Evidence for vertical line nodes in Sr2RuO4 from nonlocal electrodynamics

By determining the superconducting lower and upper critical fields <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>H</a:mi><a:mrow><a:mi mathvariant="normal">c</a:mi><a:mn>1</a:mn></a:mrow></a:msub><a:mrow><a:mo>(</a:mo><a:mi>T</a:mi><a:mo>)</a:mo></a:mrow></a:mrow></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>H</c:mi><c:mrow><c:mi mathvariant="normal">c</c:mi><c:mn>2</c:mn></c:mrow></c:msub><c:mrow><c:mo>(</c:mo><c:mi>T</c:mi><c:mo>)</c:mo></c:mrow></c:mrow></c:math>, respectively, in a high-purity spherical <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>Sr</e:mi><e:mn>2</e:mn></e:msub><e:msub><e:mi>RuO</e:mi><e:mn>4</e:mn></e:msub></e:mrow></e:math> sample via ac-susceptibility measurements, we obtain the temperature dependence of the coherence length <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>ξ</f:mi></f:math> and the penetration depth <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>λ</g:mi></g:math> down to <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mn>0.04</h:mn><h:msub><h:mi>T</h:mi><h:mi>c</h:mi></h:msub></h:mrow></h:math>. Given the high sample quality, the observed <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msup><i:mi>T</i:mi><i:mn>2</i:mn></i:msup></i:math> dependence of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>λ</j:mi></j:math> at low temperatures cannot be explained in terms of impurity effects. Instead, we argue that the weak type-II superconductor <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msub><k:mi>Sr</k:mi><k:mn>2</k:mn></k:msub><k:msub><k:mi>RuO</k:mi><k:mn>4</k:mn></k:msub></k:mrow></k:math> has to be treated in the nonlocal limit. By comparing our data with existing theory in that limit, the penetration depth in <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:msub><l:mi>Sr</l:mi><l:mn>2</l:mn></l:msub><l:msub><l:mi>RuO</l:mi><l:mn>4</l:mn></l:msub></l:mrow></l:math> agrees with a gap structure having vertical line nodes, while horizontal line nodes cannot account for the observation. The work highlights the potential benefits of purifying other unconventional superconductors in order to access the fascinating nonlocal regime in more materials and to determine their Cooper pair wave functions. Published by the American Physical Society 2024