Doping dependence of scattering rate for linear-in-temperature resistivity in cuprate superconductors

The origin of the linear-in-temperature (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>T</a:mi></a:math>-linear) resistivity in cuprate superconductors remains a profound mystery in condensed matter physics. Here, we investigate the dependence of the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>T</b:mi></b:math>-linear resistivity coefficient on doping, i.e., <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>A</c:mi><c:mn>1</c:mn></c:msub><c:mrow><c:mo>(</c:mo><c:mi>p</c:mi><c:mo>)</c:mo></c:mrow></c:mrow></c:math>, for three typical regions in the temperature versus doping phase diagram of hole-doped cuprates, from which the doping dependence of the scattering rate, i.e., <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>α</d:mi><d:mn>1</d:mn></d:msub><d:mrow><d:mo>(</d:mo><d:mi>p</d:mi><d:mo>)</d:mo></d:mrow></d:mrow></d:math>, is further derived. It is found that for region I (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>p</e:mi><e:mo><</e:mo><e:msup><e:mi>p</e:mi><e:mo>*</e:mo></e:msup></e:mrow></e:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>T</f:mi><f:mo>></f:mo><f:msup><f:mi>T</f:mi><f:mo>*</f:mo></f:msup></f:mrow></f:math>), <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msub><g:mi>α</g:mi><g:mn>1</g:mn></g:msub><g:mrow><g:mo>(</g:mo><g:mi>p</g:mi><g:mo>)</g:mo></g:mrow></g:mrow></g:math> is almost a constant; for region II (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>p</h:mi><h:mo>></h:mo><h:msup><h:mi>p</h:mi><h:mo>*</h:mo></h:msup></h:mrow></h:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>T</i:mi><i:mo>></i:mo><i:msub><i:mi>T</i:mi><i:mi>coh</i:mi></i:msub></i:mrow></i:math>), <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msub><j:mi>α</j:mi><j:mn>1</j:mn></j:msub><j:mrow><j:mo>(</j:mo><j:mi>p</j:mi><j:mo>)</j:mo></j:mrow><j:mo>∝</j:mo><j:mi>p</j:mi></j:mrow></j:math>; for region III (<k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>p</k:mi><k:mo>></k:mo><k:msup><k:mi>p</k:mi><k:mo>*</k:mo></k:msup></k:mrow></k:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mi>T</l:mi><l:mo><</l:mo><l:msub><l:mi>T</l:mi><l:mi>coh</l:mi></l:msub></l:mrow></l:math>), <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:msub><m:mi>α</m:mi><m:mn>1</m:mn></m:msub><m:mrow><m:mo>(</m:mo><m:mi>p</m:mi><m:mo>)</m:mo></m:mrow><m:mo>∝</m:mo><m:mi>p</m:mi><m:mrow><m:mo>(</m:mo><m:msub><m:mi>p</m:mi><m:mi>c</m:mi></m:msub><m:mo>−</m:mo><m:mi>p</m:mi><m:mo>)</m:mo></m:mrow></m:mrow></m:math>, where <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:msup><n:mi>T</n:mi><n:mo>*</n:mo></n:msup></n:math> is the onset temperature of the pseudogap phase, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:msup><o:mi>p</o:mi><o:mo>*</o:mo></o:msup></o:math> indicates the doping at which <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:msup><p:mi>T</p:mi><p:mo>*</p:mo></p:msup></p:math> goes to zero, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:msub><q:mi>T</q:mi><q:mi>coh</q:mi></q:msub></q:math> marks the onset of antinodal quasiparticle coherence, and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:msub><r:mi>p</r:mi><r:mi mathvariant="normal">c</r:mi></r:msub></r:math> is the doping where the low-temperature linear behavior in the overdoped regime vanishes. Moreover, the deduced <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:mrow><t:msub><t:mi>α</t:mi><t:mn>1</t:mn></t:msub><t:mrow><t:mo>(</t:mo><t:mi>p</t:mi><t:mo>)</t:mo></t:mrow></t:mrow></t:math> relations are verified with the experimental data from previous reports. The discovered scattering rate versus doping relationship will shed light on the scattering mechanism underlying the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mi>T</u:mi></u:math>-linear resistivity in cuprate superconductors. Published by the American Physical Society 2024