Interplay between charge ordering and superconducting correlations in the extended Hubbard model

Abstract We examine effects of charge ordering on superconducting correlations in the extended Hubbard model with Falicov-Kimball coupling in two dimensions. Charge orderings are generated by f -electron distributions on the localized f orbitals, which act as an internal potential for itinerant d electrons moving in the Hubbard d band. For the small finite cluster of $$L=4 \times 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mo>×</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> sites the model is studied exactly over the complete set of f -electron distributions, while for larger clusters the projector Quantum-Monte-Carlo method and the reduced set of f -electron distributions (the periodic, phase separated and phase segregated configurations) is used. It is found that the enhancement of superconducting correlations in the d -wave channel depends strongly on the type of f -electron ordering and changes significantly with f and d electron concentration ( $$n_f$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>f</mml:mi> </mml:msub> </mml:math> , $$n_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> ) as well as with interband Coulomb interaction $$U_{fd}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>fd</mml:mi> </mml:mrow> </mml:msub> </mml:math> . In particular, it is found that for small values of $$U_{fd}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>fd</mml:mi> </mml:mrow> </mml:msub> </mml:math> and $$n_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> the superconducting correlations are the most significantly enhanced for segregated configurations (all f -electrons clump together), for all f -electron concentrations, while for higher d -band fillings axial stripes (bands) with f -electron concentrations $$n_f \sim 0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> yield the largest enhancement of superconducting correlations. The region of axial striped phases is systematically reduced with increasing $$U_{fd}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>fd</mml:mi> </mml:mrow> </mml:msub> </mml:math> and for sufficiently large $$U_{fd}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>fd</mml:mi> </mml:mrow> </mml:msub> </mml:math> ( $$U_{fd}\sim 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mi>fd</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> ) it persists only in the region of small $$n_f$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>f</mml:mi> </mml:msub> </mml:math> and $$n_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>d</mml:mi> </mml:msub> </mml:math> values.