Robustness of bipolaronic superconductivity to electron-density–phonon coupling

Abstract

We study bipolaron formation and bipolaronic superconductivity on a square lattice, where electrons couple to both local Holstein phonons via on-site charge density and nonlocal bond Su-Schrieffer-Heeger phonons via modulation of hopping amplitudes. Using an unbiased diagrammatic Monte Carlo method, we investigate how the interplay between these two types of electron-phonon coupling affects the bipolaron binding energy, effective mass, spatial extent (quantified by the mean-squared radius), and the superconducting transition temperature Tc. We find that, in some parameter space, the moderate Holstein coupling, though detrimental to Tc when acting alone, can enhance superconductivity when combined with the bond SSH coupling by further compressing the bipolaron without significantly increasing its mass. Similarly, introducing bond SSH coupling into a Holstein bipolaron reduces its size while keeping the effective mass nearly unchanged, leading a higher Tc. These effects give rise to nonmonotonic behavior and reveal a cooperative regime in which both couplings work together to enhance superconductivity. We further examine phonon frequency asymmetry, particularly the case ωH/t=2ωB/t, and show that in the deep adiabatic regime, adding Holstein coupling can even raise Tc when combined with bond SSH coupling. These results highlight the distinct and complementary roles of local Holstein and nonlocal bond SSH electron-phonon couplings, and suggest strategies for optimizing high-Tc superconductivity in systems with multiple phonon modes.

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