%0 Journal Article
%T High-Temperature Superconductivity—An Electron Transfer Phenomenon
%A Joachim Sonntag
%J World Journal of Condensed Matter Physics
%P 67-76
%@ 2160-6927
%D 2024
%I Scientific Research Publishing
%R 10.4236/wjcmp.2024.144007
%X The <i>increase</i> of the critical temperature <i>T</i><i><sub>c</sub></i> for superconductivity in Al<sub>1</sub><sub>&#8722;</sub><i><sub>x</sub></i>(SiO<sub>2</sub>)<i><sub>x</sub></i> cermets with increasing <i>x</i> correlates with a <i>decrease</i> of the electron density <i>n</i> due to electron transfer, expressed by <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mrow>
   <msub>
    <mi>T</mi>
    <mi>c</mi>
   </msub>
   </mrow><mo>/</mo><mrow>
   <msub>
    <mi>T</mi>
    <mrow>
     <mi>c</mi><mo>,</mo><mi>max</mi></mrow>
   </msub>
   </mrow></mrow>
  <mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mi>&#x03B3;</mi><mo>&#x22C5;</mo><msup>
   <mi>n</mi>
   <mn>2</mn>
  </msup>
  </mrow>
</math>

 (*). Behind the formula (*) and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mrow>
   <msub>
    <mi>T</mi>
    <mi>c</mi>
   </msub>
   </mrow><mo>/</mo><mrow>
   <msub>
    <mi>T</mi>
    <mrow>
     <mi>c</mi><mo>,</mo><mi>max</mi></mrow>
   </msub>
   </mrow></mrow>
  <mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mn>82.6</mn><msup>
   <mrow>
    <mrow><mo>(</mo>
     <mrow>
      <mi>P</mi><mo>&#x2212;</mo><mn>0.16</mn></mrow>
    <mo>)</mo></mrow></mrow>
   <mn>2</mn>
  </msup>
  </mrow>
</math>

, which is characteristic of hole-doped cuprat high-temperature superconductors, lies a general phenomenon, namely electron transfer, which equalizes potential differences in the material and leads to a strong reduction of <i>n</i>. <i>P</i> is the fraction of holes filled by the transferred electrons. A quantitative consideration gives <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mrow>
   <msub>
    <mi>T</mi>
    <mi>c</mi>
   </msub>
   <mrow><mo>(</mo>
    <mi>x</mi>
   <mo>)</mo></mrow></mrow><mo>/</mo><mrow>
   <msub>
    <mi>T</mi>
    <mrow>
     <mi>c</mi><mo>,</mo><mi>max</mi></mrow>
   </msub>
   </mrow></mrow>
  <mo>=</mo><mn>1</mn><mo>&#x2212;</mo><msup>
   <mrow>
    <mrow><mo>(</mo>
     <mrow>
      <mfrac>
       <mrow>
        <mn>1</mn><mo>&#x2212;</mo><mi>x</mi></mrow>
       <mrow>
        <mn>1</mn><mo>&#x2212;</mo><msub>
         <mi>x</mi>
         <mn>0</mn>
        </msub>
        </mrow>
      </mfrac>
      </mrow>
    <mo>)</mo></mrow></mrow>
   <mn>2</mn>
  </msup>
  </mrow>
</math>

 (**), where <i>x</i> is the doping concentration and <i>x</i><sub>0</sub> is the concentration at which superconductivity begins. At <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>x</mi><mo>=</mo><msub>
%K High-Tc Superconductor
%K Electron Transfer
%K Electron Density
%K Hole Density
%K &#8220
%K P = 1/8&#8221
%K Anomaly
%K Jahn-Teller Effect
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=137150