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Li B.,Chongqing University | Lin D.-H.,JD Duz Institute for Superconductivity
International Journal of Modern Physics B | Year: 2013

The magnetic penetration depth formula in MgB2 is more complex than that in BCS superconductors due to the existence of exotic two energy gap in MgB2. A new simplified relationship between the penetration depth and temperature is presented, which is derived from the two-fluid model by means of numerical fitting method, and the physical meaning is relatively clear. © 2013 World Scientific Publishing Company. Source


Fan J.D.,Chongqing Academy of Science and Technology | Fan J.D.,JD Duz Institute for Superconductivity | Fan J.D.,Southern University and A&M College | Malozovsky Y.M.,Chongqing Academy of Science and Technology | Malozovsky Y.M.,JD Duz Institute for Superconductivity
Journal of Superconductivity and Novel Magnetism | Year: 2010

We study the possibility of multiple paring for more than two particles or two quasiparticles in terms of the BCS model. We consider the multiple pairs of particles in terms of the BCS Hamiltonian for two different ground states: in a quiescent Fermi sea model and in the BCS ground state. In case of quasiparticles, we consider the multiple quasiparticle pairs in terms of the BCS ground state only. Although there is no interaction between Cooper's type pairs in terms of the BCS Hamiltonian, yet we have shown that four particles or two/four quasiparticles can be paired and form a bound state in the singlet state with just twice the bound state energy of a single Cooper's pair. In the case of a pair of quasiparticles, the bound state exists as a result of the large quasiparticle density of states and the residual interaction between two quasiparticles which is described by the off-diagonal terms in the BCS Hamiltonian written in terms of quasiparticles. In the case of four particles, the bound state exists only as a result of the Pauli principle and the sharp Fermi edge. In the BCS model, a quartet of bound fermions indeed represents a boson, and the many-particle system of the composite of bosons can undergo the conventional Bose condensation of a boson gas. The temperature of the Bose condensation corresponds to the conventional temperature of Bose condensation for non-interacting bosons where each boson has quadruple mass (4m) and the boson density is one-quarter (n/4) of fermions density. A similar conclusion remains valid in the case of the particle-hole resonance in a quiescent Fermi sea. We have shown that in the particle-hole channel there exists the multiple particle-hole resonance for four particles and four holes in a quiescent Fermi sea model similar to the case of two particles and two holes resonance. We have shown that there is no particle-hole resonance in the case of the BCS ground state because there is no hole-type of excitations in the BCS ground state. Nevertheless we have shown that in the BCS ground state quasiparticle pairs can form bound pairs similar to the Cooper's pair of particles due to the off-diagonal terms in the BCS Hamiltonian. The bound pairs of quasiparticles exist as a result of extremely large quasiparticle density of states. We also discuss the formation of a quartet of quasi-particles and the Bose condensation of the multiple pairs of quasiparticles. © Springer Science+Business Media, LLC 2010. Source


Malozovsky Y.M.,Chongqing Academy of Science and Technology | Malozovsky Y.M.,JD Duz Institute for Superconductivity | Fan J.D.,Chongqing Academy of Science and Technology | Fan J.D.,JD Duz Institute for Superconductivity | Fan J.D.,Southern University and A&M College
Journal of Superconductivity and Novel Magnetism | Year: 2010

We study the effect of quantum and classical phase fluctuations on the phase transitions in the system of Josephson-junction arrays. We employed a variational method for calculating the Gaussian type fluctuation of the phase in the Josephson-junction array lattice systems without and with an external magnetic field. We investigate the spectrum of collective excitations and the effects of collective excitations on the transport properties of Josephson-junction arrays. We showed that the Hamiltonian for the lattice system of the Josephson junction is the same as the Hamiltonian for the classical or quantum two-dimensional interacting rotators. We also showed that the dynamics of fluctuations of the phase in the lattice system of Josephson junction is very similar to the lattice dynamics of the lattice in crystals. We also showed that in the lattice system of Josephson junctions there is the collective acoustic mode similar to the acoustic mode in the crystal lattice, and this mode may lead to the dissipation of the Josephson current in the superconducting array of Josephson junctions. The speed of sound of the collective acoustic mode of the phase fluctuation depends on the Josephson coupling energy and the Coulomb charging energy. The contribution of the collective acoustic mode to the low temperature specific heat is the same as the contribution of the acoustic phonons to the specific heat of crystals. We also discuss the future development of results and their application. © Springer Science+Business Media, LLC 2010. Source


Malozovsky Y.M.,JD Duz Institute for Superconductivity | Fan J.D.,JD Duz Institute for Superconductivity | Fan J.D.,Chongqing Academy of Science and Technology CAST | Fan J.D.,Southern University and A&M College
Journal of Superconductivity and Novel Magnetism | Year: 2010

We consider the formation of polarons in three different situations: (1) the formation of a polaron in the crystal due to the electron-phonon interaction, (2) the formation of a polaron in the presence of a quiescent Fermi sea, and the (3) the formation of polarons in an interacting Fermi gas, and Fermi liquids, including charge and spin polarization or magnetic polarization. We develop the perturbation diagram approach to the polaron problem and show that the series of maximally crossed and repeated one-phonon (Tamm-Dancoff approximation) diagrams leads to the series of the ladder diagrams which is equivalent to the well-known Bethe-Salpeter equation. We show that the polaron mass cannot exceed the triple mass of an electron and the bound state for the electron-optical phonon interaction exists for any strength of the electron-phonon coupling constant in 3D, and the bound state always exists in 2D case even for the electron-acoustic phonon interaction. We consider the polaron effect in the presence of a quiescent Femi sea and show that the polaron effect leads both to the appearance of the insulating gap and the formation of the quasiparticles with the dispersion law similar to the quasiparticle spectrum in the BCS model of superconductivity. We show that the polarization effect in the case of interacting Fermi gas leads to the polaron caused by the exchange-correlation hole and the electron spectrum again is an insulating with the dispersion law of quasiparticles similar to the BCS model. We show that the interaction potential in polaronic effect in the case of Femi liquid is the same as the Landau interaction function for Fermi liquid. Moreover, we also consider spin and magnetic polaronic effects in Fermi liquids. We show that in the case of repulsive Hubbard model in the spin channel appears the spin gap with the spectrum of quasiparticles again similar to the BCS model of quasiparticles. © Springer Science+Business Media, LLC 2010. Source


Fan J.D.,Chongqing Academy of Science and Technology | Fan J.D.,JD Duz Institute for Superconductivity | Malozovsky Y.M.,JD Duz Institute for Superconductivity | Malozovsky Y.M.,Southern University and A&M College
International Journal of Modern Physics B | Year: 2013

In terms of an exact equation for the thermodynamic potential due to interaction between two particles and based on Green's function method; we have derived the Landau expansion of the thermodynamic potentials in terms of the variation of the quasiparticle distribution function. We have also derived the expansion of the thermodynamic potential in terms of the variation of an exact single particle (not quasiparticles), this derivations lead to the relationship between the interaction function for two quasiparticles and the interaction energy between two particles as shown. Further, in terms of the four-point vertex part we are led to the Pauli exclusion principle. © 2013 World Scientific Publishing Company. Source

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