Inhibition of the Fermi velocity renormalization in a graphene sheet by the presence of a conducting plate

Silva, Jeferson Danilo L.; Braga, Alessandra N.; Pires, Wagner P.; Alves, Van Sérgio; Alves, Danilo T.; Marino, E. C.

doi:10.1016/j.nuclphysb.2017.04.014

Cited by 12 publications

(12 citation statements)

References 21 publications

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“…Using the small-mass limit (m 2 ≪ k 2 ) the term 4m 2 =k 2 can be neglected in Eq. (14). Furthermore, since we are studying the model in the static approximation, with λ ¼ e 2 =16ϵv F < 1, hence, we have…”

Section: B the Fermion Self-energymentioning

confidence: 99%

“…Therefore, the renormalization of v F is straightforward within this quantum-electrodynamical approach. Indeed, in similar systems, the use of quantum field theory techniques has been shown very useful for describing electronic properties in both perturbative [4,5,[13][14][15][16][17][18][19][20][21] and nonperturbative [6][7][8][22][23][24][25][26] approaches. In particular, the random phase approximation (RPA), which is equivalent to leading order in the 1=N approximation [6], has been used in the description of some properties of suspended [8,26] and doped [25,27,28] graphene.…”

Section: Introductionmentioning

confidence: 99%

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Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions in largeNexpansion

et al. 2020

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Recently the renormalization of the band gap m, in both tungsten diselenide (WSe 2) and molybdenumm disulfide (MoS 2), has been experimentally measured as a function of the carrier concentration n. The main result establishes a decreasing of hundreds of meV, in comparison with the bare band gap, as the carrier concentration increases. These materials are known as transition metal dichalcogenides and their lowenergy excitations are, approximately, described by the massive Dirac equation. Using pseudo-quantum electrodynamics (PQED) to describe the electromagnetic interaction between these quasiparticles and from renormalization group analysis at the large-N limit, we obtain that the renormalized mass describes the band gap renormalization with a function given by mðnÞ=m 0 ¼ ðn=n 0 Þ C λ =2 , where m 0 ¼ mðn 0 Þ and C λ is a function of the coupling constant λ ¼ πα=4, where α is the fine-structure constant. We compare our theoretical results with the experimental findings for WSe 2 and MoS 2 , and we conclude that our approach is in agreement with these experimental results for reasonable values of λ. Thereafter, we consider the coupling of massless Dirac particles with the Gross-Neveu interaction, which generates a mass for the Dirac field through the gap equation, and PQED. In this case, we show that there exists a critical coupling constant, namely, λ c ≈ 0, 66 in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For λ > λ c , the renormalized mass decreases while for λ < λ c it increases with the carrier concentration.

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Section: B the Fermion Self-energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions in largeNexpansion

et al. 2020

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“…Because of that, it has been applied to describe the electromagnetic interaction in 2D materials, such as graphene [43][44][45][46], silicene [47], and transition metal dichalcogenides [47][48][49][50][51]. Within the myriad of results it has given rise to, we allude in hindsight to dynamical mass generation for fermion at zero and finite temperature [52][53][54], interaction-driven quantum valley Hall effect [55], quantum corrections of the electron g-factor [56], electron-hole pairing (excitons) in transition metal dichalcogenides [57,58], optical infrared conductivity of graphene [59], emergence of a dynami-cally generated mass with Gross-Neveu interaction [60], Yukawa potential in the plane [61,62], and PQED cavity effects [63,64].…”

Section: Introductionmentioning

confidence: 99%

Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane

Ozela,

Alves,

Magalhães

et al. 2021

Preprint

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Chiral symmetry breaking comes from the mass dynamically generated through interaction of Dirac fermions for both quantum electrodynamics in (2+1)D (QED3) and (3+1)D (QED4). In QED3, the presence of a Chern-Simons (CS) parameter affects the critical structure of the theory, favoring the symmetric phase where the electron remains massless. Here, we calculate the main effects of a Pseudo-Chern-Simons (PCS) parameter θ into the dynamical mass generation of Pseudo quantum electrodynamics (PQED). The θ-parameter provides a mass scale for PQED at classical level and appears as the pole of the gauge-field propagator. After calculating the full electron propagator with the Schwinger-Dyson equation at quenched-rainbow and large-N approximations, we conclude that θ affects the critical parameters related to the fine-structure constant, αc(θ), and to the number of copies of the matter field, Nc(θ), by favoring the symmetric phase. In the continuum limit (Λ → ∞), nevertheless, the θ-parameter do not affect the critical parameters. We also compare our analytical results with numerical findings of the integral equation for the mass function of the electron.

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“…Therefore, the renormalization of v F is straightforward within this quantumelectrodynamical approach. Indeed, in similar systems, the use of quantum field theory techniques has been shown very useful for describing electronic properties [4,5,[10][11][12][13][14][15]. Nevertheless, the effects of GN interactions coupled to PQED have been less discussed [16].…”

Section: Introductionmentioning

confidence: 99%

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions

Fernández,

Alves,

Nascimento

et al. 2020

Preprint

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Recently the renormalization of the band gap m, in both WSe2 and MoS2, has been experimentally measured as a function of the carrier concentration n. The main result establishes a decreasing of hundreds of meV, in comparison with the bare band gap, as the carrier concentration increases. These materials are known as transition metal dichalcogenides and their low-energy excitations are, approximately, described by the massive Dirac equation. Using Pseudo Quantum Electrodynamics (PQED) to describe the electromagnetic interaction between these quasiparticles and from renormalization group analysis, we obtain that the renormalized mass describes the band gap renormalization with a function given by m(n)/m0 = (n/n0) C λ /2 , where m0 = m(n0) and C λ is a function of the coupling constant λ. We compare our theoretical results with the experimental findings for WSe2 and MoS2, and we conclude that our approach is in agreement with these experimental results for reasonable values of λ. In addition we introduced a Gross-Neveu (GN) interaction which could simulate an disorder/impurity-like microscopic interaction. In this case, we show that there exists a critical coupling constant, namely, λc ≈ 0, 66 in which the beta function of the mass vanishes, providing a stable fixed point in the ultraviolet limit. For λ > λc, the renormalized mass decreases while for λ < λc it increases with the carrier concentration.

show abstract

Inhibition of the Fermi velocity renormalization in a graphene sheet by the presence of a conducting plate

Cited by 12 publications

References 21 publications

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions in largeNexpansion

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions in largeNexpansion

Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane

Renormalization of the band gap in 2D materials through the competition between electromagnetic and four-fermion interactions

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