Dual origin in the temperature dependence of the coupling parameter for the strange metal state in heavily overdoped cuprate superconductor

The real and imaginary parts of the self-energy in the wide energy range have been evaluated from high-resolution angle-resolved photoemission spectroscopy (ARPES) spectra of a heavily overdoped single-layer cuprate superconductor (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mrow><a:mi>Bi</a:mi><a:mo>,</a:mo><a:mi>Pb</a:mi><a:mo>)</a:mo></a:mrow><a:mn>2</a:mn></a:msub><a:msub><a:mi>Sr</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi>CuO</a:mi><a:mrow><a:mn>6</a:mn><a:mo>+</a:mo><a:mi>δ</a:mi></a:mrow></a:msub></a:mrow></a:math> in the normal state. The real part of the self-energy has the zero-point crossing at <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>−</b:mo><b:mn>0.6</b:mn></b:mrow></b:math> eV, where the lifetime broadening takes maximum and the ARPES spectral intensity is significantly suppressed forming a high-energy anomaly (HEA). The self-energy part responsible for the HEA is almost temperature independent and the coupling parameter is <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi>λ</c:mi><c:mtext>HEA</c:mtext></c:msub><c:mspace width="0.16em"/><c:mo>∼</c:mo><c:mn>1</c:mn></c:mrow></c:math> at 300 K, indicating strongly correlated nature of the strange metal state. Meanwhile, the self-energy part responsible for the low-energy kink (LEK) near the Fermi level shows significant temperature dependence: it is <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>λ</e:mi><e:mtext>LEK</e:mtext></e:msub><e:mspace width="0.16em"/><e:mo>∼</e:mo><e:mn>0.1</e:mn></e:mrow></e:math> at 300 K but enhances steeply below <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mo>∼</g:mo><g:mn>150</g:mn><g:mspace width="0.222222em"/><g:mi mathvariant="normal">K</g:mi></g:mrow></g:math> up to <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msub><j:mi>λ</j:mi><j:mtext>LEK</j:mtext></j:msub><j:mspace width="0.16em"/><j:mo>∼</j:mo><j:mn>0.8</j:mn></j:mrow></j:math>, leading to the total coupling strength of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:msub><l:mi>λ</l:mi><l:mtext>tot</l:mtext></l:msub><l:mo>=</l:mo><l:msub><l:mi>λ</l:mi><l:mtext>HEA</l:mtext></l:msub><l:mo>+</l:mo><l:msub><l:mi>λ</l:mi><l:mtext>LEK</l:mtext></l:msub><l:mo>=</l:mo><l:mn>1.8</l:mn></l:mrow></l:math> at 20 K. The temperature-dependent enhancement cannot be explained by the electron-phonon interaction with a fixed magnitude of the Eliashberg function, which suggests an unexplored mechanism that enhances the coupling parameter at lower temperatures. Our results clearly indicate distinct energy scales in the self-energy, providing insight into the strange metal state as well as the temperature-dependent interplay of many-body interactions.