ABSTRACT
We take a piece of tin and cool it down; at a temperature T0 = 3.7°K we find a specific heat anomaly (Fig. 1-1a). Below T0 the tin is in a new thermodynamical state. What has happened? (a) The electronic specific heat C of a superconductor (in zero magnetic field) as a function of temperature (qualitative plot). Above T<sub>0</sub> (in the normal phase) <inline-formula> <alternatives> <mml:math display="inline"> <mml:mrow> <mml:msub> <mml:mtext>C</mml:mtext> <mml:mo stretchy="false">(</mml:mo> </mml:msub> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mtext>per</mml:mtext> <mml:mspace width="0.25em"/> <mml:mtext>atom</mml:mtext> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msub> <mml:mo>~</mml:mo> <mml:msubsup> <mml:mtext>k</mml:mtext> <mml:mtext>B</mml:mtext> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mtext>T</mml:mtext> <mml:mo>/</mml:mo> <mml:msub> <mml:mtext>E</mml:mtext> <mml:mtext>F</mml:mtext> </mml:msub> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429497032/d2b0510a-8f84-4d3a-8776-dff0770e5b14/content/eq1.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429497032/d2b0510a-8f84-4d3a-8776-dff0770e5b14/content/eq1.tif</a>"/> </alternatives> </inline-formula> where E<sub>F</sub> is the Fermi energy. At the transition point T<sub>0</sub>, C has a discontinuity. At ≪ T<sub>0</sub>, C is roughly exponential C ~ exp (− 1.76 T<sub>0</sub>/T). (b) Free energy of the superconducting phase (F<sub>S</sub>) and of the normal phase (F<sub>n</sub>) versus temperature. The two curves meet (with the same slope) at the transition point T = T<sub>0</sub>. At T = 0 the difference F<sub>n</sub> – F<sub>S</sub> is of order <inline-formula> <alternatives> <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mtext>k</mml:mtext> <mml:mtext>B</mml:mtext> </mml:msub> <mml:msub> <mml:mtext>T</mml:mtext> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>/</mml:mo> <mml:msub> <mml:mtext>E</mml:mtext> <mml:mtext>F</mml:mtext> </mml:msub> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429497032/d2b0510a-8f84-4d3a-8776-dff0770e5b14/content/eq2.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429497032/d2b0510a-8f84-4d3a-8776-dff0770e5b14/content/eq2.tif</a>"/> </alternatives> </inline-formula> per atom. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429497032/d2b0510a-8f84-4d3a-8776-dff0770e5b14/content/fig1_1.tif"/>
