Graphene Spectroscopy

Colloquium: Graphene spectroscopy D. N. Basov and M. M. Fogler Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA A. Lanzara and Feng Wang Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Yuanbo Zhang ( 远波) State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China (Dated: October 2, 2018) Spectroscopic studies of electronic phenomena in graphene are reviewed. A variety of methods and techniques are surveyed, from quasiparticle spectroscopies (tunneling, photoemission) to methods probing density and current response (infrared optics, Raman) to scanning probe nanoscopy and ul- trafast pump-probe experiments. Vast complimentary information derived from these investigations is shown to highlight unusual properties of Dirac quasiparticles and many-body interaction effects in the physics of graphene. PACS numbers: 81.05.Uw, 73.20.-r, 03.65.Pm, 82.45.Mp CONTENTS (2D) allotrope of carbon is characterized by a number of su- perlative virtues (Geim, 2009), e.g., a record-high electronic I. Introduction1 mobility at ambient conditions (Morozov et al., 2008), excep- A. Scope of this review1 B. Graphene morphology2 tional mechanical strength (Lee et al., 2008a), and thermal C. Electronic structure of graphene neglecting interactions3 conductivity (Balandin et al., 2008; Ghosh et al., 2008) Re- D. Many-body effects and observables4 markable properties of graphene have ignited tremendous in- terest that resulted in approximately 50,000 publications at the II. Quasiparticle properties6 1 A. Dirac spectrum and chirality6 time of writing. A number of authoritative reviews have been B. Renormalization of Dirac spectrum8 written to survey this body of literature but no single review C. Landau quantization 10 can any longer cover the entire topic. The purpose of this Col- III. Current/density response and collective modes 11 loquium is to overview specifically the spectroscopic experi- A. Optical conductivity 11 ments that have helped to shape the modern understanding of B. Plasmons 12 the physical properties of graphene. While selected topics in C. Phonons 15 graphene spectroscopy have been discussed,2 here we aim to D. Electron-phonon and electron-plasmon interaction 16 present a panoramic view of physical phenomena in graphene IV. Induced effects 18 emerging from both spectroscopy and imaging (Fig.1C). A. Inhomogeneities and disorder 18 Spectroscopic observables can be formally categorized as B. Substrate-induced doping 19 C. Moire´ patterns and energy gaps 19 either quasiparticle or current/density response functions. The D. Elastic strain 20 former are fermionic, the latter are bosonic. The former is E. Photo-induced effects 22 traditionally measured by photoemission and tunneling spectroscopy, while the latter can be investigated by, e.g., optical V. Bilayer and multilayer graphene 23 spectroscopy. Yet it may be possible to infer both quasiparti- VI. Outlook 25 cle and collective properties from the same type of measurements. For example, fine anomalies of the quasiparticle spec- arXiv:1407.6721v1 [cond-mat.mes-hall] 24 Jul 2014 Acknowledgments 25 tra seen in photoemission can give information about interac- References 26 tions between quasiparticles and collective modes (Sec. III.D) I. INTRODUCTION 1See Castro Neto et al. (2009); Das Sarma et al. (2011); Katsnelson(2012); Kotov et al. (2012); McCann and Koshino(2013); and Peres(2010). A. Scope of this review 2See Orlita and Potemski(2010) for optics, Dresselhaus et al. (2012) and Ni et al. (2008b) for Raman scattering, Li and Andrei(2012) for scanning Graphene is a single atomic layer of sp2-hybridized carbon tunneling spectroscopy, and Connolly and Smith(2010) for other scanned atoms arranged in a honeycomb lattice. This two-dimensional probes. 2 FIG. 1 (Color online) Panel A: a schematic of the π-band dispersion of SLG showing Dirac cones at K and K0 points. After (Orlita and Potemski, 2010). Panel B: the definitions of the intra (γ0) and interlayer (γ1–γ4) hopping parameters of Bernal-stacked graphene materials. [For their experimental values, see, e.g., (Zhang et al., 2008a).] Panel C: the energy scales of electronic phenomena in graphene along with the corresponding frequency ranges and spectroscopic methods. The asterisk (*) denotes compatibility of a method with high magnetic fields. Conversely, optical conductivity, which is a collective re- field probes are employed (Sec. III.B) Mosaic structure and sponse, enables one to infer, with some approximation, the defects may affect momentum and energy resolution of the parameters of a quasiparticle band-structure (Secs. III.A, II.B, measurement. Graphene differs widely in terms of these pa- II.C, andV). rameters depending on preparation method. Mechanical ex- Finding such connections is facilitated by spectacular tun- foliation of graphite typically produces single, bi-, and multi- ability of graphene. For example, with photoemission or tun- layer graphene (SLG, BLG, and MLG, respectively) of a few neling techniques one can monitor the chemical potential µ µm in size, although occasionally samples of dimensions of of graphene as a function of the electron concentration N hundreds of µm can be obtained. Exfoliated samples can be and thereby extract the thermodynamic density of states. The transferred onto insulating substrates, after which they can be same physical quantity can be measured by a very different gated and subject to transport measurements. The sign and the technique, the scanning single-electron transistor microscopy. magnitude of carrier concentration N in gated samples can be In our analysis of such complementary data we focus on precisely controlled over a wide range. The lower bound on what we believe are the most pressing topics in the physics jNj ∼ 1010 cm−2 is set by inhomogeneities (Sec. IV.A). The of graphene, e.g., many-body effects. Additionally, our re- upper bound jNj ∼ 1013 cm−2 is limited by the dielectric view covers information obtained by scanned probes and out- breakdown strength of the substrate, although still higher jNj of-equilibrium methods that greatly expand available means are achievable by electrolytic gating .3 The carrier concentra- to study graphene in space and time domains. Finally, we tion can also be controlled by doping (Chen et al., 2008). briefly address phenomena that arise when physical properties Morphologically, exfoliated samples are single crystals. of graphene are altered via its environment and nanostructur- They hold the record for transport mobility µtr although ing. it varies much with the type of the substrate. Currently, high-quality hexagonal boron nitride (hBN) substrates enable 5 2 one to achieve µtr ∼ 10 cm =Vs, which is about an or- B. Graphene morphology der of magnitude higher than what is typical for graphene on SiO2 and corresponds to µm-scale mean-free path (Dean Graphene can be isolated or fabricated in a number of dif- et al., 2010; Mayorov et al., 2011b). The highest mobility ferent forms, which is an important consideration in spectroscopy. Effectiveness of a given spectroscopic tool depends on the accessibility of the sample surface to the incident ra- diation. The size of the accessible area must normally be 3See Efetov and Kim(2010); Ju et al. (2011); Mak et al. (2009); Newaz et al. larger than the wavelength of the incident beam unless near- (2012); and Xia et al. (2009b). 3 ∼ 106 cm2=Vs is demonstrated by exfoliated graphene that structural defects of CVD graphene are wrinkles and folds in- is suspended off a substrate and subject to current annealing duced by transfer process and also by thermal expansion of (Bolotin et al., 2008; Du et al., 2008; Elias et al., 2011). Me- graphene upon cooling. Grain boundaries are other common chanical instabilities limit the size of suspended devices to 1– defects that have been directly imaged by micro-Raman (Li 2 µm and restrict the maximum jNj to a few times 1011 cm−2. et al., 2010), transmission electron microscopy (Huang et al., Large-area graphene can be made by another method: epi- 2011), scanning tunneling microscopy (Koepke et al., 2013; taxial growth on SiC by thermal desorption of Si (van Bom- Tapaszto´ et al., 2012), and near-field microscopy (Fei et al., mel et al., 1975). Epitaxial graphene may contain a single 2013). The corresponding domain sizes range between 1– or many dozens of layers. The initial layer (layer number 20 µm. On the other hand, graphene single crystals with di- L = 0) has strong covalent bonds to the SiC substrate and mension ∼ 0:5 mm have been grown on Cu by CVD (Li et al., is electronically different from the ideal SLG (de Heer et al., 2011). Transport mobilities of CVD-grown graphene and epi- 2007). The morphology and electron properties of the sub- taxial graphene on SiC are roughly on par. sequent layers, L > 0, depend on which SiC crystal face it At the opposite extreme of spatial scales are nanocrystals is grown: the Si-terminated (0001) face or the C-terminated and nanoribbons. Graphene crystals of nm-size can be syn- (0001)¯ face.4 According to de Heer et al. (2011), the Si-face thesized by reduction of graphene oxide5 or by ultrasonic grown graphene is orientationally ordered and has the Bernal cleavage of graphite in an organic solvent (Hernandez et al., stacking (as in graphite). The structure of the C-face epitaxial 2008; Nair et al., 2012). Laminates of such crystals can be of graphene is consistent with a stacking where every other layer macroscopic size amenable to X-ray and Raman spectroscopy. is rotated by approximately ±7◦ with respect to a certain av- Nanocrystals can also be grown epitaxially on patterned SiC erage orientation. The rotations inhibit interlayer tunneling so surface (de Heer et al., 2011). Graphene nanoribbons (GNRs) that the band structure of each layer is similar to SLG (see also can be produced by lithography, nanoparticle etching, and un- Sec.

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