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Graphene can find great potential applications in the future electronic devices. In bilayer graphene, the relative rotation angle between graphene layers can modulate the interlayer interaction and hence induces rich physical phenomena. We systematically study the temperature dependent magnetoresistance (MR) properties in the epitaxial bilayer graphene (BLG) grown on the SiC substrate. High quality BLG is synthesized by molecular beam epitaxy in ultra-high vacuum. We observe the negative MR under a small magnetic field applied perpendicularly at temperature < 80 K, which is attributed to a weak localization effect. The weak localization effect in our epitaxial BLG is stronger than previously reported ones in epitaxial monolayer and multilayer graphene system, which is possibly because of the enhanced interlayer electron transition and thus the enhanced valley scattering in the BLG. As the magnetic field increases, the MR exhibits a classical Lorentz MR behavior. Moreover, we observe a linear magnetoresistance behavior in a large field, which shows no saturation for the magnetic field of up to 9 T. In order to further investigate the negative and linear magnetoresistance, we conduct angle-dependent magnetoresistance measurements, which indicates the two-dimensional magnetotransport phenomenon. We also find that the negative MR phenomenon occurs under a parallel magnetic field, which may correspond to the moiré pattern induced local lattice fluctuation as demonstrated by scanning tunneling microscopy measurement on an atomic scale. Our work paves the way for investigating the intrinsic properties of epitaxial BLG under various conditions.
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Keywords:
- epitaxial bilayer graphene /
- magnetotransport /
- negative magnetoresistance /
- scanning tunneling microscopy
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图 1 (a) 在6H-SiC(0001)表面外延双层石墨烯的结构示意图; (b)生长过程在BLG/SiC表面监测获得的RHEED图案; (c)在BLG/SiC表面获得的STM形貌图, 尺寸为200 nm × 200 nm, U = 1.50 V, It = 50 pA; (d)在BLG/SiC表面获得的原子分辨STM形貌图, 尺寸为10 nm × 10 nm, U = 0.90 V, It = 100 pA. 图中可以看到莫尔周期调制
Figure 1. (a) Structure diagram in bilayer graphene grown on 6H-SiC(0001). (b) RHEED patterns obtained by monitoring the BLG/SiC surface during growth. (c) STM morphology on BLG/SiC surface. Size: 200 nm × 200 nm, U = 1.50 V, It = 50 pA. (d) Atomic-resolved STM morphology obtained on BLG/SiC surface. Size: 10 nm × 10 nm, U = 0.90 V, It = 100 pA. Moiré period modulation can be seen in the figure
图 2 在无外加磁场下测量的BLG/SiC(0001)表面电阻-温度曲线, 其中插图显示为磁电阻测量的结构示意图
Figure 2. Temperature-resistance curve measured on BLG/SiC (0001) surface without an applied magnetic field. The illustration shows a schematic diagram of the structure of magnetoresistance measurement.
图 3 (a)垂直磁场条件下在–9—9 T范围内不同温度条件的MR vs. B图; (b)垂直磁场条件下小磁场区域MR vs. B图; (c)垂直磁场条件下中等磁场区域MR vs. B图; (d)垂直磁场条件下较大磁场区域MR vs. B图; (e)不同温度条件下的霍尔测试
Figure 3. (a) MR vs. B diagram at different temperatures in the range of –9–9 T under vertical magnetic field; (b) MR vs. B diagram of small magnetic field under vertical magnetic field; (c) MR vs. B diagram of medium magnetic field under vertical magnetic field; (d) MR vs. B diagram of large magnetic field under vertical magnetic field; (e) Hall test at different temperatures.
图 4 (a) 2 K条件下, 旋转样品以改变磁场与样品夹角时的MR vs. B图, 其中θ = 0°代表磁场与样品垂直情况; (b) 图(a)中小磁场范围局部放大图; (c) 由图4(a)拟合的结果, 其中
$ \theta $ 是磁场与竖直方向的夹角, 横坐标代表外加磁场的竖直分量; (d) 水平磁场条件下(θ = 90°)不同温度的MR vs. B图Figure 4. (a) MR vs. B diagram by rotating sample and hence varing the magnetic field B direction θ, where θ = 0° represents the perpendicular condition of magnetic field and sample; (b) local enlargement of panel (a) at small and medium magnetic field range; (c) diagram according to the fitting results in Fig. 4(a), where θ is the angle between the magnetic field and the vertical direction, and the abscissa represents the vertical component of the external magnetic field; (d) MR vs. B plots at different temperatures under horizontal magnetic field (θ = 90°).
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[1] Du X, Skachko I, Barker A, Andrei E Y 2008 Nature Nanotechnol. 3 491
Google Scholar
[2] Miller D L, Kubista K D, Rutter G M, Ruan M, De Heer W A, First P N, Stroscio J A 2009 Science 324 924
Google Scholar
[3] Sharpe A L, Fox E J, Barnard A W, Finney J, Watanabe K, Taniguchi T, Kastner M A, Goldhaber-Gordon D 2019 Science 365 605
Google Scholar
[4] Lu X, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G, Bachtold A, MacDonald A H, Efetov D K 2019 Nature 574 653
Google Scholar
[5] Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R C, Jarillo-Herrero P 2018 Nature 556 80
Google Scholar
[6] Sevak Singh R, Wang X, Chen W, Ariando, Wee A T S 2012 Appl. Phys. Lett. 101 183105
Google Scholar
[7] Freitas P P, Ferreira R, Cardoso S, Cardoso F 2007 J. Phys.: Condensed Matter 19 165221
Google Scholar
[8] Chuang C, Yang Y, Elmquist R E, Liang C T 2016 Mater. Lett. 174 118
Google Scholar
[9] Willke P, Amani J A, Sinterhauf A, Thakur S, Kotzott T, Druga T, Weikert S, Maiti K, Hofsass H, Wenderoth M 2015 Nano Lett. 15 5110
Google Scholar
[10] McCann E, Kechedzhi K, Fal'ko V I, Suzuura H, Ando T, Altshuler B L 2006 Phys. Rev. Lett. 97 146805
Google Scholar
[11] Parish M M, Littlewood P B 2005 Phys. Rev. B 72 094417
Google Scholar
[12] Demokritov S O, Serga A A, Demidov V E, Hillebrands B, Kostylev M P, Kalinikos B A 2003 Nature 426 159
Google Scholar
[13] Abrikosov A A 1998 Phys. Rev. B 58 2788
Google Scholar
[14] Zhou Y B, Wu H C, Yu D P, Liao Z M 2013 Appl. Phys. Lett. 102 093116
Google Scholar
[15] Wang W J, Gao K H, Li Z Q, Lin T, Li J, Yu C, Feng Z H 2014 Appl. Phys. Lett. 105 182102
Google Scholar
[16] Butz B, Dolle C, Niekiel F, Weber K, Waldmann D, Weber H B, Meyer B, Spiecker E 2014 Nature 505 533
Google Scholar
[17] Kisslinger F, Ott C, Heide C, Kampert E, Butz B, Spiecker E, Shallcross S, Weber H B 2015 Nat. Phys. 11 650
Google Scholar
[18] Rein M, Richter N, Parvez K, Feng X L, Sachdev H, Kläui M, Müllen K 2015 ACS Nano 9 1360
Google Scholar
[19] Creeth G L, Strudwick A J, Sadowski J T, Marrows C H 2011 Phys. Rev. B 83 195440
Google Scholar
[20] Gopinadhan K, Jun Shin Y, Yang H 2012 Appl. Phys. Lett. 101 223111
Google Scholar
[21] Brzhezinskaya M, Kononenko O, Matveev V, Zotov A, Khodos, II, Levashov V, Volkov V, Bozhko S I, Chekmazov S V, Roshchupkin D 2021 ACS Nano 15 12358
Google Scholar
[22] Baker A M R, Alexander-Webber J A, Altebaeumer T, Janssen T J B M, Tzalenchuk A, Lara-Avila S, Kubatkin S, Yakimova R, Lin C T, Li L J, Nicholas R J 2012 Phys. Rev. B 86 235441
Google Scholar
[23] Meng L, Chu Z D, Zhang Y, Yang J Y, Dou R F, Nie J C, He L 2012 Phys. Rev. B 85 235453
Google Scholar
[24] Liao Z M, Zhou Y B, Wu H C, Han B H, Yu D P 2011 Europhys. Lett. 94 57004
Google Scholar
[25] Brar V W, Zhang Y, Yayon Y, Ohta T, McChesney J L, Bostwick A, Rotenberg E, Horn K, Crommie M F 2007 Appl. Phys. Lett. 91 122102
Google Scholar
[26] Zhang X, Xue Q Z, Zhu D D 2004 Phys. Lett. A 320 471
Google Scholar
[27] Wang Y, Liu E, Liu H, Pan Y, Zhang L, Zeng J, Fu Y, Wang M, Xu K, Huang Z, Wang Z, Lu H Z, Xing D, Wang B, Wan X, Miao F 2016 Nat. Commun. 7 13142
Google Scholar
[28] Cai C Y, Chen J H 2018 Chin. Phys. B 27 067304
Google Scholar
[29] Wakabayashi J, Sano K 2011 J. Phys. Soc. Jpn. 81 013702
Google Scholar
[30] Lundeberg M B, Folk J A 2010 Phys. Rev. Lett. 105 146804
Google Scholar
[31] Hong S J, Rodríguez-Manzo J A, Kim K H, Park M, Baek S J, Kholin D I, Lee M, Choi E S, Jeong D H, Bonnell D A, Mele E J, Drndić M, Johnson A T C, Park Y W 2016 Synth. Met. 216 65
Google Scholar
[32] Finney J, Sharpe A L, Fox E J, Hsueh C L, Parker D E, Yankowitz M, Chen S W, Watanabe K, Taniguchi T, Dean C R, Vishwanath A, Kastner M, Goldhaber-Gordon D 2021 PNAS 119 e2118482119
Google Scholar
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