Observations of New Dirac Points in One-Dimensionally-Rippled

Jul 31, 2015 - Department of Physics, Korea University, Seoul 136-713, Republic of ... Department of Physics, Sungkyunkwan University (SKKU), Suwon ...
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Observations of New Dirac Points in One-Dimensionally-Rippled Graphene on Hexagonal BN Using Scanning Tunneling Spectroscopy Won-Jun Jang,†,‡ Min Wook Lee,† Howon Kim,†,§ Sangwoo Park,∥ Seong Jun Jung,∥ Sungjoo Lee,∥,⊥,# Young Jae Song,*,∥,∇ and Se-Jong Kahng*,† †

Department of Physics, Korea University, Seoul 136-713, Republic of Korea Center for Axion and Precision Physics Research, Institute for Basic Science, Daejeon 305-701, Republic of Korea § The Institute for Solid State Physics, The University of Tokyo, 5-1-5, Kashiwa-no-ha, Kashiwa 277-8581, Japan ∥ SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University (SKKU), Suwon 440-746, Republic of Korea ⊥ Center for Human Interface Nanotechnology (HINT), Samsung-SKKU Graphene Center, Sungkyunkwan University (SKKU), Suwon 440-746, Republic of Korea # College of Information and Communication Engineering, Sungkyunkwan University (SKKU), Suwon 440-746, Republic of Korea ∇ Department of Physics, Sungkyunkwan University (SKKU), Suwon 440-746, Korea ‡

ABSTRACT: Theories predicted that one-dimensional superlattice potentials in graphene would induce new Dirac points, instead of gap opening, due to lattice-induced chirality of charge carriers, but experimental evidence is rarely available in the literature. Here, we report observations of new Dirac points in one-dimensionally rippled graphene on hexagonal boron nitride (h-BN) using scanning tunneling microscopy and spectroscopy. The rippled graphene, formed due to thermal procedures, showed two new Dirac points above and below the Fermi level. The energy difference between a new Dirac point and the Fermi level was proportional to 1/L, where L was the period of a ripple, in agreement with theoretical predictions. Our study shows that the one-dimensional periodic potential is an accessible component for controlling the electronic properties of graphene.

1. INTRODUCTION Superlattice potentials in semiconductors are useful tools for engineering their electronic-transport and optoelectronic properties.1 They give rise to additional mini-band structures in which the effective mass of charge carriers is significantly modified. At the mini-Brillouine zone boundary, energy gaps open to have unusual characteristics, such as Wannier−Stark ladder and semiconductor lasing. In graphene, different kinds of modifications of band structures are induced by superlattice potentials. Because of two atom sublattices, graphene is described by two component spinor-like wave functions and the Dirac equation, and it does not have a gap opening with superlattice potentials.2 Instead, both one- and two-dimensional superlattice potentials in graphene would induce new Dirac points in addition to the original Dirac point, and the energy differences between the new and original Dirac points are inversely proportional to the superlattice period L.3,4 In experiments, the 1/L dependence of new Dirac points has been studied in two systems, graphene on hexagonal boron nitride (h-BN) and bilayer graphene.5,6 In both systems, twodimensional superlattice potentials were produced in the form of moiré patterns, due to the angular twisting between © XXXX American Chemical Society

graphene and hexagonal BN (h-BN) or between two graphene layers. However, the experimental evidence of the 1/L dependence in the graphene with a one-dimensional superlattice potential is not available in the literature.7,8 Here, we report the observations of new Dirac points in a one-dimensionally rippled graphene on h-BN using scanning tunneling microscopy and spectroscopy (STM and STS). The rippled structures were formed by thermal procedures after high temperature growth. Two new Dirac points were observed, and their energy differences from the original Dirac point were inversely proportional to the superlattice periods, in agreement with theoretical calculations. The asymmetry between electron and hole in our one-dimensionally rippled graphene was also observed. Received: June 18, 2015 Revised: July 29, 2015

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DOI: 10.1021/acs.jpcc.5b05835 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

2. EXPERIMENTAL SECTION We performed our experiments using a home-built STM system that has a base pressure below 7 × 10−11 Torr and the sample temperature of 80 K. A Pt/Rh wire was used for a STM tip, and the STS measurement was performed by a Lock-in technique (1500 Hz, 5 mV modulation, and open feedback). The method to prepare the graphene/h-BN/Cu sample was reported elsewhere.9,10 Briefly, h-BN films (2−3 nm thickness) were grown on Cu foils (0.1 mm thickness) by chemical vapor deposition (CVD) of borazine at 1300 K, followed by the growth of graphene on the h-BN films by CVD of methane at 1300 K. Au/Ti electrodes were fabricated on top of graphene to have reliable electrical contacts for sample bias as shown in Figure 1a.

undergoes contraction. The expanded graphene and h-BN tend to form 1D rippled structures on contracted metal. It was reported that the former cases of 1D moiré patterns were formed on the surface of the cubic atomic arrangement of the (100) facet. Because our graphene was grown on h-BN not directly on metal (100), we tend to consider the latter as the origin of our 1D rippled structures. More STM images of rippled structures and corresponding cross sections are showin in Figure 2a−d. From the cross

Figure 1. (a) Scheme of our STM experiment. Vs is the sample bias. (b) STM image obtained from a graphene/h-BN/Cu foil. Image size: 50 nm × 50 nm, sample bias: Vs = −0.3 V, tunneling current: I = 0.1 nA. (c) Atomic-resolution STM image obtained from the region denoted with a dotted square in (b). Image size: 5 nm × 5 nm, sample bias: Vs = 0.4 V, tunneling current: I = 0.1 nA. (d) Height profiles obtained along the blue and the green arrows of (c).

Figure 2. (a−c) STM images obtained from a graphene/h-BN/Cu foil, showing the rippled structures of different periods L = 2.6, 2.0, and 1.1 nm. Image size: 7 nm × 7 nm, sample bias: Vs = 0.7 V, tunneling current: I = 0.1 nA. (d) Height profiles obtained along the blue, red, and green arrows shown in (a), (b), and (c). (e) Relation between amplitudes and periods of rippled graphene structures. The gray line is the linear fit. (f) 1D models depicting graphene/h-BN/Cu foil before thermal expansion (left) and after thermal expansion without (middle) and with (right) rippled deformation.

3. RESULTS AND DISCUSSIONS Figure 1b and c show typical large and atomic scale STM images obtained from the graphene/h-BN/Cu sample, respectively. In the large scale image, steplike structures were observed due to the subsurface structures of h-BN and Cu. In the atomic scale image, honeycomb lattices of graphene were clearly resolved along with additional one-dimensional (1D) ripple structures. The periodic 1D rippled structures are better visualized in the cross sections of Figure 1d, which are taken along the green and the blue arrows of Figure 1c. The formation of 1D rippled structures has been previously reported in the graphene grown on metal surfaces such as Cu(100), Fe(110), and Ir(100).11−13 Their formations are explained by the mismatch of either lattice constants or thermal expansion coefficients between graphene and substrate lattices. In the former, 1D rippled structures showed moiré patterns of which periods are determined by the angular misorientations between graphene and substrate. In the latter, 1D rippled structures are considered to have geometric corrugations caused by additional strain built in cooling processes after growth. Graphene grows at 1300 K, and the thermal expansion coefficients of graphene and h-BN are negative whereas that of metal is positive.14,15 When they are cooled down after growth, both graphene and h-BN undergo expansion, but metal

sections, the periods and the amplitudes of the rippled structures are extracted, and their relations are plotted in Figure 2e, which shows that the amplitude is proportional to the period.16,17 This can be explained by a simple 1D model depicted in Figure 2f. For a given length D and additional length ΔD, a 1D object can form sinusoidally rippled structures of various period L’s, with two ends kept fixed due to electrostatic interactions such as friction between graphene and substrate. Because the addtional length ΔD is caused by thermal expansion coefficient mismatch, we have (ΔD/D) = α·ΔT, where α is the difference of the thermal expansion coefficient of two materials and ΔT is the difference between growth and measurement temperature. From the sinusodal function, we can also impose length conservation, i.e. D + ΔD = ∫ D0 dx(1 + ((d/dx)A sin(π/L)x)2)1/2, where A is the amplitude of the ripple. By solving these two equations assuming A ≪ L, we obtained the proportional relation, A = (1/π)(αΔT)1/2L. Using the thermal expansion coefficients of graphene (or hBN) and Cu, −6.8 × 10−6 K−1 (−2.7 × 10−6 K−1) and 1.7 × 10−5 K−1, respectively, we obtained ΔT = 1150 K, which is close to the difference between growth and measurement temperature, 1300 and 80 K, respectively. Related to our 1D B

DOI: 10.1021/acs.jpcc.5b05835 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C model, it is still relevant to have a question if the two ends of graphene are pinned. Although we do not have direct evidence for pinning, we believe there could be some mechanisms to fix graphene at the step structures of BN. At the step structures, graphene needs to be slightly bent and has chances to have stronger interaction with the underlying structures than at flat terrace regions. Thereby, graphene can have local friction during thermal expansion. We performed STS measurements at several points in a rippled graphene with L = 3.6 nm. Figure 3b shows differential

Figure 3. (a) STM image of a rippled structure with a period L = 3.6 nm. Image size: 14 nm × 14 nm, sample bias: Vs = 0.4 V, tunneling current: I = 0.1 nA. (b) Differential conductance (dI/dV) spectra obtained at 6 different positions denoted with colored dots. The yellow and green dotted lines indicate the energy positions of new Dirac points.

Figure 4. (a−d) STM images obtained from a graphene/h-BN/Cu foil, showing the rippled structures of different periods L = 3.6, 2.7, 1.7, and 1.1 nm. Image size: 14 nm × 14 nm, sample bias: Vs = 0.4 V, tunneling current: I = 0.1 nA. All the scale bars are 5 nm. (e−h) Fast Fourier transform images of (a−d). All the scale bars are 1/nm. (i) Differential conductance (dI/dV) spectra obtained from (a−d). Each spectrum represents an average of dI/dV spectra obtained from 100 positions at each STM image. The black, blue, red, and green dI/dV curves were obtained from (a), (b), (c), and (d), respectively. (f) Relation between the energy position of the new Dirac points END and 1/L. L is the period of the ripple. The solid lines are linear fits.

conductance curves (dI/dV) measured by STS at 6 positions marked with colored dots in Figure 3a. In STS, dI/dV approximates the local electron density of state (LDOS) of the sample. In graphene, the LDOS, ρ(E) = (2Ac/π)(|E|/v2F), where Ac is the unit cell area given by 3√3a2/2, where a = 0.246 nm. The shapes of all the dI/dV curves in Figure 3a look the same, having reasonable V-like shapes near the Fermi level. The coincidence of the original Dirac point and the Fermi level has been previously observed in the graphene on h-BN.10,18 Because the graphene has a linear dispersion between energy (ε) and momentum (k), ε = ℏvFk, where ℏ is Planck constant and vF is the Fermi velocity, the mini-Brillouin zone boundary for the superlattice potential of period L = 3.6 nm falls on the energy ε = 0.57 eV. But, there is no bandgap opening at the mini-Brillouin zone boundary in Figure 3a. Instead, two weak dips are visible at −0.47 and +0.75 eV. These dip features without bandgap opening are similar to the results, observed in 2D superlattice graphene on h-BN.5 The chirality of the Dirac Fermions prevents bandgap opening at the mini-Brillouin zone boundary, as long as the potential does not break the sublattice symmetry of graphene.5 We assign the two minima in the dips as new Dirac points caused by the superlattice potential of rippled graphene structures. To confirm the correlation between the weak dips and the periodic potential of rippled structures, we performed more STS measurements with the rippled graphene of different periods. Figure 4a−d show 4 STM images of rippled graphene with periods 3.6, 2.7, 1.7, and 1.1 nm, and Figure 4i shows corresponding dI/dV curves. The periods are determined from fast Fourier transform images (Figure 4e−h). All the dI/dV curves clearly show two dips above and below the Fermi level denoted with green and yellow arrows, respectively. The energies of minima or new Dirac points END are measured from the dI/dV curves and plotted as a function of 1/L in Figure 4j. The plot clearly shows that END and 1/L have a linear

relationship. Based on the effective Hamiltonian and tightbinding calculations, it was previously predicted that graphene with 1D superlattice potential should have new Dirac points at the energy END = EF ± ℏvF(π/L), where vF is the Fermi velocity of the original Dirac point.3,4 From linear fitting of our data, we measured the slope to extract the Fermi velocities vF’s. They are 0.94 ± 0.09 × 106 and 0.64 ± 0.12 × 106 m/s, for electron and hole, respectively, which showed good agreement with those of 2D superlattice graphene on h-BN.19 In fact, both END and vF for electron and hole showed asymmetry, probably because there were contributions from both next nearest-neighbor hopping and next nearest-neighbor interlayer hopping.5,20,21 The next-nearest-neighbor hopping is enhanced, when the atomic lattice undergoes deformation caused by thermal expansion.22,23 The data points that spread and barely fit the lines in Figure 4j may be caused by at least two limitations of our theoretical models. First, the ripples studied in experiments showed finite sizes less than 100 nm, although the periodic boundary condition was considered in theoretical models. Second, the ripples in experiments were not perfectly uniform, in contrast to theoretical models. We were unable to observe spatial variation in dI/dV at a small length scale of a few nanometers, as shown in Figure 3, but there could be spatial variations at some larger length scale.

4. CONCLUSIONS In summary, one-dimensionally rippled graphene was formed in our graphene/h-BN/Cu system. We observed no gap opening C

DOI: 10.1021/acs.jpcc.5b05835 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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(13) Locatelli, A.; Wang, C.; Africh, C.; Stojic, N.; Mentes, T. O.; Comelli, G.; Binggeli, N. Temperature-Driven Reversible Rippling and Bonding of a Graphene Superlattice. ACS Nano 2013, 7 (8), 6955− 6963. (14) Chialvo, A. A.; Vlcek, L.; Cummings, P. T. Surface Strain Effects on the Water−Graphene Interfacial and Confinement Behavior. J. Phys. Chem. C 2014, 118, 19701−19711. (15) Muniz, A. R.; Fonseca, A. F. Carbon-Based Nanostructures Derived from Bilayer Graphene with Zero Thermal Expansion Behavior J. Phys. Chem. C20151191745810.1021/acs.jpcc.5b05602. (16) Wang, C.; Lan, L.; TanPhys, H. The Physics of Wrinkling in Graphene Membranes under Local Tension. Phys. Chem. Chem. Phys. 2013, 15, 2764. (17) Bao, W.; Miao, F.; Chen, Z.; Zhang, H.; Jang, W.; Dames, C.; Lau, C. N. Controlled Ripple Texturing of Suspended Graphene and Ultrathin Graphite Membranes. Nat. Nanotechnol. 2009, 4, 562. (18) Xue, J.; Javier, S. Y.; Bulmash, D.; Jacquod, P.; Deshpande, A.; Watanabe, K.; Taniguchi, T.; Pablo, J. H.; LeRoy, B. J. Scanning Tunnelling Microscopy and Spectroscopy of Ultra-flat Graphene on Hexagonal Boron Nitride. Nat. Mater. 2011, 10, 282. (19) Xue, J.; Sanchez-Yamagishi, J.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; LeRoy, B. J. Long-Wavelength Local Density of States Oscillations Near Graphene Step Edges. Phys. Rev. Lett. 2012, 108, 016801. (20) Meng, L.; He, W.-Y.; Zheng, H.; Liu, M.; Yan, H.; Yan, W.; Chu, Z.-D.; Bai, K.; Dou, R.-F.; Zhang, Y.; et al. Strain-induced onedimensional Landau level quantization in corrugated graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 205405. (21) Jang, W.-J.; Kim, H.; Shin, Y.-R.; Wang, M.; Jang, S. K.; Kim, M.; Lee, S.; Kim, S.-W.; Song, Y. J.; Kahng, S.-J. Observation of SpatiallyVarying Fermi Velocity in Strained-Graphene directly grown on Hexagonal Boron Nitride. Carbon 2014, 74, 139−145. (22) Pereira, V. M.; Castro Neto, A. H.; Peres, N. M. R. Tightbinding Approach to Uniaxial Strain in Graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 045401. (23) Kretinin, A.; Yu, G. L.; Jalil, R.; Cao, Y.; Withers, F.; Mishchenko, A.; Katsnelson, M. I.; Novoselov, K. S.; Geim, A. K.; Guinea, F. Quantum Capacitance Measurements of Electron-Hole Asymmetry and Next-Nearest-Neighbor Hopping in Graphene. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 165427.

but two new Dirac points above and below the Fermi level in STM and STS. The energy difference between a new Dirac point and the Fermi level was proportional to the period of a ripple. Our study experimentally shows that the one-dimensional periodic potential can be used to control the electronic properties of graphene.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail address: [email protected] (Y. J. Song). *E-mail address: [email protected] (S.-J. Kahng). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the Ministry of Education Science and Technology of the Korean government through National Research Foundation (Grant nos. 2012-01013222; 2014-11051782; 2011-0030046; 2012R1A1A1041416; IBS-R017-D1-2015-a00).

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REFERENCES

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DOI: 10.1021/acs.jpcc.5b05835 J. Phys. Chem. C XXXX, XXX, XXX−XXX