Electronic structure of transferred graphene/h-BN van der Waals heterostructures with nonzero stacking angles by nano-ARPES

TL;DR

This study uses nano-ARPES to investigate how different stacking angles in transferred graphene/h-BN heterostructures affect their electronic structures, revealing Moiré superlattice effects and angle-dependent interactions.

Contribution

It provides the first nanoscale ARPES measurements of transferred graphene/h-BN with nonzero stacking angles, linking superlattice features to stacking geometry.

Findings

Six replicas of graphene Dirac cones observed at superlattice Brillouin zone centers

Superlattice size and rotation angle match AFM measurements

Interaction strength decreases with increasing stacking angle

Abstract

In van der Waals heterostructures, the periodic potential from the Moir\'e superlattice can be used as a control knob to modulate the electronic structure of the constituent materials. Here we present a nanoscale angle-resolved photoemission spectroscopy (Nano-ARPES) study of transferred graphene/h-BN heterostructures with two different stacking angles of 2.4{\deg} and 4.3{\deg} respectively. Our measurements reveal six replicas of graphene Dirac cones at the superlattice Brillouin zone (SBZ) centers. The size of the SBZ and its relative rotation angle to the graphene BZ are in good agreement with Moir\'e superlattice period extracted from atomic force microscopy (AFM) measurements. Comparison to epitaxial graphene/h-BN with 0{\deg} stacking angles suggests that the interaction between graphene and h-BN decreases with increasing stacking angle.

Equations

$$\lambda =\frac{(1+\delta )a}{\sqrt{2(1+\delta )(1-cos\varphi )+{\delta }^2}}(1)$$

$$tan\theta =\frac{sin\varphi }{(1+\delta )-cos\varphi }(2)$$

Full text

keywords: graphene/h-BN, van der Waals heterostructure, Moir$\acute{e}$ potential, nanoscale angle-resolved photoemission spectroscopy (nano-ARPES)

I Introduction

Van der Waals heterostructures are designed heterostructures made by stacking different two dimensional materials which are held together through weak van der Waals interaction GeimVDW . Such heterostructures not only broaden the range of materials that can be assembled and investigated, but also provide an important playground for discovering new properties different from the constituent materials and for realizing new quantum phenomena. In the past few years, graphene/h-BN has emerged as a model van der Waals heterostructure. It is an ideal system for making high quality graphene devices, with reduced ripples and higher mobility HoneNano2010 ; LeRoyNatureMater11 . Moreover, the moir$\acute{e}$ superlattice induced by the lattice mismatch and crystal orientation can significantly modify the electronic properties of graphene, leading to various novel quantum phenomena including the self-similar Hofstadter butterfly states GeimNature13 ; KimNature13 ; GBNgap ; GeimNaturePhys2014 and topological currents GeimSci14 . There are also major changes in the electronic properties, e.g. emergence of second-generation Dirac cones (SDCs) GeimNature13 ; KimNature13 ; GBNgap ; GeimNaturePhys2014 , renormalization of the Fermi velocity LouieNaturePhys08 ; FalkoMiniband ; JvdBPRB12 ; Guinea , gap opening at the Dirac pointDFTgap ; GBNgap ; DGGPRL13 ; GeimSci14 ; NovoselovNphys2014 and gate-dependent pseudospin mixing FWangGate . Although graphene/h-BN heterostructure has been studied by various transport and STM measurements GeimNature13 ; KimNature13 ; GBNgap ; GeimNaturePhys2014 ; LeRoyNaturePhys12 , direct angle-resolved photoemission spectroscopy (ARPES) measurements of the modulated electronic band structure have been missing.

Hexagonal Boron nitride (h-BN) shares similar honeycomb lattice structure with graphene, yet with a $\delta$ $\approx$1.8$\%$ larger lattice constant. The breaking of the inversion symmetry by distinct boron and nitrogen sublattices leads to a large band gap (5.97 eV) in the $\pi$ band, which is in sharp contrast to the gapless Dirac cones in graphene. By placing graphene atop h-BN, the different lattice constant and relative stacking angle $\phi$ between graphene and h-BN lead to moir$\acute{e}$ pattern. The moir$\acute{e}$ pattern periodicity is

[TABLE]

where a is the lattice constant of graphene. The relative rotation angle $\theta$ of the moir$\acute{e}$ pattern with respect to the graphene lattice is given by

[TABLE]

Figure 1(a,b) shows the dependence of the moir$\acute{e}$ periodicity and rotation angle on $\phi$. The moir$\acute{e}$ periodicity quickly decreases with increasing $\phi$ and the rotation angle of the moir$\acute{e}$ pattern also strongly depends on $\phi$. For example, when $\phi$ changes from 0*∘* to 4.3*∘, the moir$\acute{e}$ periodicity $\theta$ changes from 14 nm to 3.2 nm, and the relative angle changes from 0∘ to 74.5∘*. The superlattice Brillouin zones (SBZs) are also rotated with respect to the Brillouin zone of graphene due to the rotated moir$\acute{e}$ pattern which is shown in Fig.1(d) schematically. One expected result of the induced moir$\acute{e}$ superlattice potential is the formation of first-generation Dirac cones (FDCs) which occur at the same energy level as the original Dirac cone (ODC) yet translated by the reciprocal lattice vector of the moir$\acute{e}$ pattern G = $\frac{2}{\sqrt{3}}$ 2$\pi$/$\lambda$. Furthermore, due to the induced moir$\acute{e}$ potential, second-generation Dirac cones (SDCs) can emerge at energies different from the ODC GeimNaturePhys2014 ; JvdBPRB12 ; MoonPRB14 ; FalkoMiniband , and they are critical for the realization of self-similar Hofstadter bufferfly states under applied magentic field.

Graphene/h-BN heterostructures can be prepared by directly growing epitaxial graphene on h-BN substrate using plama-enhanced chemical vapor deposition (PE-CVD) ZhangGY or by transferring exfolicated graphene onto the h-BN substrates HoneNano2010 ; LeRoyNatureMater11 . While the stacking angle in PE-CVD grown samples is fixed to 0*∘* ZhangGY , the stacking angle in transferred graphene/h-BN samples can be carefully aligned and is widely tunable LeRoyNaturePhys12 ; NovoselovNphys2014 ; Coryscience . With increasing stacking angle, the interaction between graphene and h-BN is expected to become weaker and commensurate-incommensurate transition has been reported NovoselovNphys2014 . The PE-CVD heterostructures with 0*∘* stacking angle and sample size up to a few hundred micrometers ($\mu$m) have been recently studied by regular ARPES, and SDCs have been reported GBNCVD . However, until now direct experimental results on the modulated band structure in graphene/h-BN with nonzero stacking angles have been missing. The challenge is related to the small sample size of a few micrometers ($\mu$m), which is much smaller than the typical ARPES beam size of 50-100 $\mu$m. By using nano-ARPES with beam size of $\sim$100 nm, we are able to obtain the electronic structure of transferred graphene/h-BN heterostructures with nonzero stacking angles for the first time. Here we report the electronic structure of such heterostructures with stacking angles of $\sim$ 2.4*∘* and $\sim$ 4.3*∘* respectively, and reveal the FDCs induced by the moir$\acute{e}$ superlattice potential.

II Methods

Transferred graphene/h-BN heterostructures were prepared using similar methods as reported HoneNano2010 ; LeRoyNatureMater11 . The entire process is shown in Figure 2. First, single layer graphene was exfoliated on polymethyl methacrylate(PMMA, MicroChem, A6, 950K)/polyvinyl alcohol(PVA, Sigma-Aldrich) stack (Fig. 2(a)). Single crystals of h-BN were grown using the method described before hBNgrow and h-BN flakes were exfoliated on a SiO2/Si wafer (Fig. 22(b)). Then the exfoliated graphene was transferred atop exfoliated h-BN flakes (Fig.2(c)). Pt electrode was deposited on one side of SiO2/Si substrate (Fig.2(d,e)) to avoid charging effect during ARPES measurements. Atomic Force Microscopy (AFM) measurements were performed to confirm the existence of moir$\acute{e}$ pattern. The extracted moir$\acute{e}$ periodicity can also be used to determine the stacking angle between graphene and h-BN. Figure 2(f) shows the extracted phase profile for sample #1. The moir$\acute{e}$ periodicity is estimated to be $5.3\pm 0.2$ nm and the stacking angle is 2.4${}^{\circ}\pm 0.2^{\circ}$ calculated from equation (1). The optical images for sample #2 during the sample preparation are shown in Fig.3(a-e). AFM measurements were also performed to verify the existence of moir$\acute{e}$ pattern afterwards. Figure 3(f) shows the extracted phase profile from AFM image. The moir$\acute{e}$ pattern periodicity and the stacking angle are extracted to be $3.2\pm 0.3$ nm and 4.3${}^{\circ}\pm 0.3^{\circ}$ respectively.

Nano-ARPES measurements were performed at the ANTARES beamline of the SOLEIL synchrotron. ANTARES beamline is equipped with two Fresnel zone plates (FZPs) to focus the beam size down to $\approx$ 120 nm. There are two sets of motor systems to change the sample position, mechanical motors SZ and ST which have large motion range with $\approx$ 5 $\mu$m resolution and piezoelectric motors PIX and PIY which have smaller motion range and better spatial resolution $\approx$ 5 nm. Samples were mounted on a nanopositioning stage which was placed at the coincident focal point of the electron analyzer and the FZPs. ANTARES can operate in two modes, the imaging mode where the photoelectron spectra (angle integrated or angle resolved) are collected by changing the sample position to create two-dimensional images of electronic states of interest, and the spectroscopy mode where the detailed band dispersions are measured at fixed sample position. The data were recorded with Scienta R4000 analyzer with photon energy of 100 eV using horizontal linear polarized light. The samples were annealed at $\approx$ 250 *∘*C until clean dispersions were obtained. The samples are kept at 80 K with vacuum better than $2\times 10^{-10}$ Torr during the ARPES measurements.

III Results and discussion

We first used the imaging mode to locate the small target graphene/h-BN flake on SiO2/Si substrate for sample #1 (red circle in Fig.2(d)). The angle-integrated intensity curves show two typical spectra as shown in Fig.4(b). The black curve with stronger intensity near EF is attributed to the Pt electron, and the blue curve with suppressed intensity near EF and a peak at $\approx$ -13 eV is attributed to the bare SiO2/Si substrate SiO2 . By integrating the spectral weight of the blue shadow area which is characteristic of SiO2/Si (Fig.4(b)), the spatial map (Fig.4(c)) shows similar shape with SiO2/Si in the optical image (Fig.4(a)). This confirms our assignment of the two types of spectra. The zoom-in intensity map around the graphene/h-BN region (Fig.4(d)) allows to further distinguish different parts (Pt, graphene, h-BN and SiO2/Si) clearly. Moreover, by integrating the spectral weight near the Fermi energy (grey shadow area in Fig.4(b)) to have a better contrast between graphene/h-BN and bare h-BN, the graphene flake can be clearly identified (Fig.4(e)).

After locating target graphene/h-BN flake, we used the spectroscopy mode to probe the modulated band structure of transferred graphene/h-BN. Figure 5 shows the intensity maps at energies from EF to -700 meV. At EF, six cloned FDCs are observed around the ODC, consistent with our previous ARPES studies on PE-CVD graphene/h-BN heterostructures GBNCVD . The corresponding SBZ (black dashed hexagon) is rotated with respect to the Brillouin zone of graphene (blue solid line) by $\approx$ 6∘, which is consistent with the calculated rotation angle for the moir$\acute{e}$ pattern $\theta$ $\approx$ 66∘ (effectively 6∘ in the map due to the six fold symmetry) from the stacking angle $\phi$ $\approx$ 2.4∘ by equation (2). The size of the pockets becomes larger with decreasing energy, consistent with the conical dispersions expected. Figure 6 further shows detailed cuts around the ODC and FDCs to reveal the modulated band structures. The dispersions from the FDCs are obvious on both sides of ODC in Fig. 6(b,c). Panels (d-f) show the dispersions along the cuts crossing the ODC and FDCs simultaneously. From the momentum distribution curves(MDCs) at the Fermi energy (Fig. 6(g)), we extract the momentum separation between the ODC and FDCs to be $0.134\pm 0.02$ ${\AA}^{-1}$ which is consistent with the moir$\acute{e}$ pattern periodicity inferred from AFM measurements. Using a Fermi velocity of 7.37 eV$\cdot{\AA}$ (1.13$\times 10^{6}$ m/s), the intersection point for 2.4 ∘ heterostructure is estimated to be at -493 meV. From ARPES measurements, the crossing point is measured to be at -490 meV (pointed by black arrows in Fig. 6(d-f)), in agreement with the estimation, however in contrast with our previous studies on 0*∘* aligned graphene/h-BN GBNCVD , no obvious signatures of SDCs are observed from the constant energy maps and band dispersions. This is possibly due to the weaker interaction between graphene and h-BN when increasing the stacking angle between graphene and h-BN.

We applied the same method to locate the target graphene/h-BN flake for sample #2. Then spectroscopy mode was used to probe the detailed band structure. Figure 7 shows the intensity maps at from EF to - 700 meV. The signal from FDCs is weak at EF and becomes more clear at -100 meV. This could be attributed to even weaker interaction between graphene and h-BN with an increasing stacking angle. The corresponding SBZ (black dashed hexagon) is rotated by $\approx$15∘ with respect to the Brillouin zone of graphene (blue solid lines in Fig.7(b)), which is consistent with the calculated moir$\acute{e}$ pattern rotation angle of 74.5∘ from the stacking angle of 4.3∘. Figure.8 shows the detailed modulated band dispersions around the ODC and FDCs. The dispersions from the FDCs are weak but still detectable on both sides of the ODC (Fig.8(b-d)). Panel (e-g) shows the dispersions along the cuts crossing the ODC and FDCs simultaneously. The momentum separation between ODC and FDCs is estimated to be 0.23$\pm$0.04 ${\AA}^{-1}$ from the MDCs at -100 meV (Fig.8(h)), consistent with the moir$\acute{e}$ pattern period extracted from AFM measurements. The ODC and FDCs intersect at around -840 meV, slightly deeper than the -770 meV calculated by moir$\acute{e}$ pattern period. The difference is possibly attributed to the error bar from AFM measurement. Similar to the graphene/h-BN sample #1 with stacking angle of the 2.4*∘*, no obvious signals of SDCs are observed from the constant energy maps or band dispersions.

IV Conclusions

We report direct experimental results on the modulated band structure in transferred graphene/h-BN heterostructures with stacking angles of 2.4∘ and 4.3∘ respectively. We observed replicas of Dirac cones translated by the reciprocal lattice vectors of the Moir$\acute{e}$ superlattice from the graphene K point. With variable stacking angle between graphene and h-BN, the size and relative angle of SBZ can be tuned. Unlike previous studies on PE-CVD grown graphene/h-BN samples with 0∘ stacking angle, no obvious signatures of SDCs are observed from the modulated band structure. This is possibly due to weaker interaction between graphene and h-BN at large stacking angle. It has been reported that at small stacking angle, there are regions of commensurate graphene stretched to fit the lattice of h-BN substrate, and there is a crossover from commensurate to incommensurate states between $\phi$ = 0 and $\phi$ $\approx$ 1.5 ∘ NovoselovNphys2014 . Such commensurate to incommensurate transition may also explain the large variations of gaps measured on graphene samples with different stacking angles. Another possibility is that PE-CVD graphene/h-BN samples may have stronger interaction between graphene and h-BN with 0∘ stacking angle compared to transferred graphene/h-BN samples with tunable stacking angles. More experiments to reveal the atomic structure at the interface with different stacking angles and their correlation with the electronic structures are important to further understand the difference.