Superconductors order parameter

Oscillations of were found in SFS multilayers for different combinations of materials [19-28]. Typically at small F layer thickness, d, phase difference

between phases of superconductor order parameters is zero (so-called zero state). With a increase exhibits first a rapid drop with a minimum for some df. After this point increases with df saturating at larger thickness. This overall TJ dj ) behavior is a signature of the 0 -phase shift in S/F hybrids [2]. At large d the critical temperature for = r exceeds for [Pg.538]

Fig. 12. The local superconductor order parameter and the local magnetic induction in the vicinity of a vortex in an Abrikosov phase. ...

Takahashi T, Kobayashi Y, Nakamura T, Kanoda K, Hilti B, Zamhounis IS (1994) Symmetry of the order parameter in organic superconductors (MDT-TTF)2Aul2 vs. (TMTSF)2C104. Physica C 235-240 2461-2462... 

In 1957, Bardeen, Cooper, and Schrieffer published their theory of superconductivity, known as the BCS theory. It predicts that under certain conditions, the attraction between two conduction electrons due to a succession of phonon interactions can slightly exceed the repulsion that they exert directly on one another due to the Coulomb interaction of their like charges. The two electrons are thus weakly bound together forming a so-called Cooper pair. It is these Cooper pairs that are responsible for superconductivity. In conventional superconductors, these electrons are paired so that their spin and orbital angular momenta cancel. They are described by a wave function, known as an order parameter. In this case the order parameter has symmetry similar to that of the wave function of s electrons and represents a singlet state. 

A more complicated but solvable problem is a definition of the order parameter for antiferromagnetics, binary alloys, superconductors etc. The dimensionless units T/Tc and 77/770 (Fig. 1.4) allow us to present the behaviour of the order parameter rj = r) T) in a form universal for many quite different systems. Moreover, in some cases even quantitative similarities hold which concerns in particular the value of the exponent (3. (The value of 77 = 0 characterizes always disordered phase.)... 

The range of coherence follows naturally from the BCS theory, and we see now why it becomes short in alloys. The electron mean free path is much shorter in an alloy than in a pure metal, and electron scattering tends to break up the correlated pairs, so dial for very short mean free paths one would expect die coherence length to become comparable to the mean free path. Then the ratio k i/f (called the Ginzburg-Landau order parameter) becomes greater than unity, and the observed magnetic properties of alloy superconductors can be derived. The two kinds of superconductors, namely those with k < 1/-/(2T and those with k > l/,/(2j (the inequalities follow from the detailed theory) are called respectively type I and type II superconductors. 

In 1962, B. Josephson recognized the implications of the complex order parameter for the dynamics of the superconductor, and in particular when one considers a system consisting of two bulk conductors connected by a weak link." This research led to tile development of a series of weak link devices commonly called Josephson junctions. See also Josephson Tunnel-Junction. These devices hold much promise for achieving ultra high-speed computers where switching time is of the order of 1CT11 second. 

Not only do the thermodynamic properties follow similar power laws near the critical temperatures, but the exponents measured for a given property, such as heat capacity or the order parameter, are found to be the same within experimental error in a wide variety of substances. This can be seen in Table 13.3. It has been shown that the same set of exponents (a, (3, 7, v, etc.) are obtained for phase transitions that have the same spatial (d) and order parameter (n) dimensionalities. For example, (order + disorder) transitions, magnetic transitions with a single axis about which the magnetization orients, and the (liquid + gas) critical point have d= 3 and n — 1, and all have the same values for the critical exponents. Superconductors and the superfluid transition in 4He have d= 3 and n = 2, and they show different values for the set of exponents. Phase transitions are said to belong to different universality classes when their critical exponents belong to different sets. 

Summary. On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in a ferromagnetic superconductor and hybrid superconductor - ferromagnetic (S/F) systems with a domain structure in an applied external magnetic field H. We study the interplay between the superconductivity localized at the domain walls and between the domain walls and show that such interplay determines a peculiar nonlinear temperature dependence of the upper critical field. For hybrid S/F systems we also study the possible oscillatory behavior of the critical temperature TC(H) similar to the Little-Parks effect. 

Multilayered superconductor/ferromagnet S/F) structures are under an intensive study now (for a recent review see e.g. [1]). The interest in such systems originates from a possibility to find new physical phenomena as well from the hope to construct new devices based on these structures. Although a ferromagnet F attached to a superconductor S is expected to suppress the order parameter in S, under certain conditions superconductivity and ferromagnetism may coexist and exhibit interesting phenomena. In most papers on S/F structures the case of collinear (parallel or antiparallel) orientations... 

Figure IV 1 2. Geometry of the insulator-superconductor boundary discussed in the text, together with a model of the order parameter, Eq.(20)...

Then, from fig.lc it is seen that SC transition onset points Tconset(H)(= Tk(H)) are at the Bloch-Gruneisen curve (dashed curve). On the other hand, such a picture is characteristic for low temperature superconductors described by s-wave BCS theory. From this analogy it may be concluded that in the cuprates the SC order parameter is of s-wave symmetry, also. Moreover, as seen from magnetic phase H-T diagram, the... 

In this paper, we concentrate on the /j+SR measurements and determine if YBa2Cu307 is a bulk. v-wave (nodeless) superconductor, as determined in Refs. 1-3, or a d-wave superconductor, whose order parameter A(k), changes sign as a function of k, as claimed in Ref. 8. In making this determination, we show that the features observed in the single-crystal data of Ref. 8 are actually due to temperature-activated fluxon de-pinning, an effect which is not readily observable in strongly pinned systems such as the early powder samples or the early heavily-twinned crystals. 

Abstract In strong-coupling superconductors with a short electron mean free path the self-energy effects in the superconducting order parameter play a major role in the phonon manifestation of the point-contact spectra at above-gap energies. We compare the expressions for the nonlinear conductivity of tunnel, ballistic, and diffusive point-contacts and show that these expression are similar and correspond to the measurements of the phonon structure in the point-contact spectra for the 7r-band of MgB2. 

Another important aspect of phase transitions in solids is the presence of soft modes. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In second-order transitions, the soft mode frequency goes to zero at Tc, but in first-order transitions, the phase change occurs before the mode frequency goes to zero. Soft modes have been found to accompany a variety of solid-state transitions, including those of superconductors and organic solids.2,5 Occurrence of soft modes in phase transitions can be inferred from Landau s treatment wherein atomic displacements may themselves be considered to represent an order parameter. 

The report of the Meissner effect stimulated the London brothers to develop the London equations, which explained this effect, and which also predicted how far a static external magnetic field can penetrate into a superconductor. The next theoretical advance came in 1950 with the theory of Ginzburg and Landau, which described superconductivity in terms of an order parameter and provided a derivation for the London equations. Both of these theories are macroscopic or phenomenological in nature. In the same year, 1950, the... 

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