Superconductivity enhancement and particle-hole asymmetry: Interplay with electron attraction in doped Hubbard model

The role of near-neighbor electron attraction V <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>V</mml:mi> </mml:math> in strongly correlated systems has been at the forefront of recent research of unconventional superconductivity. However, its implications in the doped Hubbard model on expansive systems remain predominantly unexplored. In this study, we employ the density-matrix renormalization group to examine its effect in the lightly doped t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>t</mml:mi> </mml:math> - t' <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mi>′</mml:mi> </mml:mrow> </mml:math> -Hubbard model on six-leg square cylinders, where t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>t</mml:mi> </mml:math> and t' <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mi>′</mml:mi> </mml:mrow> </mml:math> are the first and second neighbor electron hopping amplitudes. In the electron-doped regime ( t'&amp;gt;0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mi>′</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ), we find that attractive V <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>V</mml:mi> </mml:math> can substantially enhance superconducting correlations, driving the system into a pronounced superconducting phase when the attraction exceeds a modest value V_c ≈ 0.5t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.5</mml:mn> <mml:mi>t</mml:mi> </mml:mrow> </mml:math> . In contrast, in the hole-doped regime ( t' &lt;0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mi>′</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ), while heightened superconducting correlations have also been observed in the charge stripe phase, the systems remain insulating with pronounced charge density wave order. Our results demonstrate the importance of the electron attraction in boosting superconductivity in broader doped Hubbard systems and highlight the asymmetry between the electron and hole-doped regimes.