Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultrarelativistic limit of graphene

Kotikov, A.V.; Teber, S.

doi:10.1103/physrevd.89.065038

Cited by 66 publications

(99 citation statements)

References 48 publications

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“…[183,185,186,[189][190][191][274][275][276][277][278][279][280][281][282][283][284][285][286][287]. Here, we review studies of the dynamics in graphite and graphene using the framework of the so-called reduced (3 + 1)-dimensional gauge theories [189,202,203,288,289]. These theories share the following common feature.…”

Section: Magnetic Catalysis In Reduced Qedmentioning

confidence: 97%

“…It is the relativistic nature of the free Hamiltonian H 0 in Eq. (289) These arguments are based on the kinematic structure of gap equation (294), which is the same as that for Eq. (259) with the Coulomb interaction.…”

Section: Gap Equation: Coexistence Of Qhf and MC Parametersmentioning

confidence: 99%

“…The electron chemical potential µ 0 is introduced by adding the term −µ 0 Ψ Ď Ψ to the Hamiltonian density (289). This term also preserves the U(4) symmetry.…”

Section: Quantum Hall Effect In Model Of Graphene With Short-range Inmentioning

confidence: 99%

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Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

2015

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a b s t r a c tA range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density. Finally, we discuss the interplay between relativistic quantum field theories (including quantum electrodynamics and quantum chromodynamics) in a magnetic field and noncommutative field theories, which leads to a new type of the latter, nonlocal noncommutative field theories.

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Section: Magnetic Catalysis In Reduced Qedmentioning

confidence: 97%

Section: Gap Equation: Coexistence Of Qhf and MC Parametersmentioning

confidence: 99%

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Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

2015

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“…The multi-loop structure of the latter has been recently explored in Refs. [31,32]. With the help of the ansatz (9), one can then see that the r.h.s.…”

Section: Leading Ordermentioning

confidence: 99%

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in the Landau gauge

2016

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The dynamical generation of a fermion mass is studied within (2 + 1)-dimensional QED with N four-component fermions in the leading and next-to-leading orders of the 1/N expansion. The analysis is carried out in the Landau gauge which is supposed to insure the gauge independence of the critical fermion flavour number, Nc. It is found that the dynamical fermion mass appears for N < Nc where Nc = 3.29, that is only about 1% larger than its value at leading order.

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“…One difference is that the gauge fixing parameter in reduced QED is twice less than the one in QED 3 . Such a difference can be taken into account with the help of our present results for QED 3 together with the multi-loop results obtained in [30,31]. The case of reduced QED, and its relation with dynamical gap generation in graphene which is the subject of active ongoing research, see, e.g., the reviews [32,33], will be considered in a separate paper [34].…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

Kotikov

Teber

2016

Phys. Rev. D

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Dynamical chiral symmetry breaking (DχSB) is studied within (2 + 1)-dimensional QED with N four-component fermions. The leading and next-to-leading orders of the 1/N expansion are computed exactly. The analysis is carried out in an arbitrary non-local gauge. Resumming the wave-function renormalization constant at the level of the gap equation yields a strong suppression of the gauge dependence of the critical fermion flavour number, Nc(ξ) where ξ is the gauge fixing parameter, which is such that DχSB takes place for N < Nc(ξ). Neglecting the weak gaugedependent terms yields Nc = 2.8469 while, in the general case, it is found that: Nc(1) = 3.0084 in the Feynman gauge, Nc(0) = 3.0844 in the Landau gauge and Nc(2/3) = 3.0377 in the ξ = 2/3 gauge where the leading order fermion wave function is finite. These results suggest that DχSB should take place for integer values N ≤ 3.

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Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultrarelativistic limit of graphene

Cited by 66 publications

References 48 publications

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in the Landau gauge

Critical behavior of (2+1)-dimensional QED:1/Nfcorrections in an arbitrary nonlocal gauge

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