Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

Khalilov, V. R.; Mamsurov, I. V.

doi:10.1140/epjc/s10052-015-3389-6

Cited by 19 publications

(13 citation statements)

References 57 publications

(97 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the net charge is nonzero and it is located inside the inner volume. In this point the situation drastically differs from the one claimed for the radiative correction for the Coulomb charge without background, where the correction to the core (point) charge compensates the induced distributed charge -see [4] for (3+1)-dimensional QED and [36] for (2+1)-dimensional theory as applied to graphene. The reason lies in the fact that the correction Q in Eq.…”

Section: Discussionmentioning

confidence: 94%

See 1 more Smart Citation

Coulomb field in a constant electromagnetic background

2016

View full text Add to dashboard Cite

Nonlinear Maxwell equations are written up to the third-power deviations from a constantfield background, valid within any local nonlinear electrodynamics including QED with a Euler-Heisenberg (EH) effective Lagrangian. The linear electric response to an imposed static finite-sized charge is found in the vacuum filled by an arbitrary combination of constant and homogeneous electric and magnetic fields. The modified Coulomb field and corrections to the total charge and to the charge density are given in terms of derivatives of the effective Lagrangian with respect to the field invariants. These are specialized for the EH Lagrangian.The large values of electromagnetic fields, close to or larger than m 2 e = 4.4 · 10 13 G = 1.6 · 10 16 V /cm, are present not only in astrophysical objects, such as pulsars, magnetars and quark stars, but also in the close vicinities of elementary particles as produced by their charges, magnetic and electric dipole moments. (For instance, the magnetic field of the neutron at the edge of its electromagnetic radius makes up the value of about 10 16 G, characteristic of magnetars.) This fact is encouraging interest in nonlinear electrodynamics that accounts for the effects of interaction between electromagnetic fields when at least one of them is large. These are, for instance, linear, quadratic and cubic responses of the vacuum, that include large "background" or "external" electromagnetic fields, to probe fields of, say, the ones produced by charges and currents. Another example of nonlinear effects is the correction to the magnetic and electric dipole moments of elementary particles and resonances owing to their self-coupling.Another circumstance that has been fueling interest in the effects of quantum electrodynamics, this time within the framework of (2+1)-dimensional space-time, is the problem of Coulomb impurities in graphene; see the most recent review in Ref [1] and also the recent paper [2]. The point is that the effective coupling in that theory is much larger, and, correspondingly, the values of the fields optimal for nonlinearity are much smaller than in the (3+1)-dimensional QED. Among the possible background fields most handy are those that admit an exact solution to the Dirac equation for the electron, which enables explicitly exploiting the Furry picture in order to take the background exactly while calculating the response functions -the polarization operators of different ranks. These are the plane-wave field (see the review [3]), the Coulomb field (dealt with in Ref.[4]), and the constant homogeneous field [5,6]. However, only the latter admits, strictly speaking, a treatment with the use of a local electromagnetic action. The local approach, thanks to its relative simplicity, proved to be very fruitful in revealing special nonlinear effects [7]. These include the consequences of nonlinearity of quantum electrodynamics stemming from the quantum phenomenon of virtual electron-positron pairs creation by a photon, the pairs interacting with an electromagnetic field befor...

show abstract

Section: Discussionmentioning

confidence: 94%

“…The electric field given by Eqs. (36), (37), (38) is continuous on the surface of the sphere r = R, the boundary of the charge (13). Note that the R-dependent, fast decreasing at (r/R) → ∞, part…”

Section: Nonlinearly Modified Coulomb Fieldmentioning

confidence: 99%

Coulomb field in a constant electromagnetic background

2016

View full text Add to dashboard Cite

show abstract

“…24, where the polarization operator in the 2 + 1-dimensional quantum electrodynamics at finite B and µ is derived. The corresponding term is associated in [24] with the contribution of virtual fermions, while the oscillatory term considered in the present work cannot be obtained in the clean limit.…”

Section: Hall Conductivitymentioning

confidence: 99%

Magnetic oscillations of the anomalous Hall conductivity

Tsaran

Sharapov

2016

Phys. Rev. B

View full text Add to dashboard Cite

It is known that the Shubnikov--de Haas oscillations can be observed in the Hall resistivity, although their amplitude is much weaker than the amplitude of the diagonal resistivity oscillations. Employing a model of two-dimensional massive Dirac fermions that exhibits anomalous Hall effect, we demonstrate that the amplitude of the Shubnikov--de Haas oscillations of the anomalous Hall conductivity is the same as that of the diagonal conductivity. We argue that the oscillations of the anomalous Hall conductivity can be observed by studying the valley Hall effect in graphene superlattices and the spin Hall effect in the low-buckled Dirac materials.Comment: 9 pages, 2 figures; final version published in PR

show abstract

“…The remaining functions describe the screening of the intra and intervalley chiral currents. The currentcurrent susceptibility for graphene has been discussed in [100][101][102], though to the best of our knowledge the intervalley current-current susceptibility has not been previously investigated. Below, it will be convenient for us to derive expressions for both functions, and present them in a form somewhat more general than those already in the literature.…”

Section: Preliminariesmentioning

confidence: 99%

Higher-order topological superconductivity from repulsive interactions in kagome and honeycomb systems

Geier

Ingham

et al. 2021

2D Mater.

View full text Add to dashboard Cite

We discuss a pairing mechanism in interacting two-dimensional multipartite lattices that intrinsically leads to a second order topological superconducting state with a spatially modulated gap. When the chemical potential is close to Dirac points, oppositely moving electrons on the Fermi surface undergo an interference phenomenon in which the Berry phase converts a repulsive electron-electron interaction into an effective attraction. The topology of the superconducting phase manifests as gapped edge modes in the quasiparticle spectrum and Majorana Kramers pairs at the corners. We present symmetry arguments which constrain the possible form of the electron-electron interactions in these systems and classify the possible superconducting phases which result. Exact diagonalization of the Bogoliubov-de Gennes Hamiltonian confirms the existence of gapped edge states and Majorana corner states, which strongly depend on the spatial structure of the gap. Possible applications to vanadium-based superconducting kagome metals AV$_3$Sb$_3$ (A=K,Rb,Cs) are discussed.

show abstract

Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

Cited by 19 publications

References 57 publications

Coulomb field in a constant electromagnetic background

Coulomb field in a constant electromagnetic background

Magnetic oscillations of the anomalous Hall conductivity

Higher-order topological superconductivity from repulsive interactions in kagome and honeycomb systems

Contact Info

Product

Resources

About