Vortex lattices (in russian)
I. Luk'yanchuk get html version...
Abstracts of Publications
Vortex lattices (in russian)
I. Luk'yanchuk get
html version...
The small book that reviews
the one of the most important phenomenon of the contemporary condenced
matter physics - the vortex lattices in superconductors superfluids and
even in the neutron stars. These vortices appear as a responce of the quantum
system on the external perturbation. They have the macroscopic size
and are detectable experimentally.
The mechanism of the current
flow in the vortex state is considered. The special emphasis to the review
of the recent studies of the vortices in the High-Tc materials is given.
For the large circule
of readers.
Znanie press, Moscow, 1991
University
course: "ELECTRODYNAMICS: applications in condensed matter"
I. Luk'yanchuk
The present one-semester course was given for
the PhD students of the Federal University of
Minas Gerais (UFMG), Brazil, in 1998. The principal
objectives of course was, despite the
introduction to the classical Electrodynamics,
to give the review of the contemporary
developments of the condensed matter physics.
Substantial attention was given to solution of the
problems and to introduction to the related technique
of the theoretical physics (vector and tensor
analysis, theory of analytic functions, methods
of statistical physics etc.).
Universidade Federal de Minas Gerais, BH-Brasil,
1998; More details... get
PDF (450K)
Magnetic
Properies of Unconventional Superconductors
Magnetic properties of unconventional superconductors
Luk'yanchuk, I.A.; Zhitomirsky, M.E.
The article reviews recent developments on magnetic properties
of superconductors with anisotropic Cooper pairing. In particular, we show
how the concept of broken symmetries is applied to the investigation of
the mixed state in superconductors with a multicomponent order
parameter. Starting from the phenomenological description in the
framework of the generalized Ginzburg-Landau theory we discuss different
types of quantized vortices appearing at H c1/ in states with and without
time reversal breaking. General classification of superconducting
phase transitions in a uniform magnetic field at H c2/ is constructed.
Vortex lattices of different forms are found in the vicinity of the upper
critical field. Symmetry arguments are used to classify phase transitions
inside the mixed state. Special attention is given to results which can
be obtained analytically. Also special emphasis is put on the open
questions of the theory.
Superconductivity review, 1, 207, (1995);
http://xxx.lanl.gov/abs/cond-mat/9501091
Diamagnetic limit of superconductivity with triplet pairing
I. A. Luk'yanchuk and V. P. Mineev
A critical magnetic field which is peculiar to superconductors with
pairs that have a nonzero orbital angular momentum has been found. This
critical field stems from the local orbital diamagnetism of the pairs.
It agrees in order of magnitude with the paramagnetic limit for superconductors
with singlet pairing.
Pis'ma Zh. Eksp. Teor. Fiz. 44, 183 (1986)
[Sov. Phys.- JETP letters 44, 233 (1986)]
Upper critical fields in p-pairing superconductors
I. A. Luk'yanchuk and V. P. Mineev
The upper critical field Hc2
for p-pairing superconductors is determined at arbitrary temperatures,
taking into account magnetic effects which originate both from spin and
orbital motion. We show that in the absence of spin-orbit interaction
the ferromagnetic -phase has the largest value of Hc2(T) of all the p-pairing
phases; in addition, we show that the phase transition from metal
to p-paired superconductor is split in two in a magnetic field, like the
phase transition from the normal to the superfluid state which
occurs in liquid 3He. We calculate the critical fields for these two transitions
in the Landau-Ginzburg region and describe the characteristics of the resulting
superconducting states. We investigate the effects of spontaneous
magnetism and of para- and diamagnetic corrections to the function Hc2(T)
for p-pairing superconductors with a spin-orbit interaction possessing
cubic symmetry. For these superconductors, the splitting of the phase
transition is found to be absent for arbitrary directions of the external
field. We discuss the anisotropy of the upper critical field
for superconducting phases with multicomponent order parameters characterized
by various representations of the cubic group, and also superconductivity
in the paramagnetic limit for superconductors with triplet pairing in the
presence of strong spin-orbit interaction.
Soviet Physics Zh. Eksp. Teor. Fiz. 93,
2045 (1987) [Sov. Phys.- JETP 66, 1168 (1987)]
Superconducting kernel symmetry for an anisotropic superconductivity near
Hc2 and phase transitions in UPt3
Luk'yanchuk, I.
The symmetry group of anisotropic Cooper pairing in
magnetic field H includes the magnetic translations and rotations around
H. On the basis of these operations Kasimir's operator which classifies
the superconducting nuclei near H C2/ is constructed. Such kernel
classification is used to find all possible reasons of kink in H
C2/(T)-dependence existence and to interpret the phase transitions
in H-T plane in the heavy-fermion superconductor UPt 3/ at the assumption
of two superconducting states coexistence. The phase transition
hones in space nonuniform state H C1/<H<H C2/ is shown to be either
the lines of superconducting order parameter parity violation
with respect to reflection in a perpendicular to magnetic field plane
or the lines of triangular vortex lattice distortion or the lines
of Abricosov's lattice period multiplication. Last case near H C1/ signifies
the phase transition with changing of magnetic vortex quantization.
J.Phys. I France 1, 1155 (1991)
Phase transitions with a change of symmetry of the mixed state in superconductors
with anisotropic pairing
M. E. Zhitomirski and I. A. Luk'yanchuk
A symmetry analysis of the normal-metal-superconductor
transition in a magnetic field is developed by means of the Landau approach.
All possible irreducible projective representations for this transition
are found. The symmetry of the vortex lattice near Hc2 is discussed.
For superconductors with anisotropic pairing a situation in which the critical
fields of two irreducible representations have close values is characteristic.
In this case, within the mixed state, a phase transition from a one-quantum
hexagonal lattice of vortices to a lattice that has either a doubled or
tripled number of flux quanta per unit cell or a reduced number of
rotational elements should arise. This theory offers the possibility of
explaining the observed phase diagram of UPt3.
Zh. Eksp. Teor. Fiz. 101 No.6 (1992)
[Sov. Phys.- JETP 74, 1046 1992)]
Symmetry of the mixed state of superconductors with anisotropic pairing
Luk'yanchuk, I.; Zhitomirsky, M
Physica C206, 373 (1993)
Heavy-Fermion
Superconductors
Structure of the superconducting phases of UBe13 and U(1 - x)Th(x)Be13
I. A. Luk'yanchuk and V. P. Mineev
Within the framework of the Landau
theory of phase transitions, we investigate the types of phase changes
which can occur between superconducting phases of the heavy-fermion compounds
U1 - xThxBe13. We show that none of these phase changes agree with the
experimentally-observed phase diagram (x,Tc), in which there is one second-order
phase transition in the region x < 1.75% from the normal to the superconducting
state and two successive second-order phase transitions for x > 1.75%.
The overall properties of U1 - xThxBe13 argue in favor of the following
two scenarios, each of which involves a sequence of phase transitions that
comes closest to the experimentally established sequence. (1) For x >1.75%
a second-order phase transition occurs from a normal to a superconducting
phase with symmetry O(T) × ; then, as the temperature decreases,
a first-order phase transition occurs to a superconducting phase with symmetry
D3(C3) × . For x < 1.75%, a phase transition of second order occurs
from the normal metal to a superconductor with symmetry D3(C3) ×
. (2) In the range x > 1.75% a second-order transition occurs from the
normal metal to a superconductor with symmetry O(D2), followed by a first-order
transition to a superconductor with symmetry D3(E); for x < 1.75%, we
have a second-order phase transition from the normal metal to a superconductor
with symmetry D3(E).
Zh. Eksp. Teor. Fiz. 95, 709 (1989)
[Sov. Phys.- JETP 68, 402 (1989)]
Model of isotropic d-wave pairing in UPt3
M. E. Zhitomirski and I. A. Luk'yanchuk
A phenomenological model is proposed
for describing the H-T-P phase diagram of the heavy-fermion superconductor
UPt3. In this model, the UPt3 is a nearly isotropic d-wave superconductor
whose transition temperature is split slightly by the crystal field. This
model agrees with all known experimental data on the phase diagram of UPt3.
The parameter values used are close to those predicted by weak-coupling
theory. Physical reasons for such isotropy of superconducting properties
are discussed.
Pis'ma Zh. Eksp. Teor. Fiz. 58,
127 (1993) [Sov. Phys.- JETP letters 58, No 2 (1993)]
Comment on ``Ginzburg-Landau theory of the phase diagram of superconducting
UPt3''
I. Luk'yanchuk, M. Sigrist, and M. Zhitomirsky
Phys.Rev.Lett.
71,
1957 (1993); get PDF
(11K)
Electron
States in Antiferromagnets
Electron paramagnetism in antiferromagnets
S. A. Brazovski, I. A. Luk'yanchuk, and
R. R. Ramazashvili, Jr.
The nature of the degeneracy of band
and localized electron states in an antiferromagnet and their behavior
in a magnetic field are analyzed. Structural features have been found in
the g-factor: At the edge of the magnetic Brillouin zone, a transverse
field does not lift the degeneracy, while localized states at defects are
completely nondegenerate.
Pis'ma Zh. Eksp. Teor. Fiz. 49, 557 (1989)
[Sov. Phys.- JETP letters 49, 644 (1989)]
Symmetry of electron states in antiferromagnets
S. A. Brazovski and I. A. Luk'yanchuk
The symmetry of the electron states
in an antiferromagnetically ordered crystal is investigated. The elements
of the two-value corepresentation apparatus for the magnetic groups are
used in a form that corresponds to the models and methods of the microscopic
theories. The symmetry restrictions on the quasiparticle spectra, on their
interaction with the magnetic field h, and on the interband matrix elements
are found. The spin-orbit effects are considered. It is shown that a
field h perpendicular to the antiferromagnetic ordering vector n does not
split the twofold degeneracy of the states at the boundary of the
magnetic Brillouin zone but shifts the spectrum extrema away from the boundary.
The results are illustrated for the case of a two-dimensional system
corresponding to the CuO2 plane in weakly doped high-temperature superconductors.
The general conclusions are applicable to itinerant antiferromagnets, including
quasi-one-dimensional compounds with a spin density wave.
Zh. Eksp. Teor. Fiz. 96, 2088 (1989)
[Sov. Phys.- JETP 69, 1180 (1989)]
Symmetry analysis of the electron wave functions in the antiferromagnetic
phase of high-temperature superconductors
S. A. Brazovski and I. A. Luk'yanchuk
An analysis of the symmetry
of the wave functions of electrons in antiferromagnetic planes of CuO2
high-temperature superconductors makes it possible to investigate the permissible
electron states at characteristic points of the magnetic Brillouin zone.
Interpretation of the results provides an opportunity for experimental
determination of the nature of carriers in high-temperature superconducting
materials, i.e., determination of whether the p-d hybridization or the
``oxygen'' model conserving the valence of copper is correct.
Zh. Eksp. Teor. Fiz. 98, 1498 (1990)
[Sov. Phys.- JETP 71, 837 (1990)]
13C
NMR in Fullerenes
High-resolution 13C nuclear magnetic resonance in alkali intercalated fullerene
C60
J. Reichenbach, F. Rachdi, I. Luk'yanchuk,
M. Ribet G. Zimmer and M. Mehring
We present the results of 13C nuclear
magnetic resonance (NMR) measurements on potassium and rubidium doped Buckminster
fullerene C60 at room temperature. By using high-resolution magic angle
spinning NMR spectroscopy we were able to identify and characterize the
different, thermodynamically stable phases. Based on an analysis of the
different NMR spectra, we discuss the effects of the intercalation on the
molecular dynamics as well as on the electronic properties in these compounds.
J.Phys.Chem. 101, 4585, (1994)
Intercalation in C60: high resolution 13C NMR results
Bernier, P.; Belahmer, Z.; Luk'Yanchuk, I.; Ribet,
M. Firlej, L.
Solid state high resolution 13C NMR has been used
to investigate the physical properties of various phases obtained
after intercalation of given chemical species in C 60. We present here
the case of molecular oxygen, which do not induce charge transfer
with the host molecules. We show that, via the magnetic characteristics
of the intercalant, information can be gained on its position and movement
in the structure. In particular, molecular oxygen is found to occupy the
middle of the octahedral site in the FCC structure of solid C 60.
Synth. metals 71, 1431 (1995)
High-resolution 13C NMR study of oxygen intercalation in C60
P. Bernier , I. Luk'yanchuk , Z. Belahmer,
M. Ribet, and L. Firlej
Solid-state high-resolution 13C
NMR has been used to investigate the physical properties of pristine C60
after intercalation with molecular oxygen. By studying the dipolar
and hyperfine interactions between Curie-type paramagnetic oxygen
molecules and 13C nuclei we have shown that neither chemical bonding nor
charge transfer results from the intercalation. The O2 molecules diffuse
inside the solid C60 and occupy the octahedral sites of the fcc crystal
lattice. The presence of oxygen does not affect the fast thermal reorientation
of the nearest C60 molecules. Using magic angle spinning we were
able to separate the dipolar and hyperfine contributions to 13C NMR spectra,
corresponding to fullerenes adjacent to various numbers of oxygen molecules.
Phys.Rev.
B53,
7535 (1996); get PDF (11K);
http://xxx.lanl.gov/abs/cond-mat/9504106
Magnetic
and Electronic Properties of Fullerenes
Electronic localization in Rb4C60 from bulk magnetic measurements
I. Lukyanchuk, N. Kirova, F. Rachdi,
C. Goze, P. Molinie and M. Mehring
The dc-magnetization measurements
were performed between 50 G and 40 kG using a superconducting quantum interference
device magnetometer on powder samples of Rb4C60. The magnetic susceptibility
reveals thermally activated behavior with an activation energy of 1200
± 100 K and a diamagnetic temperature-independent part d=-3 ×
10 - 4 emu/mol. By calculation of the related magnetic moments and by comparison
with the NMR and EPR data we conclude that the additional electrons are
localized on the C60 molecule and form a spin-singlet ground state. The
temperature-dependent paramagnetism is due to thermally excited electrons.
Strong electron correlations and lattice distortions (crystal field or/and
Jahn-Teller effect) are discussed as a possible origin for the lowest unoccupied
molecular orbital (LUMO) level splitting and for gap formation. The experimental
results are in good agreement with the existence of Jahn-Teller or
crystal-field distortions, providing the t1u LUMO level degeneracy is lifted.
Phys.Rev.
B51
3978 (1995); get
PDF (29K)
Insulator-metal transition in Rb4C60 under pressure: Jahn-Teller
theory versus NMR experiments
Kerkoud, R.; Auban-Senzier, P.; Jerome, D.; Brazovskii,
S.; Kirova, N.; Lukyanchuk, I.; Rachdi, F.; Goze, C.
NMR experiments on Rb 4C60 performed under pressure are presented.
The temperature dependence of the 13C NMR relaxation rate 1/T1 shows two
activated behaviors coexisting at ambient pressure; the lowest activation
energy disappears under pressure in favor of the emerging Korringa law.
The theory is suggested to describe the Rb 4/C 60/ as a Jahn-Teller crystal
with corresponding consequences for electronic band spectra and for self-trapped
states. Experiments are interpreted in terms of two relaxation channels:
one due to intramolecular triplet excitons; the other being related to
electron-hole excitations through an indirect band gap.
Synth. metals, 77, 205 (1996)
Insulator-metal transition in Rb4C60 under pressure from 13C NMR
R.Kerkoud, P.Auban-Senzier, D.Jerome, S.Brazovskii,
I.Luk'yanchuk, N.Kirova, F.Rachdi, C.Goze.
Journ.
of Phys. and Chem. of Solids, 57, 143 (1996),
get
PDF (799K)
Superconductivity
of Boron Carbide Nanoparticles
Superconducting RNi 2B 2C (R=Y,Lu) nanoparticles: size effects and weak
links
Maser, W.K. Bernier, P. Luk'yanchuk, I. Molinie,
P, Lefrant, S. Redlich, P. and Ajayan, P.M.
The potential
of the arc discharge technique for the growth of complex nanocrystalline
systems is demonstrated here with the formation of quaternary
superconducting nanoparticles belonging to the recently
discovered intermetallic boron carbide family RNi 2/B
2/C (R=Y, Lu). The nanoparticles, which were embedded in a
glassy carbon matrix and had T c/-15 K, are reported to exhibit
magnetic behavior characterized by finite size effects and weak Josephson
links between the particles. The formation and characterization of
the nanoparticles are detailed.
Adv. Materials, 9, 503 (1997)
Phase transition between the cholesteric and twist grain boundary C phases
Luk'yanchuk, I.A.
The upper critical temperature Tc2 for the phase transition between
the cholesteric phase (N*) and the twist grain boundary C phase with the
layer inclination tilted to the pitch axis (TGBCt) in thermotropic liquid
crystals is determined by the mean field Chen-Lubensky approach. We show
that the N*-TGBCt phase transition is split in two with the appearance
of either the TGBA or the TGB2q phase in a narrow temperature interval
below Tc2. The latter phase is novel in being superposed from two degenerate
TGBCt phases with different (left and right) layers inclinations
to the pitch axis.
Phys.
Rev. E57, 574 (1998); get
PDF (22K); http://xxx.lanl.gov/abs/cond-mat/9711024
Comment on ''Minimal Surfaces, Screw Dislocations, and Twist Grain Boundaries''
I. Luk'yanchuk
http://xxx.lanl.gov/abs/cond-mat/9910350
(2000)
Phase
Transition and Modulated Phases in Crystals
A novel type of incommensurate phase in quartz: the elongated-triangle
phase
P. Saint-Grégoire, E. Snoeck, C. Roucau,
I. Luk'yanchuk and V. Janovec
We present evidence for
a thermodynamically stable incommensurate elongated-triangle (ELT) phase
in quartz, observed by transmission electron microscopy at the apha-beta
structural transition. The phase sequence on cooling is: incommensurate
equilateral-triangle (EQT) phase (ferroelectric)-incommensurate ELT (ferroelectric
and ferroelastic)-uniform phase. The ELT blocks could be responsible
for the large light scattering in the vicinity of the alpha-beta transition
Pis'ma Zh. Eksp. Teor. Fiz. 64, 376
(1996) [Sov.
Phys.- JETP letters 64, 410 (1996)]; get
PDF (23K);
http://xxx.lanl.gov/abs/cond-mat/9511002
Basal-plane incommensurate phases in hexagonal-close-packed structures
I. Luk'yanchuk
A. Jorio and M. A. Pimenta
An Ising model with competing interactions
is used to study the appearance of incommensurate phases in the basal plane
of a hexagonal-close-packed structure. The calculated mean-field phase
diagram reveals various 1q-incommensurate and lock-in phases. The results
are applied to explain thebasal-plane incommensurate phase in some compounds
of the A'A''BX4 family, like K2MoO4, K2WO4, Rb2WO4, and to describe the
sequence of high-temperature phase
transitions in other compounds of this family
Phys.
Rev. B57 , 5086 (1998),; get
PDF (16K); http://xxx.lanl.gov/abs/cond-mat/9711174
Ferroelastic properties of the ELT phase in quartz
P. Saint-Gregoire, I.
Luk'yanchuk.
Ferrolectrics, submitted (2000);
Elongated-Triangle (ELT) Phase in Quartz as an Incommensurate Ferroelastic
P. Saint-Grégoire, I. Luk'yanchuk and N. Aliouane
We analyse ferroelastic blocks and deformations
in the quartz ELT phase in the frame of domain textures model. We show
that the estimation of the ferroelastic strain is consistent with the conclusion
driven form the small angle light scattering and show that the ferroelastic
blocks are the origin of optical inhomogeneities.
Ferrolectrics, submitted (2000); get
PDF (160K);
Thermodynamics of the incommensurate state in Rb2WO4: The Lifshitz point
in A2BX4 compounds
I. Luk'yanchuk
, A. Jorio and P. Saint-Grégoire
We consider the evolution of the phase transition from the parent hexagonal
phase P63/mmc to the orthorhombic phase Pmcn that occurs in several compounds
of the A2BX4 family and depends on the hcp lattice parameter c/a. For compounds
of K2SO4 type with c/a larger than the threshold value 1.26 the direct
first-order transition Pmcn<-->P63/mmc is characterized by a large entropy
jump ~Rln2. For compounds Rb2WO4,K2MoO4,K2WO4 with c/a<1.26 this transition
occurs via an intermediate incommensurate (Inc) phase. Differential scanning
calorimetry measurements were performed in Rb2WO4 to characterize the thermodynamics
of the Pmcn<-->Inc<-->P63/mmc transitions. It was found that both
transitions are again of the first order with entropy jumps 0.2·Rln2
and 0.3·Rln2. Therefore at c/a~1.26 the A2BX4 compounds reveal an
unusual Lifshitz point where three first-order transition lines meet. We
propose the coupling of crystal elasticity with BX4 tetrahedra orientation
as a possible source of the transitions discontinuity
Phys.
Rev. B61 , 3147 (2000); get
PDF (6K); http://xxx.lanl.gov/abs/cond-mat/9902138
Stress induced change of the Lifhsitz Point Type in A2BX4 compounds
I. Luk'yanchuk,
and P. Saint-Grégoire
Ferrolectrics, submitted (2000); get
PDF (45K);
Vortices
in Superconductor with k~1/sqrt(2)
Theory of superconductor with kappa close to 1/sqrt(2)
I. Luk'yanchuk
As was firstly shown by E. Bogomolny, the critical
Ginzburg-Landau (GL) parameter sqrt(2) at which a superconductor changes
its behavior from type-I to type-II, is the special highly degenerate point
where Abrikosov vortices do not interact and therefore all vortex states
have the same energy. Developing a secular perturbation theory we studied
how this degeneracy is lifted when kappa is slightly different from
sqrt(2) or when the GL theory is extended to the higher terms in T-Tc.
We constructed a simple secular functional, that depends only on few experimentally
measurable phenomenological parameters and therefore is quite efficient
to study the vortex state of superconductor in this transitional region
of kappa. On this base, we calculated such vortex state properties as:
critical fields, energy of the normal-superconductor interface, energy
of the vortex lattice, vortex interaction energy etc., and compared them
with previous results that were based on bulky solutions of GL equations.
Phys. Rev. B, accepted (2001);
http://xxx.lanl.gov/abs/cond-mat/0009030