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Dynamical friction and stellar orbital motion in spiral galaxies with dark matter composed of ultralight bosons in the state of {rotating} Bose-Einstein condensate (BEC) are studied. It is found that the dynamical friction force is significantly affected by the topological charge of the vortex structure of the BEC core with the strongest effect at distances near the galactic center. It is also shown that the ultralight dark matter self-interaction plays an important role in studying the dynamical friction., Comment: 12 pages, 5 figures

The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of few atomically thick layers and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to $N$ planes and contains $N$ vector fields with Maxwell`s action modified by non-local form factors whose explicit form is determined. Taking into account the polarization function, the explicit formulae for the screened electromagnetic interaction are presented in the case of two and three layers. For a heterostructure with two atomically thick layers and charged fermions described by the massless Dirac equation, the dynamical gap generation of the excitonic type is studied. It is found that additional screening due to the second layer increases the value of the critical coupling constant for the gap generation compared to that in graphene., Comment: 17 pages, 1 figure

We study viscoelastic response in Weyl semimetals with broken time-reversal symmetry. The principal finding is that topology and anisotropy of the Fermi surface are manifested in the viscoelasticity tensor of the electron fluid. In the dynamic (interband) part of this tensor, the anisotropy leads to a qualitatively different, compared with isotropic models, scaling with frequency and the Fermi energy. The components of the viscosity tensor determined by the Fermi-surface properties agree in the Kubo and kinetic formalisms; the latter, however, misses the anomalous Hall viscosity originating from filled states below the Fermi surface. The anisotropy of the dispersion relation is also manifested in the acceleration and relaxation terms of the hydrodynamic equations providing means to probe the anisotropy in transport experiments., Comment: 10+19 pages, 4 figures; published version

In gapped bilayer graphene, similarly to conventional semiconductors, Coulomb impurities (such as nitrogen donors) may determine the activation energy of its conductivity and provide low temperature hopping conductivity. However, in spite of the importance of Coulomb impurities, nothing is known about their electron binding energy $E_b$ in the presence of gates. To close this gap, we study numerically the electron binding energy $E_b$ of a singly charged donor in BN-enveloped bilayer graphene with the top and bottom gates at distance $d$ and gate-tunable gap $2\Delta$. We show that for $10 < d < 200$ nm and $1 < \Delta < 100$ meV the ratio $E_b/\Delta$ changes from 0.4 to 1.5. The ratio $E_b/\Delta$ stays close to unity because of the dominating role of the bilayer polarization screening which reduces the Coulomb potential well depth to values $\sim \Delta$. Still the ratio $E_b/\Delta$ somewhat decreases with growing $\Delta$, faster at small $\Delta$ and slower at large $\Delta$. On the other hand, $E_b/\Delta$ weakly grows with $d$, again faster at small $\Delta$ and slower at large $\Delta$. We also studied the effect of trigonal warping and found only a small reduction of $E_b/\Delta$., Comment: 12 pages, 6 figures

We study chirality production in the pseudoscalar inflation model of magnetogenesis taking into account the Schwinger effect and particle collisions in plasma in the relaxation time approximation. We consider the Schwinger production of one Dirac fermion species by an Abelian gauge field in two cases: (i) the fermion carries only the weak charge with respect to the U(1) group and (ii) it is also charged with respect to another strongly coupled gauge group. While the gradient-expansion formalism is employed for the description of the evolution of gauge field, plasma is described by hydrodynamical approach which allows us to determine the number, energy density, and chirality of produced fermions. It is found that while chirality production is very efficient for both, weakly and strongly interacting fermions, the resulting gauge field is typically stronger in the case of strongly interacting fermions due to suppression of the Schwinger conductivity by particle collisions., Comment: 16 pages, 6 figures

The generation of magnetic fields during inflation in an electromagnetic model with a non-local form factor in Maxwell`s action is studied. The equations of motion for the electromagnetic field are derived and solved. It is found that the conformal symmetry breaking due to the non-local form factor does not lead to the generation of magnetic fields during inflation in the absence of interaction with the inflaton field. If such a coupling takes place, then the presence of the form factor inhibits the generation of primordial magnetic fields compared to the case where the non-local form factor is absent., Comment: 7 pages

We calculate optical conductivity for bilayer dice lattices in commensurate vertically aligned stackings. The interband optical conductivity reveals a rich activation behavior unique for each of the four stackings. We found that the intermediate energy band, which corresponds to the flat band of a single-layer dice lattice, plays a different role for different stackings. The interband selection rules, which are crucial for the single-layer lattice, may become lifted in bilayer lattices. The results for effective and tight-binding models are found to be in qualitative agreement for some of the stackings and the reasons for the discrepancies for others are identified. Our findings propose optical conductivity as an effective tool to distinguish between different stackings in bilayer dice lattices., Comment: 22 pages, 14 multi-panel figures

We introduce and classify nonequivalent commensurate stackings for bilayer dice or $\mathcal{T}_3$ lattice. For each of the four stackings with vertical alignment of sites in two layers, a tight-binding model and an effective model describing the properties in the vicinity of the threefold band-crossing points are derived. Focusing on these band-crossing points, we found that although the energy spectrum remains always gapless, depending on the stacking, different types of quasiparticle spectra arise. They include those with flat, tilted, anisotropic semi-Dirac, and $C_3$-corrugated energy bands. We use the derived tight-binding models to calculate the density of states and the spectral function. The corresponding results reveal drastic redistribution of the spectral weight due to the inter-layer coupling that is unique for each of the stackings., Comment: 15 pages, 9 multi-panel figures

The nature of dark matter (DM) remains one of the unsolved mysteries of modern physics. An intriguing possibility is to assume that DM consists of ultralight bosonic particles in the Bose-Einstein condensate (BEC) state. We study stationary DM structures by using the system of the Gross-Pitaevskii and Poisson equations, including the effective temperature effect with parameters chosen to describe the Milky Way galaxy. We have investigated DM structure with BEC core and isothermal envelope. We compare the spherically symmetric and vortex core states, which allows us to analyze the impact of the core vorticity on the halo density, velocity distribution, and, therefore, its gravitational field. Gravitational field calculation is done in the gravitoelectromagnetism approach to include the impact of the core rotation, which induces a gravimagnetic field. As result, the halo with a vortex core is characterized by smaller orbital velocity in the galactic disk region in comparison with the non-rotating halo. It is found that the core vorticity produces gravimagnetic perturbation of celestial body dynamics, which can modify the circular trajectories., Comment: 17 pages, 11 figures

A key feature of ultra-light dark matter composed by bosons is the formation of superfluid Bose-Einstein condensate (BEC) structures on galactic scales. We study collisions of BEC solitonic and vortex structures in the framework of the Gross-Pitaevskii-Poisson model. It is found that the superfluid nature of bosonic dark matter leads to the formation of quantized vortex lines and vortex rings in interference patterns formed during collisions. Calculating the gravitational wave luminosity, we demonstrated that quantum interference patterns affect notably the gravitational wave radiation. We reveal that superfluid self-gravitating BECs can form stable localized vortex structures which remain robust even after a head-on collision., Comment: 9 pages, 8 figures

The electric and chiral current response to the time- and coordinate-dependent pseudoelectric field $\mathbf{E}_5$ in Weyl semimetals is studied. It is found that $\mathbf{E}_5$ leads to an electric current in the direction perpendicular to the field and the wave vector of the field-inducing perturbation. We dubbed this phenomenon the anomalous pseudo-Hall effect. The response of the chiral or valley current to the pseudoelectric field is also found to be nontrivial. Since the wave vector for $\mathbf{E}_5$ cannot be neglected, the frequency profile of the chiral conductivity is drastically different from its electric counterpart showing a step-like feature instead of a smooth Drude peak. The proposed effects can be investigated by driving sound waves in Weyl semimetals with broken time-reversal symmetry., Comment: 18 pages, 7 multi-panel figures

Semiclassical contributions to the gravitational action include various terms with zero, two, and four derivatives of the metric as well as nonlocal form factors for these terms. Contributions to some of these terms could be confused with others on a specific metric background or for a particular gauge fixing. We present a critical analysis of the recent works where the tensor structure and the number of derivatives in the action of gravity were not properly taken into account. Taking these relevant aspects into account, we show that although some contributions owing to the quantum fluctuations of massive or massless scalar as well as fermion and vector fields may be attributed to the "running" of the cosmological constant, in reality they correspond to the fourth derivative terms of the action., Comment: Explanations extended, results unchanged, fits the published version. 15 pages, 1 figure

We study the generation of the chiral charge during axion inflation where the pseudoscalar inflaton field $\phi$ couples axially to the electromagnetic field through the term $(\beta/M_p)\phi\,\boldsymbol{E}\cdot\boldsymbol{B}$ with dimensionless coupling constant $\beta$. To describe the evolution of electromagnetic field and determine $\langle\boldsymbol{E}\cdot\boldsymbol{B}\rangle$ sourcing the chiral asymmetry during inflation due to the chiral anomaly, we employ the gradient expansion formalism. It operates with a set of vacuum expectation values of bilinear electromagnetic functions and allows us to take into account the backreaction of generated fields on the inflaton evolution as well as the Schwinger production of charged fermions. In addition, we include the chiral magnetic effect contribution to the electric current $\boldsymbol{j}_{\rm CME}=e^{2}/(2\pi^2)\mu_{5}\boldsymbol{B}$, where $\mu_5$ is the chiral chemical potential which quantifies the chiral charge production. Solving a set of equations for the inflaton field, scale factor, quadratic functions of the electromagnetic field, and the chiral charge density (chiral chemical potential), we find that the chirality production is quite efficient leading to the generation of a large chemical potential at the end of axion inflation., Comment: 13 pages, 2 figures. arXiv admin note: text overlap with arXiv:2109.01651

The p-wave superfluid is characterized by nontrivial topological characteristics essential for fault-tolerant quantum state manipulation. However, the practical realization of the p-wave state remains a challenging problem. We study the s- and p-wave superfluidity in mixtures of fermionic and spinor bosonic gases and derive a general set of the gap equations for these superfluid states. Numerically solving the gap equations for the s-wave state, we quantify the physical conditions for the realization of the pure p-wave state in a well-controlled environment of atomic physics in the absence of an admixture of the s-wave state., Comment: 9 pages, 2 figures

Axion inflation coupled to the Standard Model (SM) hypercharge gauge sector represents an attractive scenario for the generation of primordial hypermagnetic fields. The description of this scenario is, however, complicated by the Schwinger effect, which gives rise to highly nonlinear dynamics. Hypermagnetogenesis during axion inflation in the absence of nonlinear effects is well studied and known to result in a hypermagnetic energy density that scales like $H^4\,e^{2\pi\xi}/\xi^5$, where $\xi$ is proportional to the time derivative of the axion-vector coupling in units of the Hubble rate $H$. In this paper, we generalize this result to the full SM case by consistently taking into account the Schwinger pair production of all SM fermions. To this end, we employ the novel gradient-expansion formalism that we recently developed in [2109.01651], and which is based on a set of vacuum expectation values for bilinear hyperelectromagnetic functions in position space. We parametrize the numerical output of our formalism in terms of three parameters ($\xi$, $H$, and $\Delta$, where the latter accounts for the damping of subhorizon gauge-field modes because of the finite conductivity of the medium) and work out semianalytical fit functions that describe our numerical results with high accuracy. Finally, we validate our results by comparing them to existing estimates in the literature as well as to the explicit numerical results in a specific inflationary model, which leads to good overall agreement. We conclude that the systematic uncertainties in the description of hypermagnetogenesis during axion inflation, which previously spanned up to several orders of magnitude, are now reduced to typically less than 1 order of magnitude, which paves the way for further phenomenological studies., Comment: 22 pages, 5 figures

We propose that chirally asymmetric plasma can be produced in the gap regions of the magnetospheres of pulsars and black holes. We show that, in the case of supermassive black holes situated in active galactic nuclei, the chiral charge density and the chiral chemical potential are very small and unlikely to have any observable effects. In contrast, the chiral asymmetry produced in the magnetospheres of magnetars can be substantial. It can trigger the chiral plasma instability that, in turn, can lead to observable phenomena in magnetars. In particular, the instability should trigger circularly polarized electromagnetic radiation in a wide window of frequencies, spanning from radio to near-infrared. As such, the produced chiral charge has the potential to affect some features of fast radio bursts., Comment: 10 pages, 1 figure, 1 table; v2: some discussions are extended, accepted for publication in Eur. Phys. J. C

We study the explosive production of gauge fields during axion inflation in a novel gradient expansion formalism that describes the time evolution of a set of bilinear electromagnetic functions in position space. Based on this formalism, we are able to simultaneously account for two important effects that have thus far been mostly treated in isolation: (i) the backreaction of the produced gauge fields on the evolution of the inflaton field and (ii) the Schwinger pair production of charged particles in the strong gauge-field background. This allows us to show that the suppression of the gauge-field production due to the Schwinger effect can prevent the backreaction in scenarios in which it would otherwise be relevant. Moreover, we point out that the induced current, $\boldsymbol{J} = \sigma \boldsymbol{E}$, also dampens the Bunch-Davies vacuum fluctuations deep inside the Hubble horizon. We describe this suppression by a new parameter $\Delta$ that is related to the time integral over the conductivity $\sigma$ which hence renders the description of the entire system inherently nonlocal in time. Finally, we demonstrate how our formalism can be used to construct highly accurate solutions for the mode functions of the gauge field in Fourier space, which serves as a starting point for a wealth of further phenomenological applications, including the phenomenology of primordial perturbations and baryogenesis., Comment: 24 pages, 7 figures

A hydrodynamic flow of electrons driven by an oscillating electric field in Dirac and Weyl semimetals is investigated. It is found that a double-peak profile of the electric current appears and is manifested in a stray magnetic field with peaks in one of the field components. The nontrivial current profile originates from the interplay of viscous and inertial properties of the electron fluid as well as the boundary conditions. Analytical results are supported by numerical calculations in samples of different geometries such as straight channels, nozzles, and cavities. The double-peak profile of the current is found to be qualitatively insensitive to a specific form of the time dependence of the oscillating electric field and is stable with respect to the sample geometry. A phase diagram and criteria for observing the double-peak structure are determined. In addition, it is shown that nozzles and cavities provide an efficient means to locally enhance or reduce the fluid velocity., Comment: 17 pages, 15 multi-panel figures; published version

Hydrodynamic instabilities driven by a direct current are analyzed in 2D and 3D relativisticlike systems with the Dyakonov-Shur boundary conditions supplemented by a boundary condition for temperature. Besides the conventional Dyakonov-Shur instability for plasmons, we find an entropy wave instability in both 2D and 3D systems. The entropy wave instability is a manifestation of the relativisticlike nature of electron quasiparticles and a nontrivial role of the energy current in such systems. These two instabilities occur for the opposite directions of fluid flow. While the Dyakonov-Shur instability is characterized by the plasma frequency in 3D and the system size in 2D, the frequency of the entropy wave instability is tunable by the system size and the flow velocity., Comment: 6+11 pages, 1+6 multi-panel figures

In the framework of Higgs inflation, we consider the electromagnetic field nonminimally coupled to gravity via the parity-preserving $\propto RF^{2}$ and parity-violating $\propto RF\tilde{F}$ terms. Using the perturbation theory to the leading order in these couplings, we study the generation of the electromagnetic field during the inflation stage. We derive the effective kinetic and axial coupling functions arising in the Einstein frame in the usual metric as well as Palatini formulations of gravity. For both formulations, we determine the power spectrum, energy density, and helicality of the generated electromagnetic fields for different values of the nonminimal coupling constants. Finally, we estimate the maximal present-day magnitude of the magnetic field as $10^{-14}-10^{-15}\,$G with the correlation length of order 10 pc., Comment: 23 pages, 10 figures

It is shown that the convective instability in electron fluids in three- and two-dimensional (3D and 2D) Dirac and Weyl semimetals is strongly inhibited. The major obstacles for electron convection are the effects of the Coulomb forces and the momentum relaxation related to the interaction with impurities and phonons. The effect of the Coulomb forces is less pronounced in 2D materials, such as graphene. However, momentum relaxation still noticeably inhibits convection making it very difficult to achieve in practice., Comment: 8+11 pages, 1+4 figures; published version

The gap generation in the dice model with local four-fermion interaction is studied. Due to the presence of two valleys with degenerate electron states, there are two main types of gaps. The intra- and intervalley gap describes the electron and hole pairing in the same and different valleys, respectively. We found that while the generation of the intravalley gap takes place only in the supercritical regime, the intervalley gap is generated for an arbitrary small coupling. The physical reason for the absence of the critical coupling is the catalysis of the intervalley gap generation by the flat band in the electron spectrum of the dice model. The completely quenched kinetic energy in the flat band when integrated over momentum in the gap equation leads to extremely large intervalley gap proportional to the area of the Brillouin zone., Comment: 15 pages, 6 figures

In order to describe magnetogenesis during inflation in the kinetic coupling model, we utilize a gradient expansion which is based on the fact that only long-wavelength (superhorizon) modes undergo amplification. For this purpose, we introduce a set of functions (bilinear combinations of electromagnetic fields with an arbitrary number of spatial curls) satisfying an infinite chain of equations. Apart from the usual mode enhancement due to interaction with the inflaton, these equations also take into account the fact that the number of relevant modes constantly grows during inflation. Truncating this chain, we show that even with a relatively small number of equations, it is possible to describe the electric and magnetic energy densities with a few percent accuracy during the whole inflation stage. We arrive at this conclusion for different types of coupling functions (increasing, decreasing, and nonmonotonic) in the regime with strong backreaction and its absence., Comment: 22 pages, 14 figures

Surface plasmon polaritons in a strained slab of a Weyl semimetal with broken time-reversal symmetry are investigated. It is found that the strain-induced axial gauge field reduces frequencies of these collective modes for intermediate values of the wave vector. Depending on the relative orientation of the separation of Weyl nodes in momentum space, the surface normal, and the direction of propagation, the dispersion relation of surface plasmon polaritons could be nonreciprocal even in a thin slab. In addition, strain-induced axial gauge fields can significantly affect the localization properties of the collective modes. These effects allow for an in situ control of the propagation of surface plasmon polaritons in Weyl semimetals and might be useful for creating nonreciprocal devices., Comment: 16 pages, 10 multi-panel figures; published version

The superconducting s-wave state in Weyl semimetals in a strong strain-induced pseudomagnetic field is investigated in a model with local four-fermion interaction. It is found that only the inter-node pairing is possible in the lowest pseudo-Landau level approximation. Unlike the case of the lowest Landau level in a conventional magnetic field, the corresponding gap equation has only a trivial solution. Nevertheless, superconductivity can be induced via the proximity effect with a usual s-wave spin-singlet superconductor. Since a pseudomagnetic field is present necessarily at the surface of a Weyl semimetal, the proximity effect is strongly affected by the pseudomagnetic field. The analysis of such an effect showed that while no gap is opened in the spectrum, the degeneracy of energy levels is lifted. The unique character of the proximity effect in Weyl semimetals can be probed via the density of states, the spectral function, and the tunneling current. The density of states does not vanish at small energies and scales linearly with the pseudomagnetic field strength. This scaling is manifested also in the tunneling current., Comment: 17 pages, 7 multi-panel figures; published version

By using the first-principles approach, we derive a system of three quantum kinetic equations governing the production and evolution of charged scalar particles by an electric field in an expanding universe. Analyzing the ultraviolet asymptotic behavior of the kinetic functions, we found the divergent parts of the electric current and the energy-momentum tensor of the produced particles and determined the corresponding counterterms. The renormalized system of equations is used to study the generation of electromagnetic fields during and after inflation in the kinetic coupling model $\mathcal{L}_{\rm EM}=-(1/4)f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ with the Ratra coupling function $f=\exp(\beta\phi/M_{p})$. It is found that the electric current of created particles is retarded with respect to the electric field. This leads to an oscillatory behavior of both quantities in agreement with the results obtained previously in phenomenological kinetic and hydrodynamical approaches., Comment: 22 pages, 4 figures

The transport properties and electron states in cylinder nanowires of Dirac and Weyl semimetals are studied paying special attention to the structure and properties of the surface Fermi arcs. The latter make the electric charge and current density distributions in nanowires strongly nonuniform as the majority of the charge density is accumulated at the surface. It is found that a Weyl semimetal wire also supports a magnetization current localized mainly at the surface because of the Fermi arcs contribution. By using the Kubo linear response approach, the direct current (DC) conductivity is calculated and it is found that its spatial profile is nontrivial. By explicitly separating the contributions of the surface and bulk states, it is shown that when the electric chemical potential and/or the radius of the wire is small, the electron transport is determined primarily by the Fermi arcs and the electrical conductivity is much higher at the surface than in the bulk. Due to the rise of the surface-bulk transition rate, the relative contribution of the surface states to the total conductivity gradually diminishes as the chemical potential increases. In addition, the DC conductivity at the surface demonstrates noticeable peaks when the Fermi level crosses energies of the surface states., Comment: 18 pages, 8 multi-panel figures; published version

Using the kinetic approach, we study the impact of the charged particles 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 $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ with the Ratra coupling function $f=\exp(\beta\phi/M_{p})$. 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 $j\propto E$. 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., Comment: 17 pages, 4 figures

We study magnetogenesis in axionlike inflation driven by a pseudoscalar field $\phi$ coupled axially to the electromagnetic (EM) field $(\beta/M_{p})\phi F_{\mu\nu}\tilde{F}^{\mu\nu}$ with dimensionless coupling constant $\beta$. 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 $\rho_{\rm EM}\sim (\sqrt{2\epsilon}/\beta)\rho_{\rm inf}$ ($\epsilon$ is the slow-roll parameter and $\rho_{\rm inf}$ 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 $\rho_{E}\sim \alpha_{\rm EM}^{-3} (\rho_{\rm tot}^{2}/M_{p}^{4})$, where $\rho_{\rm tot}=3H^{2}M_{p}^{2}$ is the total energy density and $\alpha_{\rm EM}$ is the EM coupling constant. For large $\beta$, produced charged particles could constitute a significant part of the Universe energy density even before the preheating stage. Numerically studying magnetogenesis in the $\alpha$-attractor model of inflation, we find that it is possible to generate helical magnetic fields with the maximal strength $10^{-15}\,{\rm G}$, however, only with the correlation length of order $1\,{\rm pc}$ at present., Comment: 24 pages, 5 figures

The hydrodynamic description of the Fermi arc surface states is proposed. In view of the strong suppression of scattering on impurities, the hydrodynamic regime for Fermi arc states should be, in principle, plausible. By using the kinetic theory, the Fermi arc hydrodynamics is derived and the corresponding effects on the bulk flow and surface collective modes are studied. For the bulk flow, the key effect of the proposed Fermi arc hydrodynamics is the modification of the corresponding boundary conditions. In a slab geometry, it is shown that, depending on the transfer rates between the surface and bulk, the hydrodynamic flow of the electron fluid inside the slab could be significantly altered and even enhanced near the surfaces. As to the spectrum of the surface collective modes, in agreement with earlier studies, it is found that the Fermi arcs allow for an additional gapless spectrum branch and a strong anisotropy of the surface plasmon dispersion relations in momentum space. The gapped modes are characterized by closed elliptic contours of constant frequency in momentum space., Comment: 17 pages, 4 figures; published version

The electron states of gapped pseudospin-1 fermions of the $\alpha-{\cal T}_3$ lattice in the Coulomb field of a charged impurity are studied. The free $\alpha-{\cal T}_3$ model has three dispersive bands with two energy gaps between them depending on the parameter $\Theta$ which controls the coupling of atoms of honeycomb lattice with atoms in the center of each hexagon, thus, interpolating between graphene $\Theta=0$ and the dice model $\Theta=\pi/4$. The middle band becomes flat one with zero energy in the dice model. The bound electron states are found in the two cases: the centrally symmetric potential well and a regularized Coulomb potential of the charged impurity. As the charge of impurity increases, bound state energy levels descend from the upper and central continua and dive at certain critical charges into the central and lower continuum, respectively. In the dice model, it is found that the flat band survives in the presence of a potential well, however, is absent in the case of the Coulomb potential. The analytical results are presented for the energy levels near continuum boundaries in the potential well. For the genuine Coulomb potential, we present the recursion relations that determine the coefficients of the series expansion of wave functions of bound states. It is shown that the condition for the termination of the series expansion gives two equations relating energy and charge values. Hence, analytical solutions can exist for a countably infinite set of values of impurity charge at fixed $\Theta$., Comment: 18 pages, 7 figures

About eight years ago it was predicted theoretically that a charged chiral plasma could support the propagation of the so-called chiral magnetic waves, which are driven by the anomalous chiral magnetic and chiral separation effects. This prompted intensive experimental efforts in search of signatures of such waves in relativistic heavy-ion collisions. In fact, several experiments have already reported a tentative detection of the predicted signal, albeit with a significant background contribution. Here, we critically reanalyze the theoretical foundations for the existence of the chiral magnetic waves. We find that the commonly used background-field approximation is not sufficient for treating the waves in hot chiral plasmas in the long-wavelength limit. Indeed, the back-reaction from dynamically induced electromagnetic fields turns the chiral magnetic wave into a diffusive mode. While the situation is slightly better in the strongly-coupled near-critical regime of quark-gluon plasma created in heavy-ion collisions, the chiral magnetic wave is still strongly overdamped due to the effects of electrical conductivity and charge diffusion., Comment: 16 pages, 2 figures. v2: the numerical values of the electrical conductivity are corrected and the results are extended to higher values of the magnetic field. Proceedings of "XIII Quark Confinement and the Hadron Spectrum - Confinement2018", 31 July - 6 August 2018, Maynooth University, Ireland

Boundary conditions for the two-dimensional fermions in ribbons of the hexagonal lattice are studied in the dice model whose energy spectrum in infinite system consists of three bands with one completely flat band of zero energy. Like in graphene the regular lattice terminations are of the armchair and zigzag types. However, there are four possible zigzag edge terminations in contrast to graphene where only one type of zigzag termination is possible. Determining the boundary conditions for these lattice terminations, the energy spectra of pseudospin-1 fermions in dice model ribbons with zigzag and armchair boundary conditions are found. It is shown that the energy levels for armchair ribbons display the same features as in graphene except the zero energy flat band inherent to the dice model. In addition, unlike graphene, there are no propagating edge states localized at zigzag boundary and there are specific zigzag terminations which give rise to bulk modes of a metallic type in dice model ribbons. We find that the existence of the flat zero-energy band in the dice model is very robust and is not affected by the zigzag and armchair boundaries., Comment: 16 pages, 7 figures

The effects of a strain-induced pseudomagnetic field on inter-node spin-triplet superconducting states in Weyl semimetals are studied by using the quasiclassical Eilenberger formalism. It is found that the Cooper pairing with spins parallel to the pseudomagnetic field has the lowest energy among the spin-triplet states and its gap does not depend on the strength of the field. In such a state, both electric and chiral superconducting currents are absent. This is in contrast to the superconducting states with the spins of Cooper pairs normal to the field, which support a nonzero chiral current and are inhibited by the strain-induced pseudomagnetic field. The corresponding critical value of the field, which separates the normal and superconducting phases, is estimated., Comment: 18 pages, 4 multi-panel figures; published version

We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ of the electromagnetic field to the inflaton field $\phi$. We consider the case where the coupling function $f(\phi)$ 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 $\epsilon$ and inflaton energy density, $\rho_{E}\sim \epsilon \rho_{\rm inf}$. 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 $n_{B}=2$ for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below $10^{-22}\,{\rm G}$. It is worth emphasizing that since the effective electric charge of particles $e_{\rm eff}=e/f$ 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 $f\propto a^{\alpha}$ and Ratra-type $f=\exp(\beta\phi/M_{p})$ coupling functions., Comment: 21 pages, 8 figures

By making use of a covariant formulation of the chiral kinetic theory in the relaxation-time approximation, we derive the first-order dissipative hydrodynamics equations for a charged chiral plasma with background electromagnetic fields. We identify the global equilibrium state for a rotating chiral plasma confined to a cylindrical region with realistic boundary conditions. Then, by using linearized hydrodynamic equations, supplemented by the Maxwell equations, we study hydrodynamic modes of magnetized rotating chiral plasma in the regimes of high temperature and high density. We find that, in both regimes, dynamical electromagnetism has profound effects on the spectrum of propagating modes. In particular, there are only the sound and Alfv\'en waves in the regime of high temperature, and the plasmons and helicons at high density. We also show that the chiral magnetic wave is universally overdamped because of high electrical conductivity in plasma that causes an efficient screening of charge fluctuations. The physics implications of the main results are briefly discussed., Comment: 27 pages, 5 figures, published version

We review the theoretical and experimental results connected with the electron states in two-dimensional Dirac systems paying a special attention to the atomic collapse in graphene. Two-electron bound states of a Coulomb impurity are considered too. A rather subtle role of a magnetic field in the supercritical charge problem in graphene is discussed. The electron states in the field of two equally charged impurities are studied and the conditions for supercritical instability to occur are determined. It is shown that the supercriticality of novel type is realized in gapped graphene with two unlikely charged impurities. For sufficiently large charges of impurities, it is found that the wave function of the occupied electron bound state of the highest energy changes its localization from the negatively charged impurity to the positively charged one as the distance between the impurities increases. The specifics of the atomic collapse in bilayer graphene is considered and it is shown that the atomic collapse in this material is not related to the phenomenon of the fall-to-center., Comment: Review Article, 39 pages, 14 figures. arXiv admin note: text overlap with arXiv:1311.0064, arXiv:1401.5992, arXiv:1611.05221, arXiv:1510.02890, arXiv:1406.5770 by other authors

The effects of strains on the low-energy electronic properties of double-Weyl phases are studied in solids and cold-atom optical lattices. The principal finding is that deformations do not couple, in general, to the low-energy effective Hamiltonian as a pseudoelectromagnetic gauge potential. The response of an optical lattice to strains is simpler, but still only one of several strain-induced terms in the corresponding low-energy Hamiltonian can be interpreted as a gauge potential. Most interestingly, the strains can induce a nematic order parameter that splits a double-Weyl node into a pair of Weyl nodes with the unit topological charges. The effects of deformations on the motion of wavepackets in the double-Weyl optical lattice model are studied. It is found that, even in the undeformed lattices, the wavepackets with opposite topological charges can be spatially split. Strains, however, modify their velocities in a very different way and lead to a spin polarization of the wavepackets., Comment: 16 pages, 5 multi-panel figures; published version with minor corrections

The motion of electron wave packets in the Dirac semimetals A$_3$Bi (A=Na,K,Rb) is studied in a semiclassical approximation. Because of the two-fold degeneracy of the Dirac points and a momentum-dependent gap term in the low-energy Hamiltonian, the associated Berry curvature is non-Abelian. In the presence of background electromagnetic fields, such a Berry curvature leads to a splitting of trajectories for the wave packets that originate from different Dirac points and chiral sectors. The nature of the splitting strongly depends on the background fields as well as the initial chiral composition of the wave packets. In parallel electric and magnetic fields, while a well pronounced valley splitting is achieved for any chirality composition, the chirality separation takes place predominantly for the initially polarized states. On the other hand, in perpendicular electric and magnetic fields, there are clear deviations from the conventional Abelian trajectories, albeit without a well-pronounced valley splitting., Comment: 15 pages, 9 multi-panel figures; published version

The nonlocal response of chiral electron fluid in a semi-infinite Weyl semimetal slab with the electric current source and drain attached to its surface is studied by using the consistent hydrodynamic framework. It is found that the Chern-Simons terms lead to a spatial asymmetry of the electron flow and the electric field. Most remarkably, the corresponding topological terms could result in a negative nonlocal resistance. In addition, they give rise to the anomalous Hall current, which is sensitive to the spatial distribution of the electric field in the plane of the contacts and depends on the orientation of the chiral shift., Comment: 17 pages, 11 multi-panel figures; published version with 1 new figure

We reveal that the p-wave superfluid can be realized in a mixture of fermionic and F=1 bosonic gases. We derive a general set of the gap equations for gaps in the s- and p-channels. It is found that the spin-spin bose-fermi interactions favor the p-wave pairing and naturally suppress the pairing in the s-channel. The gap equations for the polar phase of p-wave superfluid fermions are numerically solved. It is shown that a pure p-wave superfluid can be observed in a well-controlled environment of atomic physics., Comment: 6 pages, 2 figures

The spectrum of collective excitations in Weyl materials is studied by using consistent hydrodynamics. The corresponding framework includes the vortical and chiral anomaly effects, as well as the dependence on the separations between the Weyl nodes in energy $b_0$ and momentum $\mathbf{b}$. The latter are introduced via the Chern-Simons contributions to the electric current and charge densities in Maxwell's equations. It is found that, even in the absence of a background magnetic field, certain collective excitations (e.g. the helicon-like modes and the anomalous Hall waves) are strongly affected by the chiral shift $\mathbf{b}$. In a background magnetic field, the existence of the distinctive longitudinal and transverse anomalous Hall waves with a linear dispersion relation is predicted. They originate from the oscillations of the electric charge density and electromagnetic fields, in which different components of the fields are connected via the anomalous Hall effect in Weyl semimetals., Comment: 19 pages, 3 multi-panel figures; published version

The hydrodynamic flow of the chiral electron fluid in a Weyl semimetal slab of finite thickness is studied by using the consistent hydrodynamic theory. The latter includes viscous, anomalous, and vortical effects, as well as accounts for dynamical electromagnetism. The energy and momentum separations between the Weyl nodes are taken into account via the topological Chern-Simons contributions in the electric current and charge densities in Maxwell's equations. When an external electric field is applied parallel to the slab, it is found that the electron fluid velocity has a nonuniform profile determined by the viscosity and the no-slip boundary conditions. Most remarkably, the fluid velocity field develops a nonzero component across the slab that gradually dissipates when approaching the surfaces. This abnormal component of the flow arises due to the anomalous Hall voltage induced by the topological Chern-Simons current. Another signature feature of the hydrodynamics in Weyl semimetals is a strong modification of the anomalous Hall current along the slab in the direction perpendicular to the applied electric field. Additionally, it is found that the topological current induces an electric potential difference between the surfaces of the slab that is strongly affected by the hydrodynamic flow., Comment: 23 pages, 6 multi-panel figures; published version

In this review we discuss a wide range of topological properties of electron quasiparticles in Dirac and Weyl semimetals. Their nontrivial topology is quantified by a monopole-like Berry curvature in the vicinity of Weyl nodes, as well as by the energy and momentum space separations between the nodes. The momentum separation, which is also known as the chiral shift, is one of the key elements of this review. We show that it can be dynamically generated in Dirac materials in a background magnetic field. We also pay a special attention to various forms of interplay between the background electromagnetic fields and the topological characteristics of Dirac and Weyl semimetals. In particular, we discuss their signature features in the transport of the electric and chiral charges, heat, as well as the quantum oscillations associated with the Fermi arc states. The origin of the dissipative transport of the Fermi arc states is critically examined. Finally, a consistent chiral kinetic theory for the description of Weyl semimetals is reviewed and its applications are demonstrated., Comment: 25 pages, 7 multi-panel figures; submitted to the special issue of the Low Temperature Physics journal devoted to the 90th anniversary of A. A. Abrikosov

The complete set of Maxwell's and hydrodynamic equations for the chiral electrons in Weyl semimetals is presented. The formulation of the Euler equation takes into account the explicit breaking of the Galilean invariance by the ion lattice. It is shown that the Chern-Simons (or Bardeen-Zumino) contributions should be added to the electric current and charge densities in Maxwell's equations that provide the information on the separation of Weyl nodes in energy and momentum. On the other hand, these topological contributions do not directly affect the Euler equation and the energy conservation relation for the electron fluid. By making use of the proposed consistent hydrodynamic framework, we show that the Chern-Simons contributions strongly modify the dispersion relations of collective modes in Weyl semimetals. This is reflected, in particular, in the existence of distinctive anomalous Hall waves, which are sustained by the local anomalous Hall currents., Comment: 6+8 pages, 1 figure; published version; a few minor typos in the definitions of $d_z$ and $b_0$ are corrected

The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and thermal Hall effects in the absence of background magnetic fields. Similarly to the anomalous Hall effect, all anomalous thermoelectric coefficients are proportional to the integer topological charge of the Weyl nodes. The dependence of the thermoelectric coefficients on the chemical potential and temperature is also studied., Comment: 20 pages, 13 multi-panel figures; published version

In the low-energy two-band as well as four-band continuum models, we study the supercritical instability in gapped bilayer graphene in the field of a charged impurity. It is found that the screening effects are crucially important in bilayer graphene. If they are neglected, then the critical value for the impurity charge as the lowest-energy bound state dives into the lower continuum tends to zero as the gap $\Delta$ vanishes. If the screened Coulomb interaction is considered, then the critical charge tends to a finite value for $\Delta \to 0$. The different scalings of the kinetic energy of quasiparticles and the Coulomb interaction with respect to the distance to the charged impurity ensure that the wave function of the electron bound state does not shrink toward the impurity as its charge increases. This results in the absence of the fall-to-center phenomenon in bilayer graphene although the supercritical instability is realized., Comment: 15 pages, 6 figures

By using the exact solutions of the Weyl equation in a constant magnetic field, the equal-time Wigner function for magnetized chiral plasma is derived. It is found that the dependence of the Wigner function on the component of momentum along the magnetic field is asymmetric and is correlated with the fermion chirality. Such a dependence is principal for reproducing the correct chiral magnetic and chiral separation effects. In the lowest Landau level approximation, the equation for the equal-time Wigner function in a strong magnetic field is derived. By making use of this equation, it is found that the longitudinal collective modes in a strong magnetic field are gapped plasmons whose gap is determined by the magnetic field. Unlike the ordinary magnetic field, an axial one allows for the dispersion law of the collective excitations asymmetric in the wave vector. The thermoelectric phenomena for chiral fermions in strong magnetic and axial magnetic fields are studied and the corresponding transport coefficients are calculated., Comment: 32 pages, 3 multi-panel figures; published version

For a generic lattice Hamiltonian of the electron states in Weyl materials, we calculate analytically the chiral (or, equivalently, valley) charge and current densities in the first order in background electromagnetic and strain-induced pseudoelectromagnetic fields. We find that the chiral response induced by the pseudoelectromagnetic fields is not topologically protected. Although our calculations reproduce qualitatively the anomalous chiral Hall effect, the actual result for the conductivity depends on the definition of the chirality as well as on the parameters of the lattice model. In addition, while for the well- separated Fermi surfaces surrounding the individual Weyl nodes the current induced by the magnetic field coincides almost exactly with the current of the chiral separation effect in linearized models, there are clear deviations when the Fermi surfaces undergo the Lifshitz transition. In general, we find that all chiral response coefficients vanish at large chemical potential., Comment: 14 pages, 6 multi-panel figures; published version