Dynamical effects on BCS-BEC crossover in the Holstein model

We present a study of the half-filled Holstein model with superconducting order employing the dynamical mean-field theory in combination with the numerical renormalization group. Here, we investigate the dynamical effects on the crossover from the BCS to Bose-Einstein condensation (BEC) regimes as the on site electron-phonon coupling g is varied for both adiabatic (t/ω₀ >>1) and antiadiabatic (t/ω₀ <1) phonons, where t is the hopping amplitude and ω₀ is the phonon frequency. It turns out that the maximum superconducting transition temperature T_c universally coincides with the critical electron-phonon coupling g_c1 where the bipolaron instability takes place in the normal state. However, in the case of the adiabatic phonon, the pairing amplitude Δ_P is suppressed with increasing the electron-phonon coupling in the BEC regime, while it increases with increasing g for the antiadiabatic phonon. Further, the calculated superfluid stiffness D_S for the adiabatic phonon decreases rapidly as increasing g together with the suppression of the coherence peak in the BEC regime. We also calculated the spectral intensities to identify BCS and BEC regimes and those results are comparable to the angle resolved photoemission spectroscopy (ARPES) experiment.