Alexei Abrikosov

Methods of quantum field theory in statistical physics

Abrikosov, Gorkov, Dzyaloshinski, Methods of quantum field theory in statistical physics Fetter, Walecka, Quantum theory of many-particle systems T. Schaefer, Quark Matter, hep-ph/0304281. J. Kogut, M. Stephanov, The Phases of QCD, Cambridge University Press (2004). K. Rajagopal, F. Wilczek, The Condensed Matter Physics of QCD, hep-ph/0011333. J. Lattimer and M. Prakash, The Physics of Neutron Stars, astro-ph/0405262. D. Kaplan, Five lectures on effective field theory, nucl-th/0510023.

Experimentally observed extended saddle point singularity in the energy spectrum of YBa2Cu3O6.9 and YBa2Cu4O8 and some of the consequences

Abstract Angle-resolved photoemission experiments show that the high temperature superconductors YBa 2 Cu 3 O 6.9 and YBa 2 Cu 4 O 8 have a spectral density which exhibits an “extended” saddle point singularity along the Γ-Y symmetry direction, centered on the Y point. This, in turn, leads to a van Hove singularity in the density of states with a divergence stronger than the well-known logarithmic one. We examine the consequences of this singularity in several limiting cases on the superconducting transition temperature, the ratio 2Δ(0)/ T c , and the isotope effect. We conclude that this singularity alone, although it can possibly lead to sufficiently high transition temperatures and a vanishingly small isotope effect, does not explain the ratio of 2Δ(0)/ T c ∼6 observed experimentally.

Conductivity of quasi-one-dimensional metal systems

Abstract A new technique is constructed for treatment of one-dimensional and quasione-dimensional metal systems with random impurities. The technique is applied for calculation of conductivity in several systems (see contents). The influence of impurity scattering on electron pairing is discussed (§ 3).

The magnetic properties of superconducting alloys

Abstract A new explanation is proposed for the magnetic properties of superconducting alloys based on the theory of G inzburg and L andau . (1) The structure of the penetrating field is found for a superconductor and the relationship between induction and field strength. The findings are compared with experimental results.

The paradox with the static conductivity of a one-dimensional metal

Abstract The method of averaging over a Gaussian random potential developed in [7] is applied for calculation of the probability distribution function of the resistance for arbitrary length of the sample and any value of the resistance. Averages of positive and negative powers of the resistance are found as well as average relative fluctuations of conductance, resistance and its log. It is demonstrated that formulas obtained by means of scale transformation [2] reproduce correctly qualitative features of these characteristics but quantitatively differ rather appreciably from the exact values.

On the theory of the Kondo effect

The Kondo effect is investigated by methods developed in the theory of fields with strong coupling. Renormalizability relations analogous to the scaling laws in the theory of second-order phase transitions are found. The behavior of the scattering amplitude of an electron by an impurity is analyzed as a function of the electron energy. Formulas are derived for the resistance as a function of the temperature and for the magnetic moment as a function of the magnetic field and temperature. For the antiferromagnetic interaction sign the resistance tends to a constant and the magnetic moment to zero asT → 0 according to power laws with universal exponents that depend only on the spin of the impurity. For sufficiently large spin the susceptibility tends to infinity asT → 0.

Influence of the gap anisotropy on superconducting properties

Abstract Some consequences of the gap anisotropy are considered: the ratio 2Δ(0)/ T c , the shape of the tunneling conductance curve, and the influence of impurities on T c . It is demonstrated that anisotropy could be the cause of properties usually attributed to other origins.

Weakly screened Coulomb interaction and properties of HTSC's

Abstract In order to explain the anisotropy of the energy gap observed in direct photoemission experiments on the basis of the “extended saddle-point singularities” in the electron-energy spectrum lying close to the Fermi level, the assumption is made that the Coulomb interactions are weakly screened, i.e. the Debye screening radius is much larger than the lattice period; this makes the electron interaction anisotropic. Another consequence of this assumption is that at low temperatures the normal-state resistivity is mostly defined by electron-electron scattering, and its temperature dependence is p ∝ T . Some aspects of the model are discussed.

Superconductivity in a quasi-one-dimensional metal with impurities

The influence of ordinary impurities on the superconducting transition is studied in a quasi-one-dimensional metal. Superconductivity is considered in a self-consistent field (BCS) approximation. It is shown that, depending on the properties of the electron-electron interaction, singlet or triplet superconductivity may appear. Impurities do not influence the critical temperature in the singlet case but destroy the triplet superconductivity. The concentration dependence of the critical temperature in the triplet case is in qualitative agreement with the experimental results for irradiated quasi-1d superconductors; therefore triplet superconductivity may be supposed in these systems. The superconducting current is calculated in the vicinity of the transition temperature and hence the longitudinal dielectric constant for not too high frequencies.

Gapless state of bismuth-type semimetals

AbstractIt is shown that in semimetals of the bismuth type under certain conditions the direct energy gap in the vicinity of theL point of the Brillouin zine can be closed. The energy spectrum is found for values of the parameters near the gap annihilation point (γ=γt0):