Order parameter and spectral function in d -wave holographic superconductors

We consider the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi></a:math>-wave holographic superconductor model with full backreaction on the metric, addressing a missing part in the literature. We have identified the gap function by comparing the fermionic spectral function with the momentum-dependent order parameter. By numerical investigations of the fermionic spectral function in the presence of a tensor condensate, we find the Fermi arc and the gapped behavior, which closely resembles angle resolved photoemission spectrum data. Moreover, we have examined the influence of the coupling constant, chemical potential, and temperature on the spectral function. We find that <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>d</c:mi></c:math>-wave fermionic spectral function can be obtained through <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>p</e:mi><e:mi>x</e:mi></e:msub></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>p</g:mi><g:mi>y</g:mi></g:msub></g:math> condensates combined with two fermion flavors. Similarly, combining <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>d</i:mi><i:mrow><i:msup><i:mi>x</i:mi><i:mn>2</i:mn></i:msup><i:mo>−</i:mo><i:msup><i:mi>y</i:mi><i:mn>2</i:mn></i:msup></i:mrow></i:msub></i:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>d</k:mi><k:mrow><k:mi>x</k:mi><k:mi>y</k:mi></k:mrow></k:msub></k:math> orbitals symmetry with two fermion flavors leads to a <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>g</m:mi></m:math>-wave spectral function.