<p>Superconductors in nano-sized shape are investigated. Superconductor and also electrons which form superconductivity have quantum nature. This means when size of superconductor is small, there appear quantum effects. The critical temperature <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$T_c$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation> becomes higher than that of a bulk superconductor. In the extremely dirty nano-sized superconductor, the critical temperature becomes much higher than that of a clean nano-sized superconductor. This is because a part of superconducting electrons concentrates in a localized state and has a high density of states. However, if the superconducting state remains localized below <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$T_c$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>, resistivity may not be zero just below <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$T_c$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>. Therefore we investigate how this localized state of superconductivity develops with decreasing temperature below <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$T_c$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>. We show this localized state extends to whole superconductor just below <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$T_c$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>.</p>

Temperature Dependence of Superconducting State in a Nano-sized Dirty superconductor

期刊论文
出版模式：

开放获取
发表日期：

2026年7月16日

查看全文

Masaru Kato,
Terukazu Nishizaki

摘要

Superconductors in nano-sized shape are investigated. Superconductor and also electrons which form superconductivity have quantum nature. This means when size of superconductor is small, there appear quantum effects. The critical temperature $T_c$ $T_{c}$ becomes higher than that of a bulk superconductor. In the extremely dirty nano-sized superconductor, the critical temperature becomes much higher than that of a clean nano-sized superconductor. This is because a part of superconducting electrons concentrates in a localized state and has a high density of states. However, if the superconducting state remains localized below $T_c$ $T_{c}$ , resistivity may not be zero just below $T_c$ $T_{c}$ . Therefore we investigate how this localized state of superconductivity develops with decreasing temperature below $T_c$ $T_{c}$ . We show this localized state extends to whole superconductor just below $T_c$ $T_{c}$ .