Infrared Spectroscopy of Landau Levels of Graphene

Jiang, Zhewei; Henriksen, Erik; Tung, L. C.; Wang, Y.-J.; Schwartz, Maurice L.; Han, Minyong; Kim, Philip; Störmer, H. L.

doi:10.1103/physrevlett.98.197403

Cited by 558 publications

(640 citation statements)

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“…The observed systematic enhancement of E F /hk F at low k F is indicative of manybody interactions 14,21,22 . Signatures of band renormalization were also observed in a previous magneto-optical study of graphene 4 . Importantly, even the smallest E F /hk F values in Fig.…”

supporting

confidence: 49%

“…Unlike conventional solids where electrons are described with the Schrödinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian 1 . Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations [2][3][4][5] . Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices.…”

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confidence: 56%

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Dirac charge dynamics in graphene by infrared spectroscopy

et al. 2008

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A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schrödinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian 1 . Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations 2-5 . Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, freestanding graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene.We investigated the reflectance R(ω) and transmission T (ω) of graphene samples on a SiO 2 /Si substrate (inset of Fig. 1a) as a function of gate voltage V g at 45 K (see the Methods section). We start with data taken at the charge-neutrality point V CN : the gate voltage corresponding to the minimum d.c. conductivity and zero total charge density (inset of Fig. 1c). Figure 1a shows R(ω) of a graphene gated structure (graphene/SiO 2 /Si) at V CN = 3 V normalized by reflectance of the substrate R sub (ω). R sub (ω) is dominated by a minimum around 5,500 cm −1 due to interference effects in SiO 2 . A remarkable observation is that a monolayer of undoped graphene markedly modifies the interference minimum of the substrate leading to a suppression of R sub (ω) by as much as 15%. This observation is significant because it enables us to evaluate the conductivity of graphene near the interference structure, as will be discussed below.Both reflectance and transmission spectra of graphene structures can be modified by a gate voltage. Figure 1b,c shows these modifications at various gate voltages normalized by data atThese data correspond to the Fermi energy E F on the electron side and similar behaviour was observed with E F on the hole side (not shown). At low voltages (<17 V), we found a dip in R(V )/R(V CN ) spectra. With increasing bias, this feature evolves into a peak-dip structure and systematically shifts to higher frequency. The T (V )/T (V CN ) spectra reveal a peak at all voltages, which systematically hardens with increasing bias. A voltage-induced increase in transmission (T (V )/T (V CN ) > 1) signals a decrease of the absorption with bias. Most interestingly, we observed that the frequencies of the main features in R(V )/R(V CN ) and T (V )/T (V CN ) all evolve approximately as √ V . To explore the quasiparticle dynamics under applied voltages, it is imperative to first discuss the two-dimensional (2D) optical conductivity of charge-neutral graphene, σ 1 (ω, V CN ) + iσ 2 (ω, V CN ), extracted from a multilayer analy...

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confidence: 56%

Dirac charge dynamics in graphene by infrared spectroscopy

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“…52 Many-body corrections to cyclotron resonance due to the interaction with the Dirac sea were calculated by Shizuya. 55 Infrared absorption data by Jiang et al 56 and Henriksen et al 57 indicate a contribution from many-body effects to the interLandau level transitions in these states.…”

Section: Introductionmentioning

confidence: 97%

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

Sári

Tőke

2013

Phys. Rev. B

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If bilayer graphene is placed in a strong perpendicular magnetic field, several quantum Hall plateaus are observed at low enough temperatures. Of these, the σxy = 4ne 2 /h sequence (n = 0) is explained by standard Landau quantization, while the other integer plateaus arise due to interactions. The low-energy excitations in both cases are magnetoexcitons, whose dispersion relation depends on single-and many-body effects in a complicated manner. Analyzing the magnetoexciton modes in bilayer graphene, we find that the mixing of different Landau level transitions not only renormalizes them, but essentially changes their spectra and orbital character at finite wave length. These predictions can be probed in inelastic light scattering experiments.

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“…This puzzling situation suggests that one cannot reach the true ground state by filling the n = 2 level alone. It is clear now that one has to diagonalize the exchange interaction (19), with mixing among the n = (0, 1, 2) orbital modes taken into account.…”

Section: Vacuum Fluctuationsmentioning

confidence: 99%

“…Quantum fluctuations of the Dirac sea are sizable, even leading to ultraviolet divergences; and one encounters such field-theoretic (or many-body) phenomena as velocity renormalization, 17 screening of charge, 18 and nontrivial Coulombic corrections to cyclotron resonance. [19][20][21][22][23] Quantum fluctuations also affect the PZM levels substantially. They work to lift 24 the orbital degeneracy of the PZM levels in bilayer graphene; each orbital mode responds to quantum fluctuations differently and gets shifted, just like the Lamb shift 25 in the hydrogen atom, where the field-theoretic effect of quantum electrodynamics was revealed for the first time historically.…”

Section: Introductionmentioning

confidence: 99%

Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels inABC-stacked trilayer graphene

Shizuya

2013

Phys. Rev. B

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In a magnetic field graphene trilayers support a characteristic multiplet of 12 zero(-energy)-mode Landau levels with a threefold degeneracy in Landau orbitals. It was earlier noted for bilayer graphene that Coulombic vacuum fluctuations, specific to graphene, lift the orbital degeneracy of such zero-energy modes and that these "Lamb-shfted" orbital modes, with filling, get mixed via the Coulomb interaction. It is pointed out that analogous orbital Lamb shift and mixing of zero-mode levels can also take place, with an enriched symmetry content, in ABC-stacked trilayer graphene; and its consequences are discussed in the light of experimental results.

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Infrared Spectroscopy of Landau Levels of Graphene

Cited by 558 publications

References 25 publications

Dirac charge dynamics in graphene by infrared spectroscopy

Dirac charge dynamics in graphene by infrared spectroscopy

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

Orbital Lamb shift and mixing of the pseudo-zero-mode Landau levels inABC-stacked trilayer graphene

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