No abstract

The crossover between the Cooper-pair condensation and the Bose-Einstein condensation of "dielectronic" molecules in two-dimensional superconductors is investigated in detail on the basis of the Nozieres and Schmitt-Rink formalism. It is shown that temperature dependence of the chemical potential p so calculated is classified into two classes as decreasing temperatures; i.e. , class (a) where p approaches the point of Bose-Einstein condensation of two-dimensional ideal Bose gas of "di-electronic" molecules, and class (b) where p diverges positively along the line of BCS-type mean-field pair condensation. This feature is rather universal irrespective of strength V of the attractive interaction of the s-wave type. While the former class (a) has been found by Schmitt-Rink, Varma, and Ruckenstein, existence of the latter class (b) is recognized here. In the case where Vis fixed, class (a) is realized for electron number density N smaller than N", which is an increasing function of V, and class (b) is realized for X larger than N". If N ))Ncr in particular, there exists a regime, where the Fermi-liquid-like description is valid, between the BCS-type mean-field transition temperature and the Fermi temperature. In the situation where V is changed with N being fixed, low-temperature states for the strong-coupling case belong to class (a) while those for the weak-coupling case belong to class (b). Therefore, with decreasing V, the chemical potential p( T), at temperatures far below the Fermi temperature, shows a discontinuous jump at V = V"(Ã) corresponding to the transition from class (a) to (b). However, this is in contradiction to a physical picture that the chemical potential should smoothly cross over between the above two limits unless the liquid-gas transition occurs. This shows in turn a necessity of improving the Nozieres and Schmitt-Rink formalism itself especially in two dimensions. A preliminary approach beyond their formalism is briefly discussed.

Single crystals of copper hydroxide compounds (1-7) containing organic sulfonate ions (ethane-1,2disulfonate, 1-octanesulfonate, p-toluenesulfonate, p-ethylbenzenesulfonate, 2-naphthalenesulfonate, 1,5naphthalenedisulfonate, and 2,6-naphthalenedisulfonate, respectively) were easily prepared by the hydrolysis of copper acetate aqueous solution containing the respective organic sulfonates. All seven compounds had distorted diamond chain magnetic networks similar to that found in azurite (Cu 3 (CO 3 ) 2 (OH) 2 ). The diamond chain units were composed of copper, hydroxide, and acetate ions and water molecules (with additional sulfonate ions in the case of 7). The anions or molecules bridged the neighbouring copper ions, and might mediate superexchange interactions between copper atoms. The chain units did not have the same structure, and were slightly different in their Cu-O bond lengths, Cu-O-Cu bridging angles and so on.Magnetic measurements revealed primarily antiferromagnetic interactions between the neighbouring copper ions and no antiferromagnetic ordering. The χ p vs. T plots showed broad maxima at around 60-80 K that are characteristic of low-dimensional magnetic networks. Compounds 1-6 were paramagnetic down to 2 K, while 7 had a diamagnetic ground state. The different magnetic properties are due to the small structural differences in the diamond chain units, because the sign and intensity of magnetic coupling between the neighbouring copper ions are sensitive to the bridging structures. Copper hydroxide compounds with different organic ions and diverse structures prepared by this hydrolysis method will facilitate the systematic study of the underlying diamond chain magnetic networks.

The problem on crossover between the Cooper-pair condensation and the Bose-Einstein condensation of “di-electronic molecules” in two-dimensional superconductors is discussed. a result based on the Nozières and Schmitt-Rink formalism is reviewed and a preliminary result beyond their formalism is presented. In the latter, effect of repulsion between electron pairs due to the exchange effect among constituent electrons plays a crucial role.