Renormalization of the Graphene Dispersion Velocity Determined from Scanning Tunneling Spectroscopy

Chae, Jungseok; Jung, Suyong; Young, Andrea; Dean, Cory; Wang, Lei; Gao, Yongxiang; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Shepard, Kenneth L.; Kim, Philip; Zhitenev, Nikolai B.; Stroscio, Joseph A.

doi:10.1103/physrevlett.109.116802

Cited by 101 publications

(163 citation statements)

References 26 publications

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“…In fact, this is what happens in graphene. Correlation effects indeed reshape the linear band dispersion of graphene [29][30][31][32]. Possible interplay among inversion symmetry breaking (spin chirality), disorders, and effective interactions may lead to a novel interacting diffusive fixed point, which allows the universal scaling in the Hall resistivity.…”

Section: Self-consistent Born Approximation As a Fixed-point Solutionmentioning

confidence: 99%

Interplay between disorder and inversion symmetry: Extreme enhancement of the mobility near the Weyl point in BiTeI

et al. 2015

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Section: Self-consistent Born Approximation As a Fixed-point Solutionmentioning

confidence: 99%

Interplay between disorder and inversion symmetry: Extreme enhancement of the mobility near the Weyl point in BiTeI

et al. 2015

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“…(2) then predicts the value of α(µ ′ ) at a different scale µ ′ . The quasiparticle renormalization is an observable effect and has been measured most notably in the two-dimesional (2D) Dirac material graphene in a wide variety of experiments using energy, density (which determines the Fermi energy), and momentum as the running scale [56][57][58][59][60] . In principle, temperature, provided it is much higher than the Fermi energy, could also be a varying scale to study the RG flow, and may very well be the most suitable scaling variable for 3D Dirac systems in terms of experimental investigations.…”

Section: Introductionmentioning

confidence: 99%

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials

et al. 2015

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We develop a theory for electron-electron interaction-induced many-body effects in threedimensional Weyl or Dirac semimetals, including interaction corrections to the polarizability, electron self-energy, and vertex function, up to second order in the effective fine structure constant of the Dirac material. These results are used to derive the higher-order ultraviolet renormalization of the Fermi velocity, effective coupling, and quasiparticle residue, revealing that the corrections to the renormalization group flows of both the velocity and coupling counteract the leading-order tendencies of velocity enhancement and coupling suppression at low energies. This in turn leads to the emergence of a critical coupling above which the interaction strength grows with decreasing energy scale. In addition, we identify a range of coupling strengths below the critical point in which the Fermi velocity varies non-monotonically as the low-energy, non-interacting fixed point is approached. Furthermore, we find that while the higher-order correction to the flow of the coupling is generally small compared to the leading order, the corresponding correction to the velocity flow carries an additional factor of the Dirac cone flavor number (the multiplicity of electron species, e.g. ground-state valley degeneracy arising from the band structure) relative to the leading-order result. Thus, for materials with a larger multiplicity, the regime of velocity non-monotonicity is reached for modest values of the coupling strength. This is in stark contrast to an approach based on a large-N expansion or the random phase approximation (RPA), where higher-order corrections are strongly suppressed for larger values of the Dirac cone multiplicity. This suggests that perturbation theory in the coupling constant (i.e., the loop expansion) and the RPA/large-N expansion are complementary in the sense that they are applicable in different parameter regimes of the theory. We show how our results for the ultraviolet renormalization of quasiparticle properties can be tested experimentally through measurements of quantities such as the optical conductivity or dielectric function (with carrier density or temperature acting as the scale being varied to induce the running coupling). Although experiments typically access the finite-density regime, we show that our zero-density results still capture clear many-body signatures that should be visible at higher temperatures even in real systems with disorder and finite doping.

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“…Motivated by the fact that most of the experiments of the Fermi velocity renormalization in graphene are performed in the presence of a weak external magnetic field [13][14][15], whereas the field-theoretical models either ignore the latter [7,8] or study the problem in the (strong field) Landaulevel regime [20], we decided to revise the topic.…”

Section: Discussionmentioning

confidence: 99%

“…A renormalization-group study of graphene predicted logarithmic corrections to the Fermi velocity as a function of doping (or energy) [7][8][9][10][11][12], which were later observed in many experiments [13][14][15]. In addition, the renormalized v F also depends strongly on the dielectric constant of the medium surrounding the graphene sample.…”

Section: Introductionmentioning

confidence: 99%

“…An important issue in this comparison is the intensity of the magnetic field. Although the calculations in reference [20] are made in the "weak" field approximation 1 , they cannot describe the experiments detecting the renormalization of the Fermi velocity [13][14][15] because these experiments are not in the Landau-level, but in the Shubnikov-de Haas regime.…”

Section: Introductionmentioning

confidence: 99%

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The influence of a weak magnetic field in the Renormalization-Group functions of (2 + 1)-dimensional Dirac systems

2016

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Abstract. The experimental observation of the renormalization of the Fermi velocity vF as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field B, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in B, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity for the massive case arises due to electronic interactions. In addition, for gapped systems, we observe a running of the mass parameter.

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Renormalization of the Graphene Dispersion Velocity Determined from Scanning Tunneling Spectroscopy

Cited by 101 publications

References 26 publications

Interplay between disorder and inversion symmetry: Extreme enhancement of the mobility near the Weyl point in BiTeI

Interplay between disorder and inversion symmetry: Extreme enhancement of the mobility near the Weyl point in BiTeI

Many-body effects and ultraviolet renormalization in three-dimensional Dirac materials

The influence of a weak magnetic field in the Renormalization-Group functions of (2 + 1)-dimensional Dirac systems

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