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We calculate optical conductivity for bilayer dice lattices whose commensurate stackings and effective models in the vicinity of band-crossing points were considered in our previous work (arXiv:2303.01452). The inter-band 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 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., 21 pages, 11 multi-panel figures

We introduce and classify nonequivalent commensurate stackings for bilayer dice or $\mathcal{T}_3$ lattice. For each of the four possible stackings, an effective low-energy model is derived. Although the energy spectrum remains always gapless with three bands interesting at the same point, depending on the stacking, different types of quasiparticle spectra arise. They include those with flat, tilted, anisotropic semi-Dirac, and three-fold-corrugated energy bands. We use the derived 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., 16 pages, 9 multi-panel 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., 9 pages, 8 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 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

In this mini review, we consider chiral asymmetry in the normal ground state of magnetized relativistic matter in the NJL model with local four-fermion interaction and QED. It is shown that the chiral shift parameter associated with the relative shift of the longitudinal momenta (along the direction of the magnetic field) in the dispersion relations for opposite chirality fermions is dynamically generated in the normal ground state. This contribution affects fermions in all Fermi levels, including those around the Fermi surface, and contributes to the non-dissipative axial current taking place in relativistic matter in a magnetic field. The chiral asymmetry of the normal ground state in QED matter in a magnetic field is characterized by an additional chiral structure. It formally looks like that of the chiral chemical potential, but is an odd function of the longitudinal component of momentum along the magnetic field. The origin of this parity-even chiral structure is directly connected with the long-range character of the QED interaction. The leading radiative corrections to the chiral separation effect in QED are calculated, and the form of the Fermi surface in the weak magnetic field is determined., Розглянуто кiральну асиметрiю нормального основного стану релятивiстської матерiї у зовнiшньому магнiтному полi в Намбу–Йона-Лазiнiо моделi з локальною чотирьох фермiонною взаємодiєю i квантовiй електродинамiцi. Показано, що параметр кiрального зсуву, який пов’язаний з вiдноснимзсувом поздовжних iмпульсiв (направлених вздовж магнiтного поля) в законах дисперсiї фермiонiв протилежних кiральностей динамiчно генерується в нормальному основному станi системи. Цей внесок має мiсце для фермiонiв на всiх рiвнях Ландау, включаючи тi, що знаходяться поблизу поверхнi Фермi, i дає внесок у бездисипативний аксiальний струм, що має мiсце в релятивiстськiй матерiї у зовнiшньому магнiтному полi. Кiральна асиметрiя нормального основного стану в квантовоелектродинамiчнiй матерiї у зовнiшньому магнiтному полi характеризується додатковою кiральною структурою. Вона формально виглядає як кiральний хiмiчний потенцiал, однак є непарною функцiєю поздовжної компоненти iмпульсу, яка направлена вздовж магнiтного поля. Причина появи цiєї кiральної структури, яка зберiгає парнiсть, прямо пов’язана з далекодiючим характером квантовоелектродинамiчної взаємодiї. Обчислено лiдируючi радiацiйнi поправки для кiрального ефекту роздiлення в квантовiй електродинамiцi i визначено форму поверхнi Фермi в слабкому магнiтному полi.

The weak interactions of neutrinos with charged fermions in a magnetized dense relativistic matter are shown to generate a non-zero chiral shift parameter for neutrinos that produces their asymmetric distribution in the momentum space in the equilibrium state. It is found that this asymmetry is too small in order to explain the largest pulsar velocities observed. The hot-spot scenario involving the topological current or some other mechanism of the hot spot formation is suggested, and it is argued that this scenario can provide the necessary large pulsar kicks., Показано, що внаслiдок слабкої взаємодiї нейтрино iз зарядженими частинками у густiй релятивiстськiй плазмi iз iндукованим за рахунок взаємодiї параметром кiрального зсуву у зовнiшньому магнiтному полi нейтрино мають асиметричний розподiл в iмпульсному просторi у рiвноважному станi. Знайдено, що вiдповiдна асиметрiя є дуже слабкою для того, щоб пояснити найвищi швидкостi пульсарiв, якi спостерiгаються. Запропоновано сценарiй для гарячих точок, який пов’язаний з топологiчним струмом або iншим механiзмом їх утворення, i аргументовано, що цей сценарiй може забезпечити генерацiю потрiбних великих швидкостей пульсарiв.

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., 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 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 surface Fermi arc states in $Z_2$ Weyl semimetals $A_3 Bi$ (A=Na, K, Rb) are studied by employing a continuum low-energy effective model. It is shown that the surface Fermi arc states can be classified with respect to the ud-parity symmetry. Because of the symmetry, the arcs come in mirror symmetric pairs. The effects of symmetry breaking terms on the structure of the Fermi arcs are also studied. Among other results, we find at least two qualitatively different types of the surface Fermi arcs. The arcs of the first type link disconnected sheets of the bulk Fermi surface, while arcs of the second type link different points of the same bulk Fermi surface sheet., Comment: 17 pages, 4 multi-panel figures; v2: published version with minor corrections, new references and a slightly reorganized text

We demonstrate that the physical reason for the nontrivial topological properties of Dirac semimetals $A_3 Bi$ (A=Na,K,Rb) is connected with a discrete symmetry of the low-energy effective Hamiltonian. By making use of this discrete symmetry, we argue that all electron states can be split into two separate sectors of the theory. Each sector describes a Weyl semimetal with a pair of Weyl nodes and broken time-reversal symmetry. The latter symmetry is not broken in the complete theory because the time-reversal transformation interchanges states from different sectors. Our findings are supported by explicit calculations of the Berry curvature. In each sector, the field lines of the curvature reveal a pair of monopoles of the Berry flux at the positions of Weyl nodes. The $Z_2$ Weyl semimetal nature is also confirmed by the existence of pairs of surface Fermi arcs, which originate from different sectors of the theory., Comment: 6 pages, 2 figures; published version with minor changes and an extended discussion

For bilayer graphene in a magnetic field at the neutral point, we derive and solve a full set of gap equations including all Landau levels and taking into account the dynamically screened Coulomb interaction. There are two types of the solutions for the filling factor $\nu=0$: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field $E_{\perp}$, and (ii) a layer-polarized solution, which is the ground state at large values of $E_{\perp}$. The critical value of $E_{\perp}$ that determines the transition point is a linear function of the magnetic field, i.e., $E_{\perp,{\rm cr}}=E_{\perp}^{\rm off}+a B$, where $E_{\perp}^{\rm off}$ is the offset electric field and $a$ is the slope. The offset electric field and energy gaps substantially increase with the inclusion of dynamical screening compared to the case of static screening. The obtained values for the offset and the energy gaps are comparable with experimental ones. The interaction with dynamical screening can be strong enough for reordering the levels in the quasiparticle spectrum (the $n=2$ Landau level sinks below the $n=0$ and $n=1$ ones)., Comment: 20 pages, 9 multi-panel figures; final published version with a more detailed comparison of the results with the experimental data

For bilayer graphene in a magnetic field at the neutral point, we derive and solve a full set of gap equations including all Landau levels and taking into account the dynamically screened Coulomb interaction. There are two types of the solutions for the filling factor $��=0$: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field $E_{\perp}$, and (ii) a layer-polarized solution, which is the ground state at large values of $E_{\perp}$. The critical value of $E_{\perp}$ that determines the transition point is a linear function of the magnetic field, i.e., $E_{\perp,{\rm cr}}=E_{\perp}^{\rm off}+a B$, where $E_{\perp}^{\rm off}$ is the offset electric field and $a$ is the slope. The offset electric field and energy gaps substantially increase with the inclusion of dynamical screening compared to the case of static screening. The obtained values for the offset and the energy gaps are comparable with experimental ones. The interaction with dynamical screening can be strong enough for reordering the levels in the quasiparticle spectrum (the $n=2$ Landau level sinks below the $n=0$ and $n=1$ ones)., 20 pages, 9 multi-panel figures; final published version with a more detailed comparison of the results with the experimental data

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $��=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane $(\tilde��_0,B)$, where $\tilde��_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, $��E\sim 10 B[T]K, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented., 14 pages, 4 figures

It is shown that the classical motion of massive particles in hyperbolic spaces $H^D$ has a bounded character in $D-1$ coordinates. Studying the Dirac equation, it is found that a bounded character of the classical motion corresponds to the effective dimensional reduction $D+1 \to 1+1$ for fermions in the infrared region in the quantum problem. This effective dimensional reduction leads to the zero critical value of coupling constant for dynamical symmetry breaking in hyperbolic spaces., Comment: 6 pages, submitted to Ukr. Phys. Journal

A method for calculation of the DWSG coefficients for operators in spaces with metric incompatible with connection is suggested based on a generalization of the pseudodifferential operators technique. By using the proposed method, the lowest DWSG coefficients are calculated for minimal operators of the second and fourth order and for nonminimal operators of the type $H^{\mu\nu} = - g^{\mu\nu} g_{\alpha\beta}\nabla^{\alpha}\nabla^{\beta} + a\nabla^{\mu}\nabla^{\nu} + X^{\mu\nu}$ in spaces with metric incompatible with connection., Comment: 13 pages, LaTeX, no figures

A method is suggested for the calculation of the DeWitt-Seeley-Gilkey (DWSG) coefficients for the operator $\sqrt{-\nabla^2 + V(x)}$ basing on a generalization of the pseudodifferential operator technique. The lowest DWSG coefficients for the operator $\sqrt{-\nabla^2} + V(x)$ are calculated by using the method proposed. It is shown that the method admits a generalization to the case of operators of the type $(-\nabla^2 + V(X))^{1/{\rm m}}$, where m is an arbitrary rational number. A more simple method is proposed for the calculation of the DWSG coefficients for the case of strictly positive operators under the sign of root. By using this method, it is shown that the problem of the calculation of the DWSG coefficients for such operators is exactly solvable. Namely, an explicit formula expressing the DWSG coefficients for operators with root through the DWSG coefficients for operators without root is deduced., 17 pages, LaTeX, no figures

It is shown that in the P,T-invariant model with the mixed Chern-Simons term the interaction of charge carriers leads to effective changing of their statistics, which depends on distance between them. In particular, in the limit of large distances fermions effectively turn into bosons., 8 pages, LATEX, Kiev Institute for Theoretical Physics preprint ITP-93-16E

We study the Dirac equation in two spatial dimensions for quasiparticles in a potential well in graphene in a homogeneous magnetic field. It is shown that, at some critical value of the potential strength, the lowest empty energy level crosses a filled negative energy level leading to the instability of the system. The critical potential strength decreases with decrease of a quasiparticle gap and becomes zero in the gapless case. It is argued that the magnetically driven instability of a charged center can be considered as a quantum mechanical counterpart of the magnetic catalysis phenomenon in graphene., Досліджено рівняння Дірака у двовимірному просторі для квазічастинок в потенційній ямі у постійному магнітному полі в графені. Показано, що для деякого критичного значення потенціалу ями найнижчий незаповнений енергетичний рівень перетинає межу заповнених електронних станів із від'ємною енергією, що приводить до нестабільності системи. Критичний потенціал зменшується зі зменшенням щілини квазічастинок і дорівнює нулю у безщілинному випадку. Аргументовано, що магнітно індукована нестабільність зарядженого центра може розглядатися як квантово-механічний аналог явища магнітного каталізу в графені.

In the tight-binding approximation, we take into account the next-to-nearest neighbor hopping in graphene that leads to nonrelativistic-like corrections in its low energy spectrum. The electronic density of states in a magnetic field is found and the fan diagram is plotted, which interpolates between those for the relativistic and nonrelativistic limiting cases. It is shown that the Berry phase for the system under consideration coincides exactly with its value for the relativistic system.

We analyze the excitonic instability in graphene by solving the Bethe–Salpeter equation for the electron-hole bound state. In the supercritical regime, we show that this equation has a tachyon in its spectrum. We argue that the excitonic instability is resolved through the formation of an electron-hole condensate leading to the gap (mass) generation in the quasiparticle spectrum. Such a gap could be observed in a free standing clean graphene. За допомогою рiвняння Бете–Солпiтера для електрон-дiркового зв’язаного стану дослiджено проблему екситонної нестабiльностi в графенi. Показано, що для надкритичної константи зв’язку спектр має тахiоннi розв’язки. Екситонна нестабiльнiсть приводить до формування електрон-дiркового конденсату та щiлини у спектрi квазiчастинок. Ця щiлина може бути спостережена у графенi без домiшок.

We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic catalysis dynamics necessarily coexist (the latter have the form of Dirac masses and correspond to excitonic condensates). This feature of graphene could lead to important consequences, in particular, for the existence of gapless edge states. Solutions of the gap equation corresponding to recently experimentally discovered novel plateaus in graphene in strong magnetic fields are described., 5 pages, no figures, v.2: to match published version