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We study the chiral separation and chiral magnetic effects in a slab of Dirac semimetal of finite thickness, placed in a constant magnetic field perpendicular to its surfaces. We utilize the Bogolyubov boundary conditions with a large Dirac mass (band gap) outside the slab. We find that, in a finite-thickness slab, the axial current density is induced by helicity-correlated standing waves and, as a consequence, is quantized. The quantization is seen in its stepped-shape dependence on the fermion chemical potential and a sawtooth-shape dependence on the thickness of the slab. In contrast to a naive expectation, there is no chiral charge accumulation anywhere in the bulk or at the boundaries of the semimetal. In the same slab geometry, we also find that a nonzero chiral chemical potential induces no electric current, as might have been expected from the chiral magnetic effect. We argue that this outcome is natural and points to the truly nonstatic nature of the latter. By taking into account a nonzero electric field of a double layer near the boundaries of the slab, we find that the low-energy modes under consideration satisfy the continuity equation for axial current density without the anomalous term. [ABSTRACT FROM AUTHOR]

We reveal a new type of supercritical behavior in gapped graphene with two oppositely charged impurities by studying the two-dimensional Dirac equation for quasiparticles with the Coulomb potential regularized at small distances accounting the lattice effects. By utilizing the variational Galerkin-Kantorovich method, we show that for supercritical electric dipole the wave function of the electron bound state changes its localization from the negatively charged impurity to the positively charged one as the distance between the impurities changes. Such a migration of the wave function corresponds to the electron and hole spontaneously created from the vacuum in bound states screening the positively and negatively charged impurities of the supercritical electric dipole, respectively. We generalize our results to a particle-hole asymmetric case, where the charges of impurities differ in signs and absolute values, and demonstrate that the necessary energetic condition for the supercriticality of novel type to occur is that the energy levels of single positively and negatively charged impurities traverse together the energy distance separating the upper and lower continua. The robustness of the supercriticality of novel type is confirmed by the study of an exactly solvable one-dimensional problem of the Dirac equation with the square well and barrier potential modeling an electric-dipole potential. [ABSTRACT FROM AUTHOR]

The surface Fermi arc states in ℤ2 Weyl semimetals A3Bi (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. [ABSTRACT FROM AUTHOR]

The gap equation for Dirac quasiparticles in monolayer graphene in constant magnetic and pseudomagnetic fields, where the latter is due to strain, is studied in a low-energy effective model with contact interactions. By analyzing solutions of the gap equation, the phase diagram of the system in the plane of pseudomagnetic and parallel magnetic fields is obtained in the approximation of the lowest Landau level. The three quantum Hall states, ferromagnetic, antiferromagnetic, and canted antiferromagnetic, are realized in different regions of the phase diagram. It is found that the structure of the phase diagram is sensitive to signs and values of certain four-fermion interaction couplings which break the approximate spin-valley SU(4) symmetry of the model. [ABSTRACT FROM AUTHOR]

The Weyl semimetal surface is modeled by applying the Bogolyubov boundary conditions, in which the quasiparticles have an infinite Dirac mass outside the semimetal. For a Weyl semimetal shaped as a slab of finite thickness, we derive an exact spectral equation for the quasiparticle states and obtain the spectrum of the bulk as well as surface Fermi arc modes. We also show that, in the presence of the magnetic field, the separation between Weyl nodes in momentum space and the length of the Fermi arcs in the reciprocal space are affected by the interactions. As a result, we find that the period of oscillations of the density of states related to closed magnetic orbits involving Fermi arcs has a nontrivial dependence on the orientation of the magnetic field projection in the plane of the semimetal surface. We conclude that the momentum-space separation between Weyl nodes and its modification due the interaction effects in the magnetic field can be measured in the experimental studies of quantum oscillations. [ABSTRACT FROM AUTHOR]

In the continuum low-energy model, we calculate the one-loop dynamical polarization functions in ABC-stacked (rhombohedral) n-layer graphene in a magnetic field. Neglecting the trigonal warping effects, they are derived as functions of wave vector and frequency at finite chemical potential, temperature, band gap, and the width of Landau levels. The analytic results are given in terms of digamma functions and generalized Laguerre polynomials and have the form of double sums over Landau levels. Various particular limits for polarization functions (static, clean, etc.) are discussed. The intralayer and interlayer screened Coulomb potentials are numerically calculated as functions of momentum and frequency. [ABSTRACT FROM AUTHOR]

By making use of the Kubo formula, we calculate the conductivity of Dirac and Weyl semimetals in a magnetic field. We find that the longitudinal (along the direction of the magnetic field) magnetoresistivity is negative at sufficiently large magnetic fields for both Dirac and Weyl semimetals. The physical reason of this phenomenon is intimately connected with the dimensional spatial reduction 3 → 1 in the dynamics of the lowest Landau level. The off-diagonal component of the transverse (with respect to the direction of the magnetic field) conductivity in Weyl semimetals contains an anomalous contribution directly proportional to the momentum-space separation between the Weyl nodes. This contribution comes exclusively from the lowest Landau level and, as expected, is independent of the temperature, chemical potential, and magnetic field. The other part of the off-diagonal conductivity is the same as in Dirac semimetals and is connected with a nonzero density of charge carriers. The signatures for experimental distinguishing Weyl semimetals from Dirac ones through the measurements of conductivity are discussed. [ABSTRACT FROM AUTHOR]

We calculate the dynamical polarization function and solve a self-consistent gap equation in the random phase approximation in undoped ABC-stacked n-layer graphene. We find that the gap is maximal in trilayer graphene and decreases monotonously for n ⩾ 4 because the effects of screening in the gap equation win over those connected with the flattening of electron bands as n increases. [ABSTRACT FROM AUTHOR]

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 Rcr 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 Rcr separating the supercritical (R < Rcr) and subcritical (R > Rcr) regimes is carried out. It is shown that the critical distance Rcr 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. [ABSTRACT FROM AUTHOR]

We study the phase diagram of a Dirac semimetal in a magnetic field at a nonzero charge density. It is shown that there exists a critical value of the chemical potential at which a first~order phase transition takes place. At subcritical values of the chemical potential the ground state is a gapped state with a dynamically generated Dirac mass and a broken chiral symmetry. The supercritical phase is the normal (gapless) phase with a nontrivial chiral structure: it is a Weyl semimetal with a pair of Weyl nodes for each of the original Dirac points. The nodes are separated by a dynamically induced chiral shift. The direction of the chiral shift coincides with that of the magnetic field and its magnitude is determined by the quasiparticle charge density, the strength of the magnetic field, and the strength of the interaction. The rearrangement of the Fermi surface accompanying this phase transition is described. [ABSTRACT FROM AUTHOR]

In bilayer graphene, the phase diagram in the plane of a strain-induced bare nematic term N0 and a top-bottom gates voltage imbalance U0 is obtained by solving the gap equation in the random-phase approximation. At nonzero M0 and U0, the phase diagram consists of two hybrid spin-valley symmetry-broken phases with both nontrivial nematic and mass-type order parameters. The corresponding phases are separated by a critical line of first- and second-order phase transitions at small and large values of Mo, respectively. The existence of a critical end point where the line of first-order phase transitions terminates is predicted. For N0 = 0, a pure gapped state with a broken spin-valley symmetry is the ground state of the system. As N0 increases, the nematic order parameter increases, and the gap weakens in the hybrid state. For U0 = 0, a quantum second-order phase transition from the hybrid state into a pure gapless nematic state occurs when the strain reaches a critical value. A nonzero U0 suppresses the critical value of the strain. The relevance of these results to recent experiments is briefly discussed. [ABSTRACT FROM AUTHOR]

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 v = 0: (i) a spin-polarized type solution, which is the ground state at small values of perpendicular electric field E&bottom;, and (ii) a layer-polarized solution, which is the ground state at large values of E&bottom;. The critical value of E&bottom; that determines the transition point is a linear function of the magnetic field, i.e., E&bottom;,cr = Eoff&bottom; + aB, where Eoff&bottom; 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). [ABSTRACT FROM AUTHOR]

Broken-symmetry quantum Hall (QH) states with filling factors v = 0, ± 1, ± 2, ± 3 in the lowest Landau level in bilayer graphene are analyzed by solving the gap equation in the random phase approximation. It is shown that in the plane of electric and magnetic fields, the critical line, which separates the spin- and layer-polarized phases at v = 0, extends to the v = ±1 QH states. The amplitudes of the gaps in the v = ± 1, ± 3, and v = ± 2 QH states are significantly smaller than the amplitude of the v = 0 gap, due to the separate filling of the n = 0 and n = 1 orbital Landau levels and the negative contribution of the Hartree term, respectively. It is shown that those values of the external electric field where the conductance is not quantized correspond to the minima of the gaps. [ABSTRACT FROM AUTHOR]

It is shown that a magnetic field dramatically affects the problem of supercritical charge in graphene, making any charge in gapless theory supercritical. The cases of a radially symmetric potential well and a Coulomb center in a homogeneous magnetic field are considered. The local density of states and polarization charge density are calculated in the first order of perturbation theory. It is argued that the magnetically induced instability of the supercritical Coulomb center can be considered as a quantum-mechanical counterpart of the magnetic catalysis phenomenon in graphene. [ABSTRACT FROM AUTHOR]

We demonstrate that the physical reason for the nontrivial topological properties of Dirac semimetals A3Bi (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 Z2 Weyl semimetal nature is also confirmed by the existence of pairs of surface Fermi arcs, which originate from different sectors of the theory. [ABSTRACT FROM AUTHOR]

We study the influence of different kinds of gaps in a quasiparticle spectrum on longitudinal and transverse optical conductivities of bilayer graphene. An exact analytical expression for magneto-optical conductivity is derived using a low-energy two-band Hamiltonian. We consider how the layer asymmetry gap caused by a bias electric field and a time-reversal symmetry breaking gap affect the absorption lines. The limit of zero magnetic field is then analyzed for an arbitrary carrier density in the two-band model. For a neutral bilayer graphene, the optical Hall and longitudinal conductivities are calculated exactly in the four-band model with four different gaps and zero magnetic field. It is shown that two different time-reversal symmetry breaking states can be distinguished by analyzing the dependence of the optical Hall conductivity on the energy of photon. These time-reversal symmetry breaking states are expected to be observed experimentally via optical polarization rotation either in the Faraday or Kerr effects. We analyze a possibility of such an experiment for a free-standing graphene, graphene on a thick substrate, and graphene on a double-layer substrate. [ABSTRACT FROM AUTHOR]