Journal of Superconductivity: Incorporating Novel Magnetism, Vol. 14, No. 4, August 2001 ( C  2001) Pseudo-Gap Phenomenon in the Sn-Doped Mercury-Based Cuprate Superconductors Anand Vyas 1 and C. C. Lam 1 Received and accepted 2 December 2000 The Sn-doped mercury-based copper oxide high temperature superconductors, with nomi- nal composition (Hg 1−x Sn x )Ba 2 Ca 2 Cu 3 O 8+δ , have been successfully fabricated. These sam- ples were used to study the pseudo-gap phenomenon in their normal phase. By means of ln[1/ρ(T ) − 1/ρ N (T )] versus 1 / T plots we found three characteristic temperatures T ∗ , T S , and T F , which describe the role of pseudo-gap phenomenon. From the stated plots, we are able to estimate the magnitude of the pseudo-gap for our samples. The pseudo-gap  PG changes into the spin pairing dipolar superconducting gap  SPDS , when the Fermi kinetic energy shrinks to zero at the critical temperature T c . It is proved that the spin pairing dipolar superconducting gap  SPDS =  (2/3) T , where,  T being the total superconducting gap of the cuprate super- conductors, which has the value determined by 2 T = 3.52 √ 3k B T c . It is also proved that the spin pairing dipolar superconducting gap is smaller than the dipolar pseudo-gap,  PG . KEY WORDS: high temperature superconductors; pseudo-gap phenomenon; pseudo-gap opening tem- perature; critical temperature of superconductor. 1. INTRODUCTION Mercury-based superconducting cuprates of Hg-1223 are receiving a great deal of heed because of their outstanding critical temperature, see [1,2], which make them truly attractive for their applications. The successful formation of the pure Hg-1223 supercon- ducting phase requires extraordinary care during each step of the sample preparation to minimize the ex- posure of the precursor materials to moisture and carbon dioxide, see [3]. In other words, the synthesis of pure mercury-based copper oxide Hg-1223 phase superconductors is rather difficult. Stabilization of Hg-1223 phase by the addition of various metallic dopants, hence, becomes very important. By improv- ing the stability of the Hg-1223 phase we can reduce the severe demands of synthesis conditions. The sub- stitution of rare-earth metal and transition metal ele- ments in R 1−x Pr x Ba 2 Cu 3 O 7 have been studied in the past, see [4,5]. It was proved experimentally that the 1 Department of Physics and Materials Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, People’s Republic of China. normal state resistivity is R-ionic dependent. They also found that the opening pseudo-gap temperature is increased with increasing the ionic size of the R- element. Since the oxygen content plays an impor- tant role in high temperature superconductors, so the oxygen deficiency will affect the properties of the superconductors. The effect of oxygen deficiency on the Y-123 superconductor has been studied carefully, see [6]. This is equivalent to the effect of hole con- centration on the superconductivity of the cuprates. On the other hand, it is well known that for an op- timally doped high temperature superconductor the in-plane resistivity decreases linearly with decreasing temperature, in the normal state, see [7]. Obviously, for underdoped samples, the deviation from the T- linear behaviour in the resistivity occurs at a temper- ature T ∗ that is far above the critical temperature of a superconductor, that is to say T ∗ > T c , where T ∗ is called the pseudo-gap opening temperature. This pseudo-gap opening temperature T ∗ has also been de- termined using different methods, see [8–15]. Though the data of T ∗ obtained from these different meth- ods are not identical with the resistivity measure- ment, nevertheless, the results are comparable. The 487 0896-1107/01/0800-0487$19.50/0 C  2001 Plenum Publishing Corporation