Interaction of both charge density waves in NbSe3 from interlayer tunneling experiments

An interlayer tunneling technique has been used for spectroscopy of charge density wave (CDW) energy gaps (Δ_1,2) in NbSe₃ subsequently opened at the Fermi surface on decreasing temperature at T _p1 = 145 K (CDW1) and at T _p2 = 60 K (CDW2). We found that the CDW2 formation is accompanied by an increase of the CDW1 gap below T _p2. The maximum enhancement of Δ₁, δΔ₁ is about 10%. The effect observed has been predicted theoretically as resulting from the joint phase locking of both CDWs with the underlying crystalline lattice below T _p2. The text was submitted by the authors in English.     

Role of anisotropy of the coupling constant in a superconductor model with singularities near the Fermi surface

The role of anisotropy of the coupling constant in the influence of nonmagnetic impurities on the behavior of the superconducting transition temperature T _c is investigated in the high-temperature superconductor (HTSC) model, where high values of T _c result from an increase in the density of states near the Fermi surface. It is shown that this model is more sensitive to impurities than the BCS model; Anderson compensation does not occur in the HTSC model, even for identical distributions of the densities of states in the superconducting and impurity channels, and the impurity contributions are no longer linear with respect to the impurity concentration in the vicinity of T _c. Anisotropy of the superconducting gap Δ and the possibility of its disappearance at certain points on the Fermi surface due to various types of pairing are manifested in the stability of the superconducting phase against the influence of impurities. Fiz. Tverd. Tela (St. Petersburg) 39, 1940–1942 (November 1997)     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

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.     

Search for the NN → 6q phase transition in the np-polarized measurements at T kin = 1–6 GeV

The measurements of np-spin observables at 0° have been performed for the first time on the Delta-Sigma experimental facility of LHE JINR up to P _n = 4.5 GeV/c using the monochromatic neutron beam. They include detailed measurements of the Δσ _L(np) spin differences and the study of the np → pn elastic charge-exchange process. In the Δσ _L(np) and −Δσ _L(I = 0) energy dependencies over the energy region T_kin = 1.2–3.7 GeV the peculiarity at 1.8 GeV was observed. Such energy behavior was predicted by the QCD approach as a signal of the NN → 6q phase transition. For the exhaustive investigation of this effect it is necessary to measure the energy dependence of the complete set of np observables with both longitudinal (L) and transverse (T) polarizations of the neutron beam and proton target. This will allow Direct Reconstruction of all three NN forward Scattering Amplitudes (DRSA) to be performed, and the observed peculiarity to be checked around T_kin = 1.8 GeV and at the higher energies using the Argand diagrams method.     

Location of the minimum of the differential tunneling resistance in a superconductor-degenerate semiconductor Schottky contact

Measurements of differential resistance in a superconductor-degenerate semiconductor junction Nb - n ^{+ +} GaAs at T = 1.6 K show close similarity to those for a conventional superconductor-insulator- normal metal junction, except for the position of the minimum which is located at 3.6 meV. Using a simple model for the charge screening at the Schottky barrier, we give an argument why this minimum is by far displaced with respect to the superconducting gap energy ( Δ _g = 1.5 meV for bulk Nb). We argue that a rebuilding of the density of states takes place at the barrier, due to the imperfect metal screening in the degenerate semiconductor. Energy states close to the degenerate semiconductor Fermi energy are depleted at the barrier and are not available for tunneling, up to an energy E_g which adds to the superconducting gap Δ _g . Received 11 November 2002 / Received in final form 21 February 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: c.nappi@cib.na.cnr.it     

Spin-orbit coupling in the superconducting phase and DDW states of high-T<Subscript>c</Subscript> cuprates

The effects of the spin-orbit coupling are considered for the high T _c cuprates with asymmetric superconducting gap (SC) and the d-density wave (DDW) phase due to its vital role in the experimental determination of the DDW state. Experiments predict an anisotropy in the DSC gap where |Δ(0,π)|>|Δ(π,0)| and the gap node deviates from the diagonal direction towards the k _x axis. Measurements also demonstrate DDW to be a possible candidate for the pseudogap in the underdoped phase. Due to the spin-orbit (SO) coupling in the low temperature orthorhombic (LTO) phase, the phase diagram of the cuprates suffers a change due to the modification of the T* value, the temperature characteristic of pseudogap, although T _c remains unaltered. Moreover, for a more generalized SO coupling, the DDW gap decreases with the angle but has no effect on the SC gap. We calculate the density of states in the various regimes of doping for the mixed SC+DDW states in the underdoped (UD) phase, SC state in the overdoped phase and also the DDW state in the UD phase and compare them with various theoretical and experimental works. The temperature dependence of the specific heat does not exhibit any qualitative change due to the SO coupling.     

Spectroscopy of quasiparticle excitations of superconducting bismuth cuprate at high pressures

We study the energy spectrum of Bi2223 (Bi_1.6Pb_0.4Sr_1.8Ca_2.2Cu₃O_x) at high hydrostatic pressures by Andreev-and tunneling-spectroscopy methods. We determine the gap anisotropy in the basal ab plane and find the following values for the parameters Δ(ϕ): Δ_max=42 mV, and Δ_min=19.5 mV (T _c =110 K and dT _c /dP=0.16 K/kbar). We detect an increase in the ratio R=2Δ_max/kT _c with pressure P; for Bi2223 cuprate, dR/dP≈0.017 kbar⁻¹. In the phonon-frequency region we detect a “softening,” due to pressure, of the high-frequency part of the phonon spectrum corresponding to “breathing” modes of oxygen, as well as other optical modes of Cu-O. The characteristic frequencies of the spectrum for ℏΩ>60 mV are found to decrease, with increasing pressure, at a rate d ln(ℏΩ)/dP≈−6.5±0.5×10⁻³ kbar⁻¹. This result explains the observed increase in the ratio 2Δ/kT _c (P) in the model of strong electron-phonon interaction. Zh. éksp. Teor. Fiz. 113, 1397–1410 (April 1998)     

Characteristic features of d pairing in bilayer cuprates under conditions of Peierls instability of the normal phase

A system of self-consistent integral equations for the superconducting gap is formulated and solved taking account of the instability of the normal phase of bilayer cuprates against charge-density waves. The critical parameters are calculated as a function of the wave vector, temperature, and doping index. It is found that the region in which superconductivity coexists with d-type charge-density waves depends strongly on the doping index. The effective energy-gap parameter, determined as the interval between the peaks of the density of states, can have a local minimum at temperatures T<T _c . Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 583–587 (10 October 1998)     

Peculiarities of crystal field effects in CeInCu2 based heavy-fermion compounds

We have studied the evolution of the inelastic neutron magnetic scattering spectra of a compound with cubic symmetry, CeInCu₂, in the temperature range 10–130 K, and also their transformation with variation of the Kondo temperature T _K due to substitution of cerium ions in the system Ce_1−x (La,Y)_xInCu₂ at T=10 K. It turns out that the energy of the transition between the ground state and excited state of the 4 f electrons (Δ_CF) in the crystal electric field in CeInCu₂ increases with growth of the population of the ground state as the temperature is reduced, with a slight change in its intensity. Such behavior is inconsistent with the notion of classical one-ion effects of the crystal electric field. We have found that the scale of the observed variations in the excitation spectra of the 4f electrons depends on the Kondo temperature T _K and is insensitive to disorder in the rare-earth sublattice. Thus, despite the fact that T _K ≪Δ_CF, hybridization with states in the conduction band has a substantial effect on all parameters of the excitation spectrum of the ground multiplet of the 4f electrons at low temperatures. Zh. éksp. Teor. Fiz. 115, 2197–2206 (June 1999) A. A. Baikov Institute of Metallurgy     

Electron Raman scattering in Tl2Ba2CuO6+x crystals

It is inferred from the position of the 2Δ peak in the electron light scattering spectra that in a sample with high T _c ≈90 K the ratio 2Δ/T _c is approximately equal to 6 and 7 for different polarizations, while in overdoped samples with T _c ≈40 and 35 K the 2Δ peak is observed only in x′y′ polarization with a substantially lower ratio 2Δ/T _c ≈3.2. With decreasing T _c in Tl₂Ba₂CuO_6+x crystals, a transition occurs from strong to weak coupling; the superconducting gap remains anisotropic at different doping levels. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 760–765 (10 December 1996)     

Heat conductivity of a nonlinear β-FPU lattice

In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce the time of computation of heat conductivity at ΔT → 0. The threshold temperature T _thr is found to behave as T _thr ∼ N ⁻³, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T _thr, phonon heat conductivity is dominant; at T > T _thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires further study.     

Analytic solution of the BCS gap equation inD dimensions (D=1, 2, 3), at finite temperatures

The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically in one, two and three dimensions, for temperatures close to zero andT _c. We work in the weak coupling limit, but allow the interaction widthν≡ħω _m/E _F to lie in the interval (0, ∞) Here,ħω _m is the maximum energy of a force-mediating boson, andE _F denotes the Fermi energy. We obtain expressions forT _c and ΔC, the jump in the electronic specific heat acrossT=T _c, in the limitsν≪1 (the usual phonon pairing) andν>1 (non-phononic pairing). This enables us to see howT _c scales with the mediating boson cut off. Our results predict a larger jump in the specific heat for the caseν>1, compared toν≪1. We also briefly touch upon the role of a van Hove singularity in the density of states.     

Sound propagation anomalies and phase diagram of chromium alloys

Calculations of the complex elastic moduli Ĉ(T) in dilute Cr alloys are compared to measurements of the velocity and damping of sound near T _N and at high temperatures T>T _N (T _N — Néel temperature). The thermodynamic calculation is based on the covalent bond model of 3d ions in a state with different numbers n of covalent electrons. The parameters A _ij ⁽ⁿ⁾ of indirect exchange between the ions of the i and j sublattices are expressed in terms of the covalent bond energy Γ _ij ⁽ⁿ⁾ . The stability of the charge and spin density waves (CDWs and SDWs) is found by a variational method and is determined by the dispersion of Γ _ij ⁽ⁿ⁾ and by the Coulomb parameters U _n. For a small structural vector Q the phase diagram contains a superantiferromagnetic phase (SAFM) at temperatures T _N<T≲2T _N. The peak of the defect |ΔE(T)| of the modulus and of the sound damping Δ_h(T _N) near the first-order SDW-SAFM transition is determined by the structure of the transitional domain. Measurements of the anomalous growth of E(T) at temperatures T>T _N make it possible to determine the magnetostriction constants λ(T) of Ce alloys in the SAFM phase on the basis of the SAFM theory. Fiz. Tverd. Tela (St. Petersburg) 41, 1467–1472 (August 1999)     

The low temperature spectral weight transfer problem in Kondo insulators

In this paper we address the problem of the spectral weight transfer in Kondo insulators (KI). We employ the X-boson approach for the periodic Anderson model, in the U →∞ limit. We calculate the two energy gaps of the system analytically: the indirect gap, Δ_ind = E_g ≃ E_mir, present in the density of states, and the direct one Δ_dir, associated with the minimum energy necessary to produce inter-band transitions. We find that the optical behavior of the system is governed by two energy scales: one of low frequency, characterized by E_g ≃ E_mir, in the mid-infrared region (MIR), which is a reminiscent of the heavy fermion E_mir peak, that appears in Kondo insulators as a broad maximum in the MIR region and that controls the low temperature transport properties, the gap opening in optical conductivity and the formation of the Drude peak, at ω = 0, in the intermediate temperature range. The other energy scale appears at high frequencies, and is characterized by the direct gap Δ_dir. According to our results, this peak controls the anomalous redistribution of spectral weight in the optical conductivity. We apply the theory in order to study the Kondo insulator FeSi, and we calculate the optical conductivity of the system and the spectral weight transfer in the optical conductivity.     

Two energy scales and breakdown of renormalizability in the Kondo problem

It is shown that a second energy scale T ₀ ≫ T _k arises in the Kondo problem. Perturbation theory is valid only in the region T > T ₀. For this reason, the transition from weak to strong coupling occurs at temperatures much higher than the Kondo temperature T _k. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 106–111 (25 July 1999)     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

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)     

Theoretical models for high-temperature superconductivity

Summary A semi-phenomenological analysis is given of the effects of certain band structure features on the gap ratios 2Δ/k _B T _c for high-T _c superconductors, including multigap systems. In addition to phonons other intermediate bosons (IB) mediating the superconducting interaction are considered. Interesting results emerge when the IB energy exceeds the widths of possible narrow peaks in the density of states associated with subbands presumably belonging to substructures such as stacked Cu−O planes. Comparison with experiment is made. In particular, data obtained by Warrenet al. via nuclear-spin relaxation on Ba₂YCu₃O_7−δ can be interpreted within the present framework in terms of a model having an IB of energy ≳1 eV, which exceeds the predicted width (≲0.3 eV) of a peak in the density of states containing the normal-state Fermi level. This suggests that the IB is not a phonon. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Giant negative magnetoresistance in a nonmagnetic semiconductor

Studies of a classical III–V semiconductor (InSb) doped with 3d magnetic ions (Mn²⁺, having a localized spin S=55/2) reveal some unexpected transport properties. It is found that the transition from the metallic to the low-temperature insulator phase occurs at an impurity concentration N _Mn∼N _cr=2× 10¹⁷ cm⁻³ and a temperature T<T _cr∼1 K. Under these conditions a giant negative magnetoresistance arises. The experimental results can be explained in terms of the onset of a hard Mott-Hubbard gap Δ in the impurity band formed by the shallow manganese acceptor in InSb at N _Mn∼N _cr. A model describing the gap formation is proposed. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 5, 358–362 (10 March 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.