Quantum phase transitions in d-wave superconductors

Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x(2)-y(2)) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x(2)-y(2))+is and d(x(2)-y(2))+id(xy) pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.     

Microstructure and structural phase transitions in iron-based superconductors

Crystal structures and microstructural features, such as structural phase transitions, defect structures, and chemical and structural inhomogeneities, are known to have profound effects on the physical properties of superconducting materials. Recently, many studies on the structural properties of Fe-based high-Tc superconductors have been published. This review article will mainly focus on the typical microstructural features in samples that have been well characterized by physical measurements. （i） Certain common structural features are discussed, in particular, the crystal structural features for different superconducting families, the local structural distortions in the Fe2Pn2 （Pn = P, As, Sb） or FeeCh2 （Ch = S, Se, Te） blocks, and the structural transformations in the 122 system. （ii） In FeTe（Se） （11 family）, the superconductivity, chemical and structural inhomogeneities are investigated and discussed in correlation with superconductivity. （iii） In the Ko.sFe1.6＋xSe2 system, we focus on the typical compounds with emphasis on the Fe-vacancy order and phase separations. The microstructural features in other superconducting materials are also briefly discussed.     

Order and quantum phase transitions in the cuprate superconductors

This is a summary of a review article appearing in Reviews of Modern Physics, July 2003. The ground state of the cuprate superconductors is described using the paradigm of competing orders. This approach has led to numerous predictions, some of which have been tested in recent nanoscale experiments.     

First and second order quantum phase transitions in multi-band superconductors

In multi-band and inter-metallic materials superconductivity can be destroyed by applying external pressure in these systems. In many cases the critical temperature is driven continuously to zero, the superconducting to normal transition being associated with a superconducting quantum critical point (SQCP). In this paper we propose a model for this type of SQCP based on the increase of hybridization as pressure is applied in the material. We study a two-band superconductor with hybridization V between these bands. We use a BCS approximation and include both inter- and intra-band attractive interactions. We show that for negligible inter-band interactions, as hybridization increases there is a second order phase transition from a superconductor to a normal state at zero temperature at a critical value of the hybridization V_c. This SQCP can be reached by pressure, since this external parameter controls hybridization in the system. We also find discontinuous transitions at zero temperature and the appearance of a gapless superconducting (GS) phase in a certain range of hybridization in the case of inter-band interactions being dominant.     

Magnetoelastic quantum fluctuations and phase transitions in the iron superconductors

We examine the relevance of magnetoelastic coupling to describe the complex magnetic and structural behavior of the different classes of the iron superconductors. We model the system as a two-dimensional metal whose magnetic excitations interact with the distortions of the underlying square lattice. Going beyond the mean field, we find that quantum fluctuation effects can explain two unusual features of these materials that have attracted considerable attention: first, why iron telluride orders magnetically at a non-nesting wave vector (π/2,π/2) and not at the nesting wave vector (π,0) as in the iron arsenides, even though the nominal band structures of both these systems are similar, and second, why the (π,0) magnetic transition in the iron arsenides is often preceded by an orthorhombic structural transition. These are robust properties of the model, independent of microscopic details, and they emphasize the importance of the magnetoelastic interaction.     

Renormalization group treatment of phase transitions in ferromagnetic superconductors

We investigate the nature of the phase transition from the superconducting to the uniformly ordered magnetic phase in ferromagnetic superconductors by renormalization group methods. For this purpose Halperin, Lubensky, Ma's application of the-expansion to pure superconductors is extended to include the influence of magnetic order as well. Our treatment shows that in the vicinity of the ferromagnetic to superconducting phase-boundary critical fluctuations of the magnetization are absorbed into fluctuations of the magnetic field. As a consequence the transition always is first order. An additional indication to the dominance of electromagnetic effects is the irrelevance of the coupling corresponding to spin flip scattering.     

Fluctuations and some strain related interaction mechanisms in structural phase transitions

Materials which undergo structural phase transitions with bilinear coupling between the spontaneous strain (e ^sp _i ) and the thermodynamic order parameter (Q) of the type λ_i e ^sp _i Q show characteristic fluctuation pattern at T > T _c. Snapshots of such pattern show tweedlike structures with butterfly shaped structure factors. Some experimental fluctuation patterns are reviewed and compared with the theoretical predictions.

At T ≤ T_c , characteristic microstructures often include structural twinning. The relevant energy expressions for order/disorder systems are recalled and their contribution to thermodynamic fluctuations are described. It is anticipated that some of the physical mechanisms may play a role also in improper ferroelastics with coupling of the type λ_i e ^sp _i Q ² _k where Qk is a component of a degenerate order parameter Q = {Qk}.     

Nonequilibrium phase transitions of vortex matter in three-dimensional layered superconductors

Large-scale simulations on the three-dimensional (3D) frustrated anisotropic XY model have been performed to study the nonequilibrium phase transitions of vortex matter in weak random pinning potential in layered superconductors. The first-order phase transition from the moving Bragg glass to the moving smectic is clarified, based on thermodynamic quantities. A washboard noise is observed in the moving Bragg glass in 3D simulations for the first time. It is found that the activation of the vortex loops plays the dominant role in the dynamical melting at high drive.     

Fluctuations in high field superconductors

We present calculations for the influence of fluctuations in high field superconductors where the critical field is limited by Pauli paramagnetism. Due to the fact that the critical field at the second order phase transition point as function of temperature may have a maximum atT≠0 the additional conductivity due to fluctuations may have a nonmonotonic temperature dependence. This way we can account for recent experimental findings by Tedrow, Meservey and Schwartz. We also calculate the additional tunneling density of states due to fluctuations. Under proper conditions it exhibits a maximum at zero frequency like in the gapless regime. Finally we show that our findings of a nonmonotonic resistivity should also apply to superconductors containing magnetic impurities such as La_3-x Gd _x In in an external field.     

Fluctuations in superconductors belowT c

Thermal fluctuations of the order parameter in the superconducting state are investigated, particularly near the transition temperature, using the time dependent Ginzburg-Landau theory. These fluctuations give rise to a contribution of the dynamical conductivity, which strongly increases as the temperature is raised towardsT _c , in contrast to the temperature dependence of the electromagnetic response due to the static order parameter. At the transition temperature this contribution joins continuously to the extra response (conductivity, susceptibility) which has been calculated and observed in the temperature region aboveT _c , where it represents the onset of superconductivity in the normal state. Particularly the dynamical conductivity due to fluctuations is calculated and discussed for bulk material, thin films and thin wires belowT _c . The temperature and frequency dependence should be observable in microwave experiments.     

Dynamic phase transitions in moving vortex structures in type II superconductors

A theoretical explanation for the I–V characteristic of type II superconductors in the vortex state is provided. The run of the experimental I–V curves is associated with discontinuities and depends on the experimental prehistory. It is conjectured that dynamic phase transitions occur in the network of mobile and immobile channels along which the vortices travel when a transport current is applied. This work has been done on the author’s own initiative.     

Group-theoretical analysis of possible structural phase transitions in the high-temperature superconductors

A group-theoretical analysis is performed for the complete condensation of order parameters at structural phase transitions (SPT's) in the high-temperature superconductors belonging to the D ¹⁷ _4h -14/mmm space group in the high-symmetry phase. As a rule, such transformations are due to a successive softening of phonons with wave vectors k ₁ = 1/2 b ₃ and k ₂ = 1/2 (b ₁ - b ₃) belonging to the K13(X) star of the Brillouin zone of a tetragonal body-centered Bravais cell. SPT's in system La_2-x Ba _x CuO₄ are considered in detail.