We study the effects of low-energy nodal quasiparticles on the classicall phase fluctuations in a
two-dimensional d-wave superconductor. The singularities of the phase-only action at T->0 are removed
in the presence of disorder, which justifies using an extended classical *XY*-model to
describe phase fluctuations at low temperatures.
We present a Monte Carlo study of the helicity moduli of an
anisotropic classical three-dimensional (3D) XY-model of
YBCO in superconducting state. It is found that both the
$ab$-plane and the $c$-axis helicity moduli, which are
proportional to the inverse square of the corresponding
magnetic field penetration depth, vary linearly with
temperature at low temperatures. The result for the
$c$-axis helicity modulus is in disagreement with the
experiments on high quality samples of YBCO. Thus we
conclude that purely classical phase fluctuations of
the superconducting order parameter cannot account for
the observed $c$-axis electrodynamics of YBCO.
*J. Phys.: Condens. Matter* **15**,
2207-2212, 2003.

We present a new method for calculating the functional derivative of the
superconducting transition temperature T_{c} with respect to the
electron-phonon coupling function
^{2}F
(). The method
relies on a highly efficient procedure for finding the largest
eigenvalue and the corresponding eigenvector of a Hermitian matrix.
The convergence problems that arise in calculation of
T_{c}/
^{2}F
()
for systems with low T_{c} and a large maximum phonon frequency
_{max}
using the method based on the pair-breaking parameter are eliminated. We apply the
new method of calculating
T_{c}/
^{2}F
() to
MgB_{2}, to the prototype strong coupling superconductor Pb and to
weak coupling (BCS) superconductor Al.
*Int. J. Modern Phys.* **13**, 1087-1093, 2002.

We investigate numerically the temperature dependence of the London penetration depth within
the mean-field treatment of the interlayer pair tunnelling model for the copper oxide superconductors.
It is found that the assumption that the pair tunnelling is the dominant pairing mechanism in YBCO
(yttrium-barium-copper oxide) is not consistent with the experimental results on this material.
We also consider the Knight shift and the dynamic spin susceptibility at a low temperature within
the model. We find that the experimental results for these quantities are consistent with a relatively
small contribution of the interlayer pair tunnelling to the pairing channel provided that, at least in
the case of the dynamic susceptibility, the in-plane pairing produces a gap of d_{x2-y2}-wave
symmetry which is non-zero within at most a few tens of meV off the Fermi line.
*J.Phys.: Condens. Matter* **11**, 9741-55, 1999.

We have carried out a Monte Carlo study of the nearest-neighbour
ferromagnetic *XY*-model on the two-dimensional (2D) Penrose lattice
and on periodically stacked (three-dimensional) 2D Penrose lattices. For
the 2D case we have examined the magnetization, specific heat, linear
susceptibility, helicity modulus and the derivative of the helicity modulus
with respect to inverse temperature. The behaviour of all of these
quantities points to a Kosterlitz-Thouless transition occurring in the
temperature range *T*_{c} = (1.0 - 1.05
*J/K*_{B}, with critical exponents that are consistent with
those obtained for crystalline (e.g., square) lattices. For the 3D stacking
of the 2D Penrose lattices, examination of the magnetization, specific heat
and linear susceptibility reveals a conventional second-order phase
transition. Through cumulant analysis and finite-size scaling we obtain a
critical temperature *T*_{c} = (2.292 /pm 0.003) *J*
and critical exponents alpha' = 0.003 /pm 0.03, beta = 0.30 /pm 0.01 and
gamma = 1.31 /pm 0.02, in agreement with previous studies of the
*XY*-model on the 3D cubic lattice.
*J. Phys.: Condens. Matter* **10**, 2303-21, 1998.

The interlayer pair tunnelling model of Anderson *et al* is
generalized to include the strong-coupling effects associated with in-plane
interactions. The equations for the superconducting transition temperature
* Tc* are solved numerically for several models of electron-optical
phonon coupling. The nonmagnetic in-plane impurity scattering suppresses
the *Tc* in all cases considered, and it is possible to obtain a
fair agreement with experiments for a reasonable choice of parameters. For
the anisotropic electron-phonon coupling proposed by Song and Annett, we
find that the interlayer pair tunnelling can stabilize the *dx2-y2*-wave
superconducting state with a high *Tc*. Moreover, in this case there
is a possibility of impurity-induced crossover from the *dx2-y2*-wave
state stabilized by the interlayer tunnelling to the s-wave state at a low
impurity concentration. We also calculate the isotope effects associated
with the in-plane oxygen optical mode and its dependence on the strength of
the interlayer pair tunnelling. Small positive values of the isotope
exponent are obtained for strengths of pair tunnelling that give high
transition temperatures.
*J. Phys.: Condens. Matter* **9**, 9007-20, 1997.

Via Monte Carlo studies of the frustrated *XY* or classical planar
model we demonstrate the possibility of a finite (nonzero) temperature
spin/gauge glass-like phase in two dimensions. Examples of both periodic
and quasiperiodic two-dimensional lattices, where a high-temperature
paramagnetic phase appears to change to a spin/gauge glass-like phase with
the lowering of temperature, are presented. The possibility of the glassy
phase is supported by our study of the temperature dependence of the
Edwards-Anderson order parameter, spin glass susceptibility, linear
susceptibility and the specific heat. Using finite-size scaling analysis
of spin glass susceptibility and the temperature dependence of the order
parameter we provide estimates of critical temperatures and exponents for
the various lattices. On the basis of these results we expect that certain
quasiperiodic as well as periodic two-dimensional arrays of superconducting
grains in suitably chosen magnetic fields should behave as superconducting
glasses at low temperatures.
*J. Phys.: Condens. Matter* **9**, 7141-59, 1997.

Monte Carlo (MC) studies of the frustrated classical planar on *XY*
model on two dimensional Penrose and octagonal lattices reveal ahigh
temperature paramagnetic state changing to a spin-glass phase as the
temperature is lowered. This scenario is supported by the temperature
dependence of the Edwards-Anderson order parameter, spin-glass
susceptibility, linear susceptibility, and the specific heat. Finite size
scaling analysis of spin-glass susceptibility and order parameter yields a
nonzero critical temperature and exponents similar to those obtained by
Bhatt and Young in their random Ising model study on a square lattice.
The results imply that certain quasiperiodic two-dimensional arrays of
superconducting grains in suitably chosen transverse magnetic fields should
behave as superconducting glasses at low temperatures.
*Physica A* **239**, 156-65, 1997.

Via extensive Monte Carlo studies we show that the frustrated
*XY*Hamiltonian on a two-dimensional Penrose lattice admits of a
spin-glass phase at low temperature. Studies of the Edwards-Anderson order
parameter, spin-glass susceptibility, and the local (linear) susceptibility
point unequivocally to a paramagnetic-to-spin-glass transition as the
temperature is lowered. The specific heat shows a rounded peak at a
temperature above the spin-glass transition temperature, as is commonly
observed in spin glasses. Our results strongly suggest that the
critical-point exponents are the same as obtained by Bhatt and Young in the
+/-*J* Ising model on a square lattice. However, unlike in the latter
case, the critical temperature is clearly finite (nonzero). The results
imply that a quasiperiodic two-dimensional array of superconducting grains
in a suitably chosen transverse magnetic field should behave as a
superconducting glass at low temperature.
*Physical Review B* **54**, R740, 1996.

It is shown that a correlation between the positions of the c-axis
longitudinal optic (LOc) phonons and "notch"-like structures in the
a-b plane conductivity of high-Tc superconductors results from phonon-mediated
interaction between electrons in different layers.
*Journal of Physics and Chemistry of Solids* **56**, 1727-8, 1995.

Calculations of the superconducting transition temperature are carried out
for a model in which the pairing is mediated by antiferromagnetic
spin-fluctuation derived from the spin susceptibility with four sharp peaks
in the corners of a square Brillouin zone and for a tight-binding electron
spectrum. The approximation, in which the electron momentum transfer in
integrals for the self-energy near Tc is taken to be fixed at the
positions of the peaks, results in a considerable simplification of the
equations for Tc. The numerical solutions of these equations, which take
under one minute on any standard UNIX workstation, are in good agreement
with previous calculations for such a model, which employed no
approximation in the momentum integral, but required a vector or a highly
parallel computer architecture. Moreover, a relatively simple structure of
the equations developed in this work offers, perhaps, more insight into the
antiferromagnetic spin-fluctuations theories of copper oxide
superconductors.
* Physical Review B* **51**, 6064-75, 1995.

The calculations of the superconducting transition temperature, including
the lowest-order vertex corrections, are carried out for three models: the
BCS-type instantaneous interaction, a retarded isotropic interaction
described by the Eliashberg spectral function and a spin-fluctuation
interaction with four delta-function peaks in the corners of a square
Brillouin zone. In the isotropic case the effect of higher-order
self-energy diagrams is to suppress the critical temperature calculated
within the mean-field approximation when the characteristic energy of the
boson responsible for the pairing is not small compared to the Fermi
energy. In the case of the model with sharp peaks in the momentum space
the vertex correction can lead to an increase of Tc.
* Physical Review B* **50**, 12774-87, 1994.

We extend the Eliashberg-type equations for disordered bulk
superconductors to the two-dimensional case and examine tunneling into
disordered Pb films. We find, in contrast to the bulk case, a
substantial effect of disorder on the tunneling density of states.
Our results resemble qualitatively the experimental results on Pb
films of varying sheet resistance (but also of varying thickness).
*Zeitschrift fur Physik B* **93**, 173-80, 1994.

We consider the effect of changes in the Coulomb interaction due to the
diffusive nature of propagation of the electron density fluctuations in
three dimensional weakly disordered strong coupling superconductor on the
low temperature tunneling density of states. Our results are completely
consistent with the experimental finding of a negligible Coulomb effect in
disordered A-15 Nb-Sn.
*Zeitschrift fur Physik B* **93**, 163-72, 1994.

The interaction between phonons and a two-dimensional (2D) electron gas is
studied beyond the Migdal approximation. The analysis of the vertex
function leads to the relative correction of the imaginary part of the
self-energy which is of the order lnr/r, where r is the ratio
of the Fermi energy and the average phonon energy. Our results strongly
suggest that the quasiparticle picture for a 2D electron gas in a 3D
lattice has to be corrected by many-particle effects even at small
l/r.
*Physical Review B* **48**, 16388-401, 1993.

We show that under fairly general conditions the self-energy effects in the
elastic tunneling conductance of a normal metal-insulator-normal metal junction arise from the dependence of the real part of the electron self-energy S(e,w)
on noninteracting electron energy e. We corroborate this by considering two
special cases: the case when S arises from electron-phonon interaction in a
metal, and the case when S is due to electron-electron interaction in a
disordered metal. A possible modification of the form of S given by the
marginal Fermi liquid theory for the normal state of oxide superconductors is
suggested, if this theory is to account for the observed linear background
tunneling conductance.
*Solid State Communications* **82**, 107-110, 1992.

We use the auxiliary boson and 1/N-expansion methods to calculate the optical
conductivity of the Anderson impurity model for all temperatures and
frequencies. A qualitative agreement between our results and experiments on
dense Kondo systems indicates that the optical properties of these systems are
dominated by single impurity effects.
*Solid State Communications* **79**, 125-130, 1991.

We have computed the temperature and magnetic field dependence of the specific
heat and magnetization for a random three-dimensional cluster of Josephson
coupled small superconducting grains. We speculate that due to a 2D-like
topology of our loose cluster the system exhibits a Kosterlitz-Thouless-like
transition in zero applied field. The temperature and the field dependence of
magnetization is similar to the one observed on low quality samples of
high-Tc oxides. However, the field and the temperature dependence of the heat
capacity for our random cluster is different from the one obtained on
high-quality samples of oxide superconductors.
*Physica C* **177**, 138-144, 1991.