<p>The physics of high-<i>T</i><sub>c</sub> superconductors, which has been a major topic in condensed matter physics for more than thirty years, reveals some features of conventional superconductors. We analyze the scaling of the condensation energy <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({{E}_{\Delta }}\)</EquationSource> <!--JETPLet2560768Shaginyan-m1--> </InlineEquation> divided by <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <!--JETPLet2560768Shaginyan-m2--> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="139" /> </InlineMediaObject> <EquationSource Format="TEX">\({{E}_{\Delta }}{\text{/}}\gamma \simeq N(0)\Delta _{1}^{2}{\text{/}}\gamma \)</EquationSource> <!--JETPLet2560768Shaginyan-m3--> </InlineEquation>, that equally applicable to both conventional and unconventional high-<i>T</i><sub>c</sub> superconductors. Here, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(N(0)\)</EquationSource> <!--JETPLet2560768Shaginyan-m4--> </InlineEquation> is the density of states, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\Delta }_{1}}\)</EquationSource> <!--JETPLet2560768Shaginyan-m5--> </InlineEquation> is the maximum value of the superconducting gap, and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <!--JETPLet2560768Shaginyan-m6--> </InlineEquation> is the Sommerfeld coefficient. Basing on this observation, we analyze experimental facts that reveal the general scaling properties of both high-<i>T</i><sub>c</sub> and ordinary superconductors, and theoretically explain that the Homes’ law <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="100" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\rho }_{{s0}}} \propto {{T}_{{\text{c}}}}\sigma ({{T}_{{\text{c}}}})\)</EquationSource> <!--JETPLet2560768Shaginyan-m7--> </InlineEquation> is applicable to the both types of superconductors. Here, <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <!--JETPLet2560768Shaginyan-m8--> </InlineEquation> is the conductivity, <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(T\)</EquationSource> <!--JETPLet2560768Shaginyan-m9--> </InlineEquation> is the temperature, <i>T</i><sub>c</sub> is the superconducting transition temperature, <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\lambda }_{D}}\)</EquationSource> <!--JETPLet2560768Shaginyan-m10--> </InlineEquation> is the zero-<i>T</i> penetration depth, and <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11448_2025_4248_Article_IEq11.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\rho }_{{s0}}}\)</EquationSource> <!--JETPLet2560768Shaginyan-m11--> </InlineEquation> is the superconducting electron density. For the first time, we also explain the reason of violation of the Homes’ law. Our theoretical results agree well with experimental facts.</p>

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General Scaling Behavior of Superconductors

  • V. R. Shaginyan,
  • A. Z. Msezane,
  • S. A. Artamonov

摘要

The physics of high-Tc superconductors, which has been a major topic in condensed matter physics for more than thirty years, reveals some features of conventional superconductors. We analyze the scaling of the condensation energy \({{E}_{\Delta }}\) divided by \(\gamma \) , \({{E}_{\Delta }}{\text{/}}\gamma \simeq N(0)\Delta _{1}^{2}{\text{/}}\gamma \) , that equally applicable to both conventional and unconventional high-Tc superconductors. Here, \(N(0)\) is the density of states, \({{\Delta }_{1}}\) is the maximum value of the superconducting gap, and \(\gamma \) is the Sommerfeld coefficient. Basing on this observation, we analyze experimental facts that reveal the general scaling properties of both high-Tc and ordinary superconductors, and theoretically explain that the Homes’ law \({{\rho }_{{s0}}} \propto {{T}_{{\text{c}}}}\sigma ({{T}_{{\text{c}}}})\) is applicable to the both types of superconductors. Here, \(\sigma \) is the conductivity, \(T\) is the temperature, Tc is the superconducting transition temperature, \({{\lambda }_{D}}\) is the zero-T penetration depth, and \({{\rho }_{{s0}}}\) is the superconducting electron density. For the first time, we also explain the reason of violation of the Homes’ law. Our theoretical results agree well with experimental facts.