Phase transitions Superconductivity

Here N(sQ is the electron density of states on the Fermi surface for one direction of spin, is the effective volume of phonon generation, is the point contact form factor, averaged over the Fermi surface. It should be noted that point contacts of sizes d > l, d l can work also in diffusive or thermal current regimes [5] and are used for the study of EPI, phase transitions, superconductivity and other interesting physical phenomena. 

Not too many theories have been formulated from this point of view and some of the more interesting cases are at the speculative stage of development. Even so, it is remarkable how some of the most enigmatic of natural phenomena have no convincing explanation apart from broken-symmetry theories. Included are the initiation or nucleation of phase transitions, superconductivity (T4.5.1), the arrow of time (entropy) and the cosmic imbalance between matter and antimatter. The beauty of the world, indeed seems to lie in approximate symmetries. 

Rao CNR and Seshadri R 1994 Phase transitions, superconductivity and ferromagnetism in fullerene systems MRS Bulletin 12 28-30... 

Phase transitions are involved in critical temperature thermistors. Vanadium, VO2, and vanadium trioxide [1314-34-7] V2O3, have semiconductors—metal transitions in which the conductivity decreases by several orders of magnitude on cooling. Electronic phase transitions are also observed in superconducting ceramics like YBa2Cu30y but here the conductivity increases sharply on cooling through the phase transition. 

In 1968, an international agreement was reached about the definition of an official (practical) scale of temperature for T> 14 K. This temperature scale IPTS-68, corrected in 1975 [11], was defined by reference fixed points given by transitions of pure substances. To extend the low-temperature range of IPTS-68, the EPT 76 [12-13] gave nine reference temperatures defined by phase transition of pure substances in particular the superconductive transition (between 0.5 and 9K) of five pure metals was introduced. Moreover,... 

One notes that,for small values of e (0 < e < 0.048) m2 becomes positive. Bearing in mind that, in the GL model the phase transition occurs where m2 changes sign (or more exactly the superconductive phase holds only for m2 < 0),it shows that,in the present approximation scheme, there is no phase transition in D = 2 + 2e dimension for very small values of e.Note that, A remains positive on the whole range of e. 

The temperature dependence of the pairing gap for the homogeneous, LOFF and DFS superconducting phases shows the phenomenon of reentrance the superconducting state is revived at finite temperatures. There exist two critical temperatures corresponding to phase transitions from the normal to the superconducting state and back as the temperature is increased from zero to finite values. 

In reality, we are more interested in the intermediate density region, where the color superconducting phase may exist in the interior of neutron stars or may be created in heavy ion collisions. Unfortunately, we have little knowledge about this region we are not sure how the deconfinement and the chiral restoration phase transitions happen, how the QCD coupling constant evolves and how the strange quark behaves in dense matter, etc. Primarily, our current... 

Figure 7. At / = 0.75, pressure as a function of/./ = / e / > and for the normal and color superconducting quark phases. The dark solid lines represent two locally neutral phases (i) the neutral normal quark phase on the left, and (ii) the neutral gapless 2SC phase on the right. The appearance of the swallowtail structure is related to the first order type of the phase transition in quark matter.

It is interesting to notice that the three pressure surfaces in Figure 7 form a characteristic swallowtail structure. As one could see, the appearance of this structure is directly related to the fact that the phase transition between color superconducting and normal quark matter, which is driven by changing parameter //,. is of first order. In fact, one should expect the appearance of a similar swallowtail structure also in a self-consistent description of the hadron-quark phase transition. Such a description, however, is not available yet. 

Contribution of pairing fluctuations to the specific heat in the hadron shell is minor for the case of the neutron pairing due to a small value of Tc < IMeV compared to the value of the neutron chemical potential f//, > 50 MeV). Therefore in the neutron channel fluctuations of the gap are relevant only in a very narrow vicinity of the critical point. However this effect might be not so small for protons, for which the chemical potential is of the order of several MeV, whereas the gap is of the order of one MeV. Therefore it seems that fluctuations may smear the phase transition in a rather broad vicinity of the critical point of the proton superconductivity. 

The inset of Fig. 2 shows that the generalization of the BCS relation Tc 0.57 A(T = 0. fiq) g(pq), between the critical temperature Tc of the superconducting phase transition and the pairing gap A at T = 0 is satisfactorily fulfilled in the domain of the phase diagram relevant for compact stars. 

Figure 3. Phase diagrams for different form-factor models Gaussian (solid lines), Lorentzian a = 2 (dashed lines) and NJL (dash-dotted). In /3-equilibrium, the colorsuperconducting phase does not exist for Co Gi. In the inset we show for the Gaussian model the comparison of the numerical result with the modified BCS formula Tf = 0.57 A(T = 0, fiq) g(Hq) for the critical temperature of the superconducting phase transition.

We have investigated the influence of diquark condensation on the thermodynamics of quark matter under the conditions of /5-equilibrium and charge neutrality relevant for the discussion of compact stars. The EoS has been derived for a nonlocal chiral quark model in the mean field approximation, and the influence of different form-factors of the nonlocal, separable interaction (Gaussian, Lorentzian, NJL) has been studied. The model parameters are chosen such that the same set of hadronic vacuum observable is described. We have shown that the critical temperatures and chemical potentials for the onset of the chiral and the superconducting phase transition are the lower the smoother the momentum dependence of the interaction form-factor is. 

The phase transition to color superconducting quark matter from the lower density regions at small temperatures (T < 5 a 10 MeV) is of first order, while the melting of the diquark condensate and the corresponding transition to normal quark matter at high temperatures is of second order. The presence... 

Sushko YV, Ito H, Ishiguro T, Horiuchi S, Saito G (1993) Magnetic-field-induced transition to resistive phase in superconducting k-(BEDT-TTF)2Cu[N(CN)2]C1. J Phys Soc Jpn 62 3372-3375... 

It has now become apparent that f-band superconductors can be understood in a normal way, like d-band ones" we have just to think about density of states, bandwidth lattice unstabilities and electron correlations to interpret it. This was clearly summarized by Smith after the discovery of superconductivity of Pa and Am. Superconductivity of Am is made by the J = 0 ground state of its six 5 f electrons as was stressed by Johansson , this could also be the case for stabilized trivalent europium metal. The importance of lattice instabilities (like in A-15 high Tc superconductors) was put forward by Fournier who showed that the very large 6T/8p slope for U was mainly due to a very targe change in the electron-phonon coupling associated with the low temperature phase transition. 

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