Unconventional Coherence Peak in Cuprate Superconductors

The Hebel-Slichter coherence peak, observed in the spin-lattice relaxation rate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>1</a:mn><a:mo>/</a:mo><a:msub><a:mi>T</a:mi><a:mn>1</a:mn></a:msub></a:math> just below the critical temperature <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>T</c:mi><c:mi mathvariant="normal">c</c:mi></c:msub></c:math>, serves as a crucial experimental validation of the Bardeen-Cooper-Schrieffer pairing symmetry in conventional superconductors. However, no coherence peak in <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mn>1</f:mn><f:mo>/</f:mo><f:msub><f:mi>T</f:mi><f:mn>1</f:mn></f:msub></f:math> has been observed in unconventional superconductors like cuprates. In this study, an unconventional coherence peak is identified for the first time using nuclear quadrupole resonance on <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:msub><h:mrow><h:mi>YBa</h:mi></h:mrow><h:mrow><h:mn>2</h:mn></h:mrow></h:msub><h:msub><h:mrow><h:mi>Cu</h:mi></h:mrow><h:mrow><h:mn>4</h:mn></h:mrow></h:msub><h:msub><h:mrow><h:mi mathvariant="normal">O</h:mi></h:mrow><h:mrow><h:mn>8</h:mn></h:mrow></h:msub></h:mrow></h:math>, pointing to a distinctive pairing symmetry. The spin-lattice relaxation rate in nuclear quadrupole resonance and nuclear magnetic resonance with nuclear spin <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>I</k:mi><k:mo>&gt;</k:mo><k:mn>1</k:mn><k:mo>/</k:mo><k:mn>2</k:mn></k:math> comprises the magnetic relaxation rate <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mn>1</m:mn><m:mo>/</m:mo><m:msubsup><m:mi>T</m:mi><m:mn>1</m:mn><m:mi>mag</m:mi></m:msubsup></m:math>, which probes magnetic fluctuations, and the quadrupole relaxation rate <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>1</o:mn><o:mo>/</o:mo><o:msubsup><o:mi>T</o:mi><o:mn>1</o:mn><o:mrow><o:mi>quad</o:mi></o:mrow></o:msubsup></o:math>, which probes charge fluctuations. By utilizing <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:mmultiscripts><q:mrow><q:mi>Cu</q:mi></q:mrow><q:mprescripts/><q:none/><q:mrow><q:mn>63</q:mn></q:mrow></q:mmultiscripts></q:mrow></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mmultiscripts><s:mrow><s:mi>Cu</s:mi></s:mrow><s:mprescripts/><s:none/><s:mrow><s:mn>65</s:mn></s:mrow></s:mmultiscripts></s:mrow></s:math> isotopes, we successfully distinguish <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mn>1</u:mn><u:mo>/</u:mo><u:msubsup><u:mi>T</u:mi><u:mn>1</u:mn><u:mi>mag</u:mi></u:msubsup></u:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>1</w:mn><w:mo>/</w:mo><w:msubsup><w:mi>T</w:mi><w:mn>1</w:mn><w:mrow><w:mi>quad</w:mi></w:mrow></w:msubsup></w:math> of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mrow><y:msub><y:mrow><y:mi>YBa</y:mi></y:mrow><y:mrow><y:mn>2</y:mn></y:mrow></y:msub><y:msub><y:mrow><y:mi>Cu</y:mi></y:mrow><y:mrow><y:mn>4</y:mn></y:mrow></y:msub><y:msub><y:mrow><y:mi mathvariant="normal">O</y:mi></y:mrow><y:mrow><y:mn>8</y:mn></y:mrow></y:msub></y:mrow></y:math> and reveal the presence of the coherence peak in <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mn>1</bb:mn><bb:mo>/</bb:mo><bb:msubsup><bb:mi>T</bb:mi><bb:mn>1</bb:mn><bb:mrow><bb:mi>quad</bb:mi></bb:mrow></bb:msubsup></bb:math> but not in <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mn>1</db:mn><db:mo>/</db:mo><db:msubsup><db:mi>T</db:mi><db:mn>1</db:mn><db:mi>mag</db:mi></db:msubsup></db:math>, in contrast to conventional superconductors. Our finding demonstrates that unconventional superconductors do not exhibit a coherence peak in <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mn>1</fb:mn><fb:mo>/</fb:mo><fb:msub><fb:mi>T</fb:mi><fb:mn>1</fb:mn></fb:msub></fb:math> when the relaxation is due to fluctuations of the hyperfine field. Conversely, a coherence peak is expected when the relaxation is caused by electric field gradient fluctuations, due to the different coherence factors between charge and magnetic fluctuations. Our successful measurements of <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mrow><hb:mn>1</hb:mn><hb:mo>/</hb:mo><hb:msub><hb:mrow><hb:mi>T</hb:mi></hb:mrow><hb:mrow><hb:mn>1</hb:mn></hb:mrow></hb:msub></hb:mrow></hb:math> for the chains of <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mrow><jb:msub><jb:mrow><jb:mi>YBa</jb:mi></jb:mrow><jb:mrow><jb:mn>2</jb:mn></jb:mrow></jb:msub><jb:msub><jb:mrow><jb:mi>Cu</jb:mi></jb:mrow><jb:mrow><jb:mn>4</jb:mn></jb:mrow></jb:msub><jb:msub><jb:mrow><jb:mi mathvariant="normal">O</jb:mi></jb:mrow><jb:mrow><jb:mn>8</jb:mn></jb:mrow></jb:msub></jb:mrow></jb:math> suggest that, should the conditions for predominant quadrupole relaxation be satisfied, this phenomenon could provide a novel approach to exploring the unconventional nature of the pairing mechanism in other superconductors. Published by the American Physical Society 2024