Two-dimensional microclusters of vortices: Shell structure and melting

The melting of two-dimensional microclusters of “particles” which repel one another according to a logarithmic law and are confined by an external quadratic potential is investigated. The model describes Abrikosov vortices in a superconducting island of vortices in a rotating superfluid liquid and electrons in a semiconductor nanostructure surrounded by a low-permittivity medium. The structure of clusters and its dependence on temperature and melting are investigated. The melting of microclusters of vortices proceeds in two stages: 1. A transition from a frozen phase into a state corresponding to rotational reorientation of crystal shells relative to one another. 2. At a higher temperature, the radial order vanishes. This is connected with the fact that the barrier for rotation of the shells is much lower than the barrier for radial breakup of the shells. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 268–273 (10 February 1997)     

Structure and melting of dipole clusters

Two-dimensional microclusters made up of particles repelled by the dipole law and confined by an external quadratic potential are considered. The model describes a number of physical systems, in particular, electrons in semiconductor structures near a metallic electrode, indirect excitons in coupled semiconductor dots etc. Two competing types of particle ordering in clusters have been revealed: formation of a triangular lattice and of a shell structure. Equilibrium configurations of clusters with N=1–40 particles are calculated. Temperature dependences of the structure, potential energy, and mean-square radial and angular displacements are studied. These characteristics are used to investigate cluster melting. Melting occurs in one or two stages, depending on N. Melting of a two-shell microcluster takes place in two stages: at low temperatures—from the frozen phase to a state with rotationally reoriented “crystalline” shells with respect to one another, followed by a transition involving breakdown of radial order. Melting in a cluster made up of a larger number of shells occurs in one stage. This is due to the fact that the potential barrier to intershell rotation is substantially lower than that to particle jumping from one shell to another for small N, and of the same order of magnitude for large N. A method is proposed for predicting the character of melting in shell clusters by comparing the potential barriers for shell rotation and intershell particle jumping. Fiz. Tverd. Tela (St. Petersburg) 40, 1379–1386 (July 1998)     

Characteristic features of the melting of two-dimensional mesoscopic Wigner clusters

Two-dimensional Wigner microclusters in a semiconductor dot are studied. Their melting is investigated in detail and it is shown that, for typical mesoscopic clusters possessing a shell structure, melting occurs in two stages: orientational melting (rotation of the shells relative to one another) and total melting, where the shells start to overlap with one another and exchange particles. An example of a “magic” microstructure which has a triangular structure and melts in a single stage is presented. For this, the temperature dependences of various quantities characterizing cluster structure are investigated. The change in the distribution of cluster configurations over local minima of the potential energy with increasing temperature is investigated. At temperatures below the temperature of total melting, a cluster is always located near the configuration of a global minimum and, at temperatures above the temperature of complete melting, a cluster can be located with finite probability near configurations corresponding to various local minima of the potential energy. Fiz. Tverd. Tela (St. Petersburg) 41, 1499–1504 (August 1999)     

Commensurability oscillations and a new phase transition in YBa2Cu3Oy single crystals

Magnetization oscillations due to the commensurability of the vortex and crystal lattice periods in YBa₂Cu₃O_y (y=6.97±0.02) single crystals are investigated using a high angular resolution magnetometer. A sharp peak in the temperature dependence of the oscillation amplitude as well as other features in the behavior of the oscillation amplitude and of the irreversible magnetization are observed at T _f ∼60 K. It is inferred that T _f is the temperature of a transition of the solid vortex state to a smectic phase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 832–837 (10 June 1999)     

Superconductivity in the Ti-D system under pressure

The pressure dependence of the superconducting transition temperature in TiD_0.74 has been measured up to 30 GPa in a diamond high-pressure chamber. It is found that the deuteride TiD_0.74 becomes a superconductor at pressures corresponding to the transition to the high-pressure ζ phase, with a transition temperature that increases from 4.17 to 4.43 K in the interval P=14–30 GPa. The value extrapolated to atmospheric pressure T _c (0)=4.0 K is significantly lower than the superconducting transition temperature (T _c =5.0 K) measured earlier in the metastable state obtained by quenching TiD_0.74 under pressure. It is assumed that the significant difference of the extrapolated value from the superconducting transition temperature in the metastable state after quenching under pressure is caused by a phase transition on the path from the stability region of the ζ phase under pressure to the region of the metastable state at atmospheric pressure. Fiz. Tverd. Tela (St. Petersburg) 40, 2153–2155 (December 1998)     

Quantum orientational melting and the phase diagram of a mesoscopic system

The “phase diagram” of a two-dimensional mesoscopic system of bosons is investigated. An example of such a system is a system of indirect magnetoexcitons in semiconductor double quantum dots. Quantum Monte Carlo calculations show the existence of quantum orientational melting. At zero (quite low) temperature, as quantum fluctuations of the particles intensify, two quantum disordering phenomena occur with increasing de Boer parameter q. First, at q≈10⁻³ the system passes to a radially ordered but orientationally disordered state, where different shells of a cluster rotate relative to one another. Then at q≈0.16 a transition to a superfluid state occurs. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 11, 817–822 (10 December 1998)     

Fermion zero modes on vortices in chiral superconductors

The energy levels of fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the class I superconducting state the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in an s-wave superconductor: E=(n+1/2)ω₀, with integral n. In class II the corresponding spectrum is E=nω₀ and thus contains a state with exactly zero energy. The effect of a single impurity on the spectrum of bound states is also considered. For class I the spectrum acquires the doubled period ΔE=2ω₀ and consists of two equidistant sets of levels, in accordance with A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998). For the class II states the spectrum is not influenced by a single impurity if the same approximation is applied. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 9, 601–606 (10 November 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The magnetic field and energy of an Abrikosov vortex in an anisotropic London superconductor

The behavior of a straight Abrikosov vortex in an anisotropic uniaxial London superconductor is studied. Analytical expressions are derived that approximately describe the magnetic field in three regions: the asymptotic region, where the distance r from the vortex line is greater than λΓ (λ is the London length and Γ is the anisotropy constant), the intermediate region λ<r<λΓ, and the region r<λ. It is found that in the intermediate region with high anisotropy the component of the magnetic field along the vortex line changes sign for a certain interval of angles between the vortex line and the anisotropy axis. Because of this the interaction of parallel vortices whose plane is parallel to the anisotropy axis has a minimum and a maximum. This means that numerous metastable vortex lattices can exist. Additional terms in the vortex self-energy are obtained, and although they are smaller than the leading logarithmic term, they display a different dependence on the angle between the vortex line and the anisotropy axis. Zh. éksp. Teor. Fiz. 111, 954–963 (March 1997)     

Dynamic magnetic permeability of a thin, high-T c superconducting wafer

The field dependence of the vibrational contribution to the dynamic magnetic permeability μ _V(H) is calculated for a thin (of thickness d∼λ) high-T _c superconducting wafer in a magnetic field parallel to the surface. The resulting curves are plotted on the basis of an exact numerical analysis of the vortex structures both for the thermodynamic-equilibrium vortex lattice and in the presence of pinning forces and the Bean-Livingston surface barrier. It is shown that the μ _V(H) curves are highly sensitive to the size factor (d/λ) and exhibit abrupt changes corresponding to a change in the number of vortex rows. The equilibrium μ _V(H) curve is found to be similar in its general behavior and absolute value (obtained with allowance for the distribution of grain sizes and with appropriate values of λ and ϰ) to the experimental μ _V(H) curve plotted at nitrogen temperature for fine-grained YBa₂Cu₃O_x with grain diameters 〈D〉∼λ in an increasing magnetic field. It is established that the main cause of the experimentally observed irreversible behavior of the μ _V(H) curves during cyclic variation of the applied magnetic field is the existence of a surface barrier to the exit of vortices from the superconductor. The lower limit H _min(B) of stability of the mixed state in the presence of an ideal surface barrier in a thin, high-T _c superconducting wafer (d∼λ) is determined, along with the range of the vortex state (H _max-H _min) for a fixed number of vortices in micrometer-size grains of the investigated YBaCuO samples. Fiz. Tverd. Tela (St. Petersburg) 39, 1943–1947 (November 1997)     

Quantum melting of mesoscopic clusters

The phase diagram of a two-dimensional mesoscopic system of charges or dipoles, whose realizations could be electrons in a semiconductor quantum dot or indirect excitons in a system of two vertically coupled quantum dots, is investigated. Quantum calculations using ab initio Monte Carlo integration along trajectories determine the properties of such objects in the temperature-quantum de-Boer-parameter plane. At zero (sufficiently low) temperature, as the quantum fluctuations of the particles increase, two types of quantum disordering phenomena occur with increasing quantum de Boer parameter q: first, for q∼10⁻⁵ the systems transform into a radially ordered but orientationally disordered state wherein various shells of the “atom” rotate relative to one another. For much larger q∼0.1, a transition occurs to a disordered state (a superfluid in the case of a system of bosons). Fiz. Tverd. Tela (St. Petersburg) 41, 1856–1862 (October 1999)     

Thermal conductivity of YbInCu4

The electrical and thermal conductivities of an YbInCu₄ polycrystalline sample have been measured within the 4.2–300-K range. The behavior of the heat conductivity has been found to change sharply above and below T _v =70–75 K, the temperature corresponding to an isostructural phase transition from a state with an integral valence (T>T _v ) to a mixed-valence state (T<T _v ) of Yb ions. A preliminary qualitative analysis of the results is presented. Fiz. Tverd. Tela (St. Petersburg) 41, 1548–1551 (September 1999)     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

Dynamic properties of an incommensurate charge density wave in monoclinic TaS3 at low temperatures

The permittivity of monoclinic TaS₃, a quasi-one-dimensional conductor with an incommensurate charge density wave (CDW), as a function of frequency and temperature has been studied. At low temperatures and at frequencies below 1 MHz, the temperature dependence of the real part of the permittivity shows a maximum shift to lower temperatures with decreasing frequency. The temperature dependence of the relaxation time consists of two branches corresponding to macroscopic regions of CDWs with long and short relaxation times τ on the microscopic scale. With decreasing temperature, the growth of τ for large CDW regions is faster than thermal activation and shows a tendency to diverge at a finite temperature while the growth of τ due to the relaxation on the microscopic scale is slower than the activation rate. Our results show that with decreasing temperature the m-TaS₃ quasi-one-dimensional conductor goes over to a glasslike state due to the strong pinning of CDWs by randomly distributed impurities and the formation of mutually interacting solitary CDW collective excitations. Zh. éksp. Teor. Fiz. 111, 988–1000 (March 1997)     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

One-dimensional localization in porous a-Si1−c Mnc

The temperature dependence of the conductance of porous silicon doped with manganese up to densities corresponding to the metallic side of the Anderson transition is investigated. It is found that in the temperature range below T=40–60 K the conductance decreases with T as G(T)∝T ^−1/3. This behavior corresponds to one-dimensional electron localization in silicon wires under conditions of inelastic electron-electron collisions with a small energy transfer. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 4, 265–269 (25 February 1998)     

Structure of the superconducting state of superconductors near the critical field Hc2 for values of the Ginzburg-Landau parameter kclose to unity

It is shown that near the transition temperature T _c the coefficients of the second and third terms in the expansion of the free energy in powers of H _c2−B (B is the magnetic field induction inside the superconductor) go to zero simultaneously for a value of κ=1 for the Ginzburg-Landau parameter. Thereby the structure of the mixed state near H _c2 for a value of the parameter κ close to unity is determined by the temperature correction to the coefficient for the third power and the coefficient for the fourth power in the expansion of the free energy in powers of H _c2−B. The values of these coefficients depend on the type of vortex lattice. Zh. éksp. Teor. Fiz. 112, 1499–1509 (October 1997)     

Characteristic features of vortex depinning in a layered superconductor

The field H*(T) for the onset of dissipation is estimated self-consistently from the results of an investigation of the transverse resistance and current-voltage characteristics of a Bi₂Sr₂CaCu₂O₈ (BSCCO-2212) single crystal in a mixed state. It is established that H* is close to H _c1 in the interval T _c/2⩽T⩽T _c. Rapid growth of H*(T), accompanied by a transformation of the current-voltage characteristics, as the temperature decreases below ≈ 40 K attests to the formation of a nonvanishing region of stability of an ordered state of the vortex system, possibly as a result of a change in the effective dimensionality of the fluxoid. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 629–634 (25 April 1997)     

Thermal stability of the magnetic parameters of epitaxial iron garnet films subjected to planar radial stresses

The effect of external planar radial pressure on the thermal stability of the magnetic parameters of epitaxial iron garnet films is investigated in the temperature range 200–500 K for external mechanical stresses in the range 0–40 kgf/mm². It is shown that external planar radial pressure can be used to improve the thermal stability of these magnetic parameters by a factor of 1.5–2, and also to alter significantly the temperature interval of single-domain behavior for orientational phase transitions near a compensation point. Zh. Tekh. Fiz. 67, 114–116 (September 1997)     

Cherenkov radiation from an Abrikosov-Josephson vortex

The Cherenkov radiation of generalized Swihart waves is investigated in connection with the slow motion of an Abrikosov-Josephson vortex, which corresponds to a 2 π kink in the phase difference of Cooper pairs on opposite sides of a tunnel junction. The radiative friction force acting on such a vortex is determined. An evaluation is made of the steady-state vortex velocity when the accelerating influence of an electric current through the Josephson junction is compensated by radiative slowing of the vortex due to Cherenkov radiation from the Abrikosov-Josephson vortex. Fiz. Tverd. Tela (St. Petersburg) 39, 444–448 (March 1997)     

Electronic structure of Ce and Sm in hydrides and the 4f collapse in YbHx

The population of the 4f, 5d, and 6s shells of rare-earth atoms in RH_x hydrides (R=Ce, Sm, Yb; x≈2–3) has been studied by the x-ray line-shift method. The population of the 5d and 6s shells of Ce and Sm atoms, and the charge on them in metals and hydrides, were determined from experiment and calculated within the Hartree-Fock-Dirac (Koopmans) model. The decrease of the charge on Ce and Sm revealed upon transition from the metal to the hydride argues unambiguously for the anionic (hydride) model. In YbH_x with x⩾2, the structural transition is accompanied by a strongly pronounced electronic transition from divalent to a noninteger-valence state . Fiz. Tverd. Tela (St. Petersburg) 40, 1393–1396 (August 1998)