Dynamical nature of chaos in electron systems of high-T c superconductors

A model of the fermion-condensation phase transition forming a plateau in the spectrum of single-particle excitations near the Fermi surface at T=0 is used to analyze those features of the spectral functions of normal states of high-T _c superconductors which are inherent in a marginal Fermi liquid contaminated by impurities. With this model, such a behavior is shown to be due to the fermion condensate, which acts as an impurity subsystem because its energy spectrum at T=0 is dispersionless. The influence of the anisotropy of condensate distribution in the Brillouin zone on the spectral functions is discussed.     

Superconductivity in the presence of fermion condensation

Fermion condensation (FC) is studied within the density functional theory. FC can fulfill the role of a boundary, separating the region of strongly interacting electron liquid from the region of strongly correlated electron liquid. Consideration of the superconductivity in the presence of FC shows that, under certain circumstances, at temperatures above T _c the superconductivity vanishes and the superconducting gap smoothly transforms into a pseudogap. The pseudogap occupies only a part of the Fermi surface, and one that shrinks with increasing temperature and vanishes at T=T*, and the single-particle excitations of the gapped area of the Fermi surface have a width γ ∼(T-T _c ). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 491–496 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

High-temperature superconductors as heterostructures

The wave-function envelope method is used to describe the electronic states of the cuprate high-T _c superconductors (HTSCs). In this method the 2D electronic states of the CuO₂ layers of a unit cell play the role of quantum wells, while the 2D states of the reservoir play the role of quantum barriers. Because of the different anisotropy of the 2D effective masses of the wells and barriers, some states on the Fermi surface (line) belong to CuO₂ layers and some states belong to the reservoir layers. This behavior of the electronic states explains characteristic features of HTSCs, such as the existence of regions on the Fermi surface with strongly different relaxation times, the weak suppression of d-type superconducting pairing by nonmagnetic scattering, and the coincidence of the angular dependence of the superconducting order parameter and the angular dependence of the electronic density of states (forward scattering predominating). The change in the signs of the components of the effective masses along the Fermi surface can result in the formation of hole pairs (biholes) or electron pairs (bielectrons) on account of the Coulomb interaction in the case of a negative reduced mass of the pairs. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 211–216 (10 August 1998)     

Electronic states of boron in superconducting MgB2 studied by11B NMR

Nuclear magnetic resonance (NMR) spectra and nuclear spin-lattice relaxation rateT ₁⁻¹ of¹¹B have been measured in superconducting polycrystalline MgB₂ with 7_c^ons = 39.5 K. It is shown that (T ₁T⁻¹ and the Knight shiftK _s are independent of temperature and nearly isotropic aboveT _c. Both of these quantities are decreased gradually in going to the superconducting state. According to NMR data the density of states near the Fermi level is flat at the scale of about 500 K. Some conclusions on the orbital content of the density of states at the Fermi level were drawn and compared with the results of the band structure calculations.     

Landau level quantization and possible superconducting instabilities in highly oriented pyrolitic graphite

Measurements of the basal-plane resistivity ρ _a(T,H) performed on highly oriented pyrolitic graphite, with magnetic field H∥c-axis in the temperature interval 2–300K and fields up to 8 T, provide evidence for the occurrence of both field-induced and zero-field superconducting instabilities. Additionally, magnetization M(T,H) measurements suggest the occurrence of Fermi surface instabilities which compete with the superconducting correlations. Fiz. Tverd. Tela (St. Petersburg) 41, 2135–2138 (December 1999)     

Effect of hydrostatic compression on the indium-impurity-induced superconducting transition in Pb<Subscript>0.3</Subscript>Sn<Subscript>0.7</Subscript>Te

This paper reports on a study of the low-temperature conductivity and parameters of the superconducting state, namely, the critical temperature T _c and the second critical magnetic field H_c2, in the (Pb_0.3Sn_0.7)_0.95In_0.05Te solid solution under hydrostatic pressure P ≤ 9 kbar at T = 4.2 K. The choice of this material has been motivated by the fact that, according to earlier observations, it undergoes a superconducting transition at T _c ∼ 2.3 K, i.e., close to the maximum value T _c ∼ 2.9 K found for the (Pb _z Sn_{1 − z} )_0.95In_0.05Te solid solutions with a lead content z ∼ 0.15–0.25. It has been demonstrated that an increase in the pressure to P ≤ 9 kbar leads to a bell-shaped dependence T _c (P). The observed dependences are assigned to the effect of hydrostatic compression on the band structure of the solid solution and indicate a shift in the position of the Fermi level E _F with increasing pressure within the impurity band of the In quasi-local states. In this case, E _F passes through a maximum in the density of impurity states at P = 3–5 kbar.     

Influence of transport current and thermal fluctuations on the resistive properties of HTSC+CuO composites

Measurements of the temperature dependence of the electrical resistance R(T) below the superconducting transition temperature have been performed at different values of the transport current in HTSC+CuO composites modeling a network of weak S-I-S Josephson junctions (S—superconductor, I—insulator). It has been shown experimentally that the temperature dependence R(T) at different values of the transport current is adequately described by means of the mechanism of thermally activated phase slippage developed by Ambegaokar and Halperin for tunnel structures. Within the framework of this model we have numerically calculated the temperature dependence of the critical current J _c(T) as defined by various criteria. Qualitative agreement obtains between the measured and calculated temperature dependences J _c(T). Fiz. Tverd. Tela (St. Petersburg) 41, 969–974 (June 1999)     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Superconductivity in impurity bands

We present a theory of superconductivity in doped insulators. In the magnetic metal state of the compound we obtain the self-consistency equations for the superconducting state in the spin-dependent impurity bands of both extended and localized states in the initial insulator gap. A BCS-type triplet pairing field is considered. We show that the superconducting gap in which single-electron extended states do not exist is overlapped by the distribution of the localized states. The formation of a latent superconducting gap is discussed in connection with the unusual properties of high-T _c compounds. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 419–424 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

A pseudopotential approach to the superconducting state parameters of (Ni33Zr67)1? x M x (M=Ti, V, Co, Cu) ternary metallic glasses

Superconductivity in ternary metallic glasses has been investigated using the model pseudopotential approach, which has been found quite successful in explaining superconductivity in metals, binary alloys and binary glasses. It is observed that this simple methodology successfully explains superconducting behaviour of ternary glasses without requiring the solution of Dirac equation for a many body problem or estimation of various interactions as required in ab-initio pseudopotential theory. In the present work superconducting state parameters of fourteen metallic glasses of (Ni-Zr)-M system (M=Ti, V, Co, Cu) have been determined in the BCS-Eliashberg-McMillan framework. It is observed that addition of V, Co, and Cu as the third element (M) to a binary metallic glass (Ni₃₃ Zr₆₇) causes the parameters λ,T _c, α, andN ₀ V to decrease, and Coulomb pseudopotential (μ*) to increase with concentration of M, showing that the presence of third element (M) causes suppression of superconducting behaviour of the alloy. The decrease inT _c with increasing concentration of third element (M) may be attributed to the modifications in density of states at the Fermi levelN(E _F), and probable changes in the band structure of the alloy due to addition of the third element (M). Slight difference is noticed when Ti is added to the Ni₃₃ Zr₆₇ alloy. In this caseT _c rises initially and then decreases with concentration of M, showing a peak at aboutx=0.05. This indicates that on addition of Ti, 3d states grow near the Fermi level and hence contribute substantially toN(E _F), favouring superconducting behaviour in this case. The present results forT _c show an excellent agreement with the experimental data. QuadraticT _c equations have been proposed, which provide successfully theT _c values of ternary metallic glasses under consideration. Paper presented at National Conference on Current Trends in Condensed Matter Research, Warangal, India, September 20–22, 2004.     

X-ray microanalysis of quaternary semiconductor solid solutions and its application to the (SnTe-SnSe):In system

A reliable technique of local chemical characterization of multicomponent semiconductor solid solutions has been developed, and the possibility of its application to the SnTe-SnSe quaternary solid solutions doped with 16 at.% In verified. The behavior of the electrical resistivity of samples of these solid solutions at low temperatures, 0.4–4.2 K, has been studied. The critical temperature T _c and the second critical magnetic field H _c2 of the superconducting transition and their dependences on the solid-solution composition have been determined. The superconducting transition at T _c≈2–3 K is due to hole filling of the In-impurity resonance states, and the observed variation of the superconducting transition parameters with increasing Se content in the solid solution is related to the extrema in the valence band and the In band of resonance states shifting with respect to one another. Fiz. Tverd. Tela (St. Petersburg) 41, 612–617 (April 1999)     

Disordering effects in superconductors with anisotropic pairing: From Cooper pairs to compact bosons

In the weak-coupling BCS-theory approximation, normal impurities do not influence the superconducting transition temperature T _c in the case of isotropic s pairing. In the case of d pairing they result in a rapid destruction of the superconducting state. This is at variance with many experiments on the disordering of high-T _c superconductors, assuming that d pairing is realized in them. As the interelectronic attraction in a Cooper pair increases, the system transforms continuously from a BCS-type superconductor with “loose” pairs to a picture of superconductivity of “compact,” strongly coupled bosons. Near such a transition substantial deviations can be expected from the universal disorder dependence of T _c , as determined by the Abrikosov-Gor’kov equation, and T _c becomes more stable against disordering. Since high-T _c super-conducting systems fall into the transitional region from BCS-type pairs to compact bosons, these results can explain their relative stability against disordering. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 258–262 (10 February 1997)     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Superconductivity

The superconducting and normal state properties are reviewed for exemplary matrix-impurity systems in the three distinct regimes of magnetic character of the impurity which have been identified. It is shown that these three regimes can be distinguished by thedetailed behavior of the depressions of 1) the superconducting transition temperatureT _c as a function of impurity concentrationn and 2) the specific heat jump ΔC atT _c as a function ofT _c . These systematics of superconductivity in the presence of local moments appear to be sufficiently well established that it is possible to 1) ascertain whether the solute spin is long-lived (magnetic) or short-lived (nonmagnetic) compared to thermal fluctuation lifetimes at superconducting temperatures, 2) determine the sign and magnitude of the conduction electron-impurity spin exchange interaction parameter ϑ and the temperature dependence of the exchange scattering of conduction electrons bylong-lived solute spins, 3) derive, in favorable cases, information pertaining to the energy level structure of rare earth ions in the crystalline electric field of their superconducting metallic host, and 4) observe magnetic-nonmagnetic transitions of an impurity induced by the application of an external pressure or variation of the composition of a binary alloy matrix. This article is based upon an invited presentation at the 1973 Summer meeting of the American Physical Society in East Lansing, Michigan, 18–20 June 1973 [Bull. Amer. Phys. Soc.18, 779 (1973)]. Supported by the U.S. Energy Research and Development Administration under Contract No. ERDA E(04-3)-34 PA 227.     

Insulator-metal transition in the single-crystal high-T c superconductor Bi-2201

Variations in the temperature behavior of resistivity, ρ(T), in the ab plane of the anisotropic single-crystal high-T _c superconductor BiSrCuO (2201 phase) have been observed at the insulator-metal (IM) transition. At low temperatures, as one approaches the transition, the Mott relation for two dimensions, ln ρ ∝ T ^−1/3, changes to ln ρ ∝ T ^−1/2, which corresponds to hopping conduction with a Coulomb gap in the density of states. Negative temperature slopes were revealed in the samples near the transition. Estimates suggest that superconductivity in these samples sets in from the Anderson insulator state. The behavior of the width of the superconducting transition and of the temperature of its onset, T _con, at the IM transition has been studied from measurements of the ac magnetic susceptibility. It is shown that in the vicinity of the IM transition the superconducting transition becomes broader, and the onset of the transition T _con shifts toward higher temperatures. This behavior is attributed to nonuniform superconductivity resulting from formation in the crystal of superconducting droplets with different values of T _c , which is caused by fluctuations in the local density of states due to the inherent disorder in the crystal. In these conditions, superconductivity has a percolation character. Fiz. Tverd. Tela (St. Petersburg) 40, 1190–1194 (July 1998)     

Enhancements of the superconducting transition temperature within the two-band model

The two-band model as introduced by Suhl, Matthias and Walker [Phys. Rev. Lett. 3, 552 (1959)] accounts for multiple energy bands in the vicinity of the Fermi energy which could contribute to electron pairing in superconducting systems. Here, extensions of this model are investigated wherein the effects of coupled superconducting order parameters with different symmetries and the presence of strong electron-lattice coupling on the superconducting transition temperature T_c are studied . Substantial enhancements of T_c are obtained from both effects.Received: 2 July 2003, Published online: 2 April 2004PACS: 74.20.-z Theories and models of superconducting state     

Segregation of impurities and vacancies on phase and antiphase boundaries in alloys

The equilibrium distribution of low-concentration impurities or vacancies is investigated in the region of a coherent phase boundary or antiphase boundary in a binary alloy. A general expression for the free energy of an inhomogeneous multicomponent alloy, which generalizes the expression previously derived for a binary alloy, is presented. Explicit formulas for the impurity concentration profile c _im(x) in terms of the distribution of the principal components of the alloy near a boundary are obtained from this expression in the mean-field and pair-cluster approximations. The shape of this profile is determined by a “preference potential” P, which characterizes the attraction of an impurity to one of the alloy components, as well as by the temperature T and the phase transition temperature T c. At small values of P/T impurities segregate on a phase boundary, and the degree of this segregation, i.e, the height of the maximum of c _im(x), in the region of the boundary increases exponentially as the ratio T _c/T increases. For P ≠ 0 the c _im(x) profile near a phase boundary is asymmetric, and as P/T increases, it takes on the form of a “worn step.” The maximum on the c _im(x) curve then decreases, and at a certain |P|≳T _c it vanishes. Segregation on an antiphase boundary is investigated in the case of CuZn ordering in a bcc alloy. The form of c _im(x) near an antiphase boundary depends significantly both on the form of the potential P and on the stoichiometry of the alloy. At small P impurities segregate on an antiphase boundary, and at fairly large P “antisegregation,” i.e., a decrease in the impurity concentration on the antiphase boundary in comparison with the value within the antiphase domains, is also possible. Zh. éksp. Teor. Fiz. 112, 714–728 (August 1997)     

Superconductivity in a simple model of the pseudogap state

An analysis is made of characteristics of the superconducting state (s-and d-pairing) using a simple, exactly solvable model of the pseudogap state produced by fluctuations of the short-range order (such as antiferromagnetic) based on a Fermi surface model with “hot” sections. It is shown that the superconducting gap averaged over these fluctuations is nonzero at temperatures higher than the mean-field superconducting transition temperature T _c over the entire sample. At temperatures T > T _c superconductivity evidently exists in isolated sections (“ drops”). Studies are made of the spectral density and the density of states in which superconducting characteristics exist in the range T > T _c however, in this sense the temperature T = T _c itself is no different in any way. These anomalies show qualitative agreement with various experiments using underdoped high-temperature superconducting cuprates.     

Charge density waves in partially dielectrized <Emphasis Type="Italic">d</Emphasis>-pairing superconductors

A self-consistent theory has been constructed for describing a superconductor with a d _x ²−y ² charge density wave caused by the appearance of a dielectric gap in antinodal sections of the two-dimensional Fermi surface. The theory explains some key features of high-temperature oxides. In particular, it has been shown that the observed large values of the ratio 2Δ(T = 0)/T _c are associated with the stronger suppression of the critical temperature T _c of the superconducting transition rather than the superconducting gap Δ at low temperatures T under the action of charge density waves. It has been predicted that there can exist two critical temperatures of the appearance and disappearance of the dielectric order parameter Σ(T) in a specific range of bare parameters of the model.     

Transverse Nernst-Ettingshausen effect, resonant scattering, and superconductivity in SnTe: In

The temperature dependences of the coefficient of the transverse Nernst-Ettingshausen effect in SnTe: In samples with different indium contents (1–16 at %) in the temperature range 100–300 K and the electrical resistivity at temperatures of 1.2–4.2 K and in magnetic fields of up to 10 kOe are investigated. The data obtained indicate the presence of resonant hole scattering into the band of quasi-local In impurity states in Sn_1?x In _x Te samples with In content x ≥ 0.05 and a superconducting transition with a critical temperature T _c ～ 1.5–2.2 K. The SnTe: In samples with the degree of filling of impurity states by electrons, which is close to 1/2, and the Fermi level ?_F pinned in the vicinity of the minimum energy dependence of the relaxation time τ(?) are characterized by inhomogeneities of a new type, i.e., inhomogeneities of the scattering parameter r = ?lnτ/?ln?| $ \varepsilon _F The temperature dependences of the coefficient of the transverse Nernst-Ettingshausen effect in SnTe: In samples with different indium contents (1–16 at %) in the temperature range 100–300 K and the electrical resistivity at temperatures of 1.2–4.2 K and in magnetic fields of up to 10 kOe are investigated. The data obtained indicate the presence of resonant hole scattering into the band of quasi-local In impurity states in Sn_1−x In _x Te samples with In content x ≥ 0.05 and a superconducting transition with a critical temperature T _c ∼ 1.5–2.2 K. The SnTe: In samples with the degree of filling of impurity states by electrons, which is close to 1/2, and the Fermi level ɛ_F pinned in the vicinity of the minimum energy dependence of the relaxation time τ(ɛ) are characterized by inhomogeneities of a new type, i.e., inhomogeneities of the scattering parameter r = ϖlnτ/∂lnɛ|, which are induced by fluctuations of the degree of filling of quasi-local states by electrons. Original Russian Text ? S.A. Nemov, V.I. Proshin, G.L. Tarantasov, R.V. Parfen’ev, D.V. Shamshur, A.V. Chernyaev, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 3, pp. 461–464.