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We study magnetogenesis in axionlike inflation driven by a pseudoscalar field φ coupled axially to the electromagnetic (EM) field (β/Mp)φFµνF µν with dimensionless coupling constant β. A set of equations for the inflaton field, scale factor, and expectation values of quadratic functions of the EM field is derived. These equations take into account the Schwinger effect and the backreaction of generated EM fields on the Universe expansion. It is found that the backreaction becomes important when the EM energy density reaches the value ρEM ∼ ( √ 2 /β)ρ inf ( is the slow-roll parameter and ρ inf is the energy density of the inflaton) slowing down the inflaton rolling and terminating magnetogenesis. The Schwinger effect becomes relevant when the electric energy density exceeds the value ρE ∼ α −3 EM (ρ 2 tot /M 4 p ), where ρtot = 3H 2 M 2 p is the total energy density and αEM is the EM coupling constant. For large β, produced charged particles could constitute a significant part of the Universe energy density even before the preheating stage. Numerically studying magnetogenesis in the α-attractor model of inflation, we find that it is possible to generate helical magnetic fields with the maximal strength 10 −15 G, however, only with the correlation length of order 1 pc at present.

We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling f 2 (φ)FµνF µν of the electromagnetic field to the inflaton field φ. We consider the case where the coupling function f (φ) decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter ǫ and inflaton energy density, ρE ∼ ǫρ inf . It affects the inflaton field evolution and leads to the scale-invariant electric power spectrum and the magnetic one which is blue with the spectral index nB = 2 for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below 10 −22 G. It is worth emphasizing that since the effective electric charge of particles e eff = e/f is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field, helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles, implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike f ∝ a α and Ratra-type f = exp(βφ/Mp) coupling functions.

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By assuming the kinetic coupling f 2 (φ)F F of the effective inflaton field φ with the electromagnetic field, we explore magnetogenesis during the inflation and preheating stages in the R 2 Starobinsky model [1]. We consider the case of the exponential coupling function f (φ) = exp(αφ/Mp) and show that for α ∼ 12 − 15 it is possible to generate the large scale magnetic fields with strength 10 −15 Gauss at the present epoch. The spectrum of generated magnetic fields is blue with the spectral index n = 1+s, s > 0. We have found that for the relevant values of the coupling parameter, α = 12 − 15, model avoids the back-reaction problem for all relevant modes.

We study the supercritical instability in gapped graphene with two charged impurities separated by distance R using the two-dimensional Dirac equation for electron quasiparticles. Attention is paid to a situation when charges of impurities are subcritical, whereas their total charge exceeds a critical one. The critical distance R_{cr} in the system of two charged centers is defined as that at which the electron bound state with the lowest energy reaches the boundary of the lower continuum. A variational calculation of the critical distance R_{cr} separating the supercritical (RR_{cr}) regimes is carried out. It is shown that the critical distance R_{cr} increases as the quasiparticle gap decreases. The energy and width of a quasistationary state as functions of the distance between two impurities are derived in the quasiclassical approximation.Comment: 12 pages, 1 figure, comments and references added, to match the published versio

Using the kinetic approach, we study the impact of the charged particle dynamics due to the Schwinger effect on the electric field evolution during inflation. As a simple model of the electric field generation, we consider the kinetic coupling of the electromagnetic field to the inflaton via the term f 2 (φ)Fµν F µν with the Ratra coupling function f = exp(βφ/Mp). The production of charged particles is taken into account in the Boltzmann kinetic equation through the Schwinger source term. Produced particles are thermalized due to collisions which we model by using the collision integral in the self-consistent relaxation time approximation. We found that the current of created particles exhibits a non-Markovian character and cannot be described by a simple Ohm's law relation j ∝ E. On the contrary, the electric current as well as the electric field are oscillatory functions of time with decreasing amplitudes and a phase difference due to the ballistic motion of charged carriers. Our qualitative results are checked by using a hydrodynamic approach. Deriving a closed system of equations for the number, current, and energy densities of charged particles and determining its solution, we find a good agreement with the results obtained in the kinetic approach.

The electron states in the field of a charged impurity in graphene in a magnetic field are studied numerically. It is shown that a charged impurity removes the degeneracy of Landau levels converting them into bandlike structures. As the charge of impurity grows, the repulsion of sublevels of different Landau levels with the same value of orbital momentum takes place leading to the redistribution of the wave function profiles of these sublevels near the impurity. By studying the polarization effects, it is shown in agreement with the recent experiments that the effective charge of impurity can be very effectively tuned by chemical potential. If the chemical potential is situated inside a Landau level, then the charge of impurity is strongly diminished. In addition, the polarization function in this case has a peak at zero momentum, which leads to the sign-changing oscillations of the screened potential as a function of distance. If the chemical potential lies between the Landau levels, then the screened potential does not change sign, the screening is minimal, and the charged impurity can strongly affect the electron spectrum.Comment: 11 pages, 7 figures; final version published in PR