till now, there are many superconductors. Is there any relationship between critical temperature of superconductor and the atomic weight & radius?
Now the isotope effect is one relationship beteen critical temperature and atomic weight.
But it can not explain high temperature superconductor.
Thanks a lot.
In high-temperature superconductors (HTSC), the relationship between critical transition temperature (Tc) and atomic weight, as well as the impact of isotopes, is complex and nuanced.
Atomic Weight and Tc: In conventional superconductors, the critical temperature (Tc) is linked to the binding energy (BE) of Cooper pairs. When thermal energy matches BE, it can disrupt these pairs, ending superconductivity. Typically, heavier elements in conventional superconductors tend to lower Tc due to decreased lattice vibrations affecting Cooper pair formation. However, HTSCs exhibit more intricate behavior, and their Tc can be significantly higher. The correlation between atomic weight and Tc in HTSCs is not straightforward; heavier elements do not necessarily result in lower Tc. The interplay of electronic, magnetic, and lattice interactions in HTSCs makes the relationship more complex and less predictable than in conventional superconductors.
As for the isotope effect in HTSCs, this effect is pronounced. For instance, replacing hydrogen with deuterium alters phonon coupling, which affects the pairing strength of Cooper pairs. This substitution can either increase or decrease Tc, depending on how the change in mass impacts lattice vibrations and electron-phonon interactions. While isotopic mass and lattice spacing indeed influence Tc, the exact relationship varies across different HTSC compounds due to their diverse and complex structural and electronic properties.
Overall, while conventional superconductors often show a clear inverse relationship between Tc and atomic weight, HTSCs do not follow such simple patterns. The isotope effect in HTSCs plays a significant role but varies widely across different materials. This complexity underscores the need for detailed study of individual HTSC compounds to understand their unique superconducting properties.
Dear Dr. Bahram
Thanks for your wonderful answer. Yes, for cryogenic superconductors, the critical temperature and atomic mass are correlated. For high-temperature superconductors, it's not so straightforward. When we select the relevant elements from the high-temperature superconductor compounds, and then select the appropriate number of elements N, we are surprised to find that the critical temperature of many high-temperature superconductors and low-temperature superconductors can be related to the atomic weight and atomic radius of the element, and it is consistent with the isotopic effect. For example, if Hg12Tl3Ba30Ca30Cu45O127 has Tc=138K, the relevant element in the middle is CuO2, a=1.87 is the sum of the radii of O and Cu, and m=96 is the sum of the atomic weights of 2O and Cu. N=3； For example, Bi2Sr2Ca2Cu3O10 (BSCCO) has Tc=110K, and the relevant element in the middle is Cu2O, a=1.87 is the sum of the radii of O and Cu, and m=143 is the sum of the atomic weights of 2O and Cu. N=3； According to this rule, 10000/(N*a)/(N*m)^0.5 establishes a relationship with Tc, and finds that more than a dozen superconductors are all in the same straight line. But I can't solve it theoretically, especially the chosen value of number of elements N. These days, I've tried to calculate N using the wavelength of de Broglie's matter wave, and it's clear that I've failed.
Maybe you can help me to fix it.
Who will exactly define the value N, is the next Nobel laureate. I believe that N depends on many parameters of crystal, first of all on the presence of electronic local states in metallic crystals.
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