabricated byetching the top hBN and depositing Cr/Au. After etching, aHall bar is shaped by reactive ion etching (CHF3 and O2).We measure the Hall bars in a dilution refrigerator with abase temperature of 55 mK. The bottom panel of Fig. 1(d)shows the schematic of the device. The two contacts at eachsample end are used as source and drain electrodes, wherewe inject current from the source to the grounded drain. Thelongitudinal and transverse voltages (Vx and Vy) are measuredbetween the two contacts along and across the sides. Thespacing between source and drain and between the voltagecontacts is 4 µm and 1 µm, respectively. We use a lock-inamplifier (Stanford Research Systems SR830) connected tothe source in series with a 100 M� resistance and apply anac voltage of 1 V, generating an ac current of 10 nA. Wesynchronize the lock-in amplifier driving the current I withthe other two lock-in amplifiers. These lock-in amplifiers arethen used to measure the resistances (Rxx = dVxdI and Rxy = dVydIat zero bias current). We apply a dc voltage (Yokogawa 7651Programmable dc Source) to the back gate (not shown in theschematic).III. TRANSPORT MEASUREMENTFigures 2(a) and 2(d) show the magnetic field B and thecarrier density n dependence of the longitudinal resistance Rxxof 12C and 13C devices. The carrier density on the horizontalaxis is estimated by measuring the classical Hall effect upto 100 mT and using the relation Rxy = Bn|e| . We also obtainconsistent values from a parallel plate capacitor model (n =CbgVbg, where Cbg is the capacitance between the graphene andthe back gate and Vbg is the back gate voltage) and Shubnikov–de Haas measurements [Rxx ∝ cos( 2πnh4eB )].For both samples, clear fanlike structures departing fromthe charge neutrality point n = 0 and expanding with mag-netic field are seen, which is attributed to the Shubnikov–deHaas (SdH) oscillations. The oscillations appear already ataround 1 T, testifying to our samples’ high mobility. Whitedotted tilted lines show the fitting to the filling factor of 1, 2,and 3 at around n = 0 (for 12C and 13C) and filling factor for2, 6, and 10 at around n = ±2.3 × 1012 cm−2 (for 12C only).Additionally, in the 12C sample, we see multiple Landaufans appearing at densities of around 4.09, 3.29, 2.30, 1.78,−2.06, and −2.31 × 1012 cm−2. This is attributed to the addi-tional Dirac points due to the unintended alignment betweenthe graphene and one of the hBNs, forming a moiré superlat-tice [31]. This results in an energy spectrum for the chargecarriers known as the Hofstadter butterfly and causes satelliteDirac peaks. Furthermore, at the intersections of the Landau043212-3SHUICHI IWAKIRI et al. PHYSICAL REVIEW RESEARCH 5, 043212 (2023)0 2 4 6 8B (T)0816R xx(k)01530R xy(k)21 3 412C13Cb10 6 2 2 6 1032112345123459875364(a) (b) (c)(f)(e)(d)FIG. 2. Quantum transport measurement of 12C (a),(b),(c) and 13C (d),(e),(f) bilayer graphene. (a),(d) Rxx as a function of magnetic fieldB and carrier density n. White dotted tilted lines fit the Shubnikov–de Haas oscillations with filling factors shown in the figure. White dottedhorizontal lines show the position at which the Brown-Zak oscillations appear. (b),(e) Example traces of the quantum Hall effect at n =1.13 × 1011 (12C) and n = 1.9 × 1011 (13C). (c),(f) Carrier density n dependence of the mobility μ and the mean free path lmfp estimated fromthe low magnetic field data.fans, it predicts horizontal lines of peaks in Rxx called Brown-Zak oscillations [32–34]. The horizontal lines in Fig. 2(a)indicate the position of φ/φ0 = 1/p with p an integer andφ0 = h/e the flux quanta. As we discuss in Appendix C, themoiré unit cell size estimated from the Brown-Zak oscillationsagrees with the one formed by graphene/hBN alignment. Thisobservation is another piece of evidence for having a high-quality sample.At a high magnetic field, we observe the quantum Halleffect, as shown in Figs. 2(b) and 2(e). For both samples, theinteger quantum Hall effect is observed up to filling factorν = 1 with quantized plateaus of Rxy and dips of Rxx. Thesignificant drop of Rxy in 12C beyond filling factor 1 (B � 7 T)is due to the Brown-Zak oscillations. We observe a similardrop whenever B crosses the horizontal lines indicated inFig. 2(a).We also estimate the mobility μ and mean free path lmfpby applying the classical Drude model to ρxx = WL Rxx (W andL are the width and the length of the sample) and ρxy = Rxyat a low magnetic field (�100 mT). From the slope of thelinear fit of Rxy up to 100 mT together with Rxx at 0 T, wedetermine μ and lmfp using the equations μ = 1ρxx (B=0)dρxydBand lmfp = h̄√πn|e| μ. As seen in Figs. 2(c) and 2(f), the mo-bility mostly ranges from 1 × 104 to 3 × 105 cm2/V s. Themobility becomes zero around charge neutrality and formsa peak with increasing n. This behavior can be attributed tothe difference in dominant scattering mechanisms (long-rangeCoulomb scattering at low density and short-range impurityscattering at high density) [35].The mean free path lmfp reaches up to 1–5 µm for both12C and 13C. This value is comparable to the one reported innatural graphene. Note that the spacing between the contactsis of the same order of magnitude as the estimated meanfree path, meaning that the transport in the sample is in theballistic regime. In this regime, the Drude model has limitedvalidity and the mobility and mean free path are lower boundestimates.Up to now, our results of transport measurement do notshow significant differences between 12C and 13C. We fur-ther perform a quantum Hall effect breakdown measurement,applying a dc current up to 10 µA so that the quantum Halleffect (plateau in ρxy and zero in ρxx) is no longer observed.In GaAs 2DEG systems, a large hysteresis in the currentsweep direction before and after the breakdown is observedtypically for odd filling factors due to dynamic nuclear po-larization (spin transfer from electrons to nuclei) [36,37]. Wedo not observe any clear hysteresis within our measurementprecision (data is not shown here). To observe the effect ofhyperfine interaction, more sophisticated measurements suchas resistivity-detected NMR [38–40] or actually building aquantum dot and performing a T1 and T2 coherence timemeasurement would be useful.IV. CONCLUSIONIn conclusion, we have presented high-mobility transportof exfoliated 12C and 13C graphene synthesized by the high-pressure-high-temperature technique. We confirmed distinctdifferences between 12C and 13C graphene by the mass andRaman spectroscopy. We also fabricated Hall bar devices andperformed quantum transport measurements, revealing highmobility and a long mean free path of these materials compa-rable to the natural graphene. Shubnikov–de Haas, quantumHall, and Brown-Zak effects up to the filling factor of onewere observed thanks to the high mobility. These results pavethe way for developing isotopically enriched graphene qubits043212-4HIGH-MOBILITY TRANSPORT IN ISOTOPICALLY … PHYSICAL REVIEW RESEARCH 5, 043212 (2023)and investigating the role of hyperfine interactions in graphenequantum dots.ACKNOWLEDGMENTSWe are grateful for fruitful discussions and technical sup-port from L. Ginzburg, C. Tong, M. Niese, P. Maerki, T.Baehler, and the ETH FIRST cleanroom facility staff. Weacknowledge financial support by the European GrapheneFlagship Core3 Project, H2020 European Research Council(ERC) Synergy Grant under Grant Agreement No. 951541,the European Union’s Horizon 2020 research and innovationprogramme under Grant Agreement No. 862660/QUANTUME LEAPS, the European Innovation Council under GrantAgreement No. 101046231/FantastiCOF, and NCCR QSIT(Swiss National Science Foundation, Grant No. 51NF40-185902). K.W. and T.T. acknowledge support from the JSPSKAKENHI (Grants No. 21H05233 and No. 23H02052) andWorld Premier International Research Center Initiative (WPI),MEXT, Japan.APPENDIX A: COHERENCE TIME ESTIMATIONFollowing the steps of [1], we studied the effect of isotopiccomposition on the lifetime τ of coherent spin states (T2)in graphene quantum dot qubits. While the different atomicmasses of 12C and 13C may affect the spin-orbit coupling, itis believed that the hyperfine interaction limits the coherencetime in graphene [1]. The limit on the coherence time set bythe hyperfine interaction (hyperfine coherence time) τhf de-pends on the composition of the spinless 12C and the spin-1/213C. It can be estimated from the hyperfine coupling strengthAhf = 0.38 µeV, the 13C concentration c13C , and the numberof atoms in a dot N using τhf = hAhf√N/c13C .Compared to natural graphene (c13C = 1.1%; N = 104 :τhf ≈ 10 µs) the purification level of our 12C sample (c13C =0.3%) would already increase the hyperfine coherence timeby a factor of two. Further decreasing the 13C concentration(99.99% purified 12C), would increase the coherence time byanother factor of five, to around τhf ≈ 100 µs. This shows thestrong sensitivity of the hyperfine coherence time on isotopiccomposition at low 12C concentrations. For a dot size of N =104 atoms, this purification level of 99.99% would alreadymean that on average just one 13C atom would be present perdot. By selecting the dots without any 13C and thus no nuclearspins, one can completely lift the limitation of the coherencetime by the hyperfine interaction.APPENDIX B: RAMAN PEAKS FITTING PARAMETERSWe fitted the Raman spectrum with Lorentzian functionA�2(ω−ω0 )2+�2 , where A is the peak amplitude, k is the wavenumber, k0 is the peak wave number, and � is the linewidth(half width at half maximum). The results are shown below.We used a single Lorentzian function for G and 2D′ peaks,the sum of two Lorentzian functions for the D + D′′ peak, andthe sum of three Lorentzian functions for the 2D peak.APPENDIX C: ESTIMATION OF MOIRÉ UNIT CELL SIZEFROM THE BROWN-ZAK OSCILLATIONWe have estimated the moiré cell size with two approaches.First, since the satellite Dirac peaks appear once all theavailable states in the moiré cell are filled, we can deter-mine the area A of the moiré cell from the average of theexcess carrier density of the electron- and hole-side peaksnep = 1.78 × 1012 cm−2 and nhp = −2.31 × 1012 cm−2. Con-sidering the fourfold degeneracy in graphene, this conditioncorresponds to A = 412 (|nep|+|nhp|) . The second approach uses theperiodicity of the Brown-Zak oscillations, which appear if arational number 1/p of flux quanta φ0 (p is an integer) passesthrough one moiré cell. 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