Charge- and spin-density waves in existing superconductors: competition between Cooper pairing and Peierls or excitonic instabilities

This review deals with the properties of superconductors with competing electron spectrum instabilities, namely, charge-density waves (CDWs) and spin-density waves (SDWs). The underlying reasons of the electron spectrum instability may be either Fermi surface nesting or the existence of Van Hove saddle points for lower dimensionalities. CDW superconductors include layered dichalcogenides, NbSe3, and compounds with the A15 and C15 structures among others. There is much evidence to show that high-Tc oxides may also belong to this group of materials. The SDW superconductors include URu2Si2 and related heavy-fermion compounds, Cr-Re alloys and organic superconductors. We review the experimental evidence for CDW and SDW instabilities in a wide range of different superconductors, and assess the competition between these instabilities of the Fermi surface and the superconducting gap. Issues concerning the superconducting order parameter symmetry are also touched upon. The accent is put on establishing a universal framework for further theoretical discussions and experimental investigations based on an extensive list of available and up-to-date references.

http://iopscience.iop.org/article/10.1088/0953-2048/14/4/201/pdf

Charge- and spin-density-wave superconductors

The transition from Townsend to glow discharge is studied via two-dimensional simulations of discharges with moderate pd values corresponding to the right branch of the Paschen curve (p is the gas pressure and d the electrode spacing). The discharge model is coupled to the external circuit model enabling simulations of subnormal oscillations during the discharge transition from the Townsend to normal regime. This transition is accompanied by radial constriction of the discharge and formation of a normal cathode spot. The electron thermal flux backscattered to the cathode is observed to be important in the Townsend regime, which contributes significantly to discharge instability by virtue of the secondary emission coefficient γ becoming an increasing function of E/N. The simulations are carried out for different gas pressures and different parameters of the external circuit. The predicted results are in agreement with experimental observations and previously published semi-analytical models.

https://iopscience.iop.org/article/10.1088/0022-3727/36/23/020/pdf

Two-dimensional simulations of the transition from Townsend to glow discharge and subnormal oscillations

Models and calculated results are presented for the flux‐pinning‐induced magnetostriction in type‐II superconductors. Three models are considered for the critical state; the original Bean model, the Kim model, and the exponential model in which the critical current density is assumed to depend exponentially on the flux density. The analytic expressions of the length change under the magnetic field are derived for specimens having infinite slab geometry and under the assumption that the reversible part of the total magnetization is negligibly small. The results are used for computer simulations and the hysteresis loops are calculated over a wide range of the relevant parameters. Since the pinning‐induced magnetostriction reveals the pinning force directly, the hysteresis loops for each model have different features which are discussed in detail. It is also shown that the pinning force of the sample can be directly inferred from the width of the magnetostriction hysteresis loop. Finally, the experimental results on high‐temperature superconductors are discussed in comparison with the calculated results.

Critical state models for flux‐pinning‐induced magnetostriction in type‐II superconductors

The results of ultrasonic, sonic and infrasonic experiments in high-Tc superconductors (HTSC) are reviewed. Some other related fields of investigation are also mentioned.

https://iopscience.iop.org/article/10.1088/0953-2048/6/3/001/pdf

Ultrasonic and related experiments in high-Tc superconductors

Elasticity study on lattice instability in BiSrCaCuO

The complete temperature-dependent elastic constants of superconducting crystals ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ (${\mathit{T}}_{\mathit{c}}$=84 K) are determined from sound-velocity data. The longitudinal modes ${\mathit{C}}_{11}$, ${\mathit{C}}_{22}$, and ${\mathit{C}}_{\mathit{L}}$ (propagating along the [110] direction) monotonically increase as temperature decreases from room temperature to ${\mathit{T}}_{\mathit{c}}$. The shear-mode elastic constants ${\mathit{C}}_{66}$ exhibit a weak variation (1%) with temperature from 250 to 80 K except for three small softening minima around 240, 140, and 100 K. The in-plane shear mode C'(=[(${\mathit{C}}_{11}$+${\mathit{C}}_{22}$)/2-${\mathit{C}}_{12}$]/2) shows not only a relatively small absolute value, but also an overall trend of softening (11%) over a wide temperature range (200--100 K). The softening of the C' mode is consistent with the local-atomic-displacements model proposed from pulsed-neutron-scattering results. A possible relation between the softening of elastic constants and superconductivity is discussed.

Elastic constants and observation of significant elastic softening in superconducting Bi2Sr2CaCu2O8 single crystals.

Two broad internal friction (attenuation as well) peaks in YBCO measured at around 120 K and 250 K are found to exhibit the characteristics of a first-order phase transition. X-ray diffraction indicates no symmetry change on cooling from room temperature but only a downward jump of the lattice parameters was observed. This is referred to as a phase-like transition (PLT) and further confirmed by stress-strain, specific heat and Debye-Waller factor measurements. There always occurs a phase-like transition at 10-30 K above T c in YBCO, BSCCO and TBCCO which disappears in the non-superconducting phases. Ultrasonic studies on single-crystal BSCCO reveal a pronounced elastic anisotropy in the c-plane and a velocity minimum associated with PLT. The overall trend of elastic stiffening below room temperature and some discrepancies and questions in elasticity measurements so far observed for high-T c oxides have been explained or clarified in terms of an abnormal fast change of lattice parameters.

Structural instability in high-T c superconducting oxides

Two internal-friction (attenuation) peaks around 95 and 130 K in the polycrystal and single crystal of Bi-Sr-Ca-Cu-O are found to be related to the superconducting transition at 84 and 107 K, respectively. The jump of lattice parameter and shape-memory effect occurring at the peak temperatures reveal the characteristics of a martensitic transition. The velocity and attenuation versus temperature of ultrasonic longitudinal waves propagating along two directions in the a-b plane at 10\ifmmode^\circ\else\textdegree\fi{} to the a and b axes and of [010] shear waves with [100] polarization were measured for the ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ single crystals. The anisotropic elasticity in the c plane is manifested. Only the longitudinal waves in a direction and the shear waves show an obvious softening minimum of velocity around 250 K, which is associated with an attenuation peak due to a phaselike transition, but other longitudinal waves reveal a monotonic stiffening from room temperature down to ${\mathit{T}}_{\mathit{c}}$. The origin of the overall trend of elastic stiffening that appears in the measurements so far for high-${\mathit{T}}_{\mathit{c}}$ oxides is discussed.

Jin Wu

Papers

Elasticity study on lattice instability in BiSrCaCuO

Elastic constants and observation of significant elastic softening in superconducting Bi2Sr2CaCu2O8 single crystals.

Structural instability in high-T c superconducting oxides

Ultrasonic study of structural instability of monocrystalline and polycrystalline Bi-Sr-Ca-Cu-O

Elastic-anisotropy and lattice instability in bi2sr2ca1cu2o8 single-crystal