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Figure 1.  Pairing gap Δ as a function of t for n = 1.0 (black solid line), n = 0.8 (red dashed line) and n = 0.6 (blue dotted line).

Figure 2.  Color maps of the dynamical structure factor S(q,ω) as functions of transferred energy and momentum along the high-symmetry directions for hopping strength (a) t/U = 0.25, (b) 0.4, (c) 0.7, and (d) 1.0 at half-filling n = 1. The red dashed line marks the dispersion of E_d. The green dotted line indicates the minimum energy to break a Cooper pair. Inset in (a): a quarter of the first BZ and three high-symmetry directions (red arrows).

Figure 3.  S(q,ω) along the high-symmetry directions for (a) t/U = 0.25, (b) 0.4, (c) 0.7, and (d) 1.0 at n = 0.8. Panel (b) shows E_d splitting into U_d and D_d (blue dotted lines) induced by doping.

Figure 4.  S(q = [π, π],ω) as a function of ω for the hopping strengths (a) t/U = 0.25, (b) 0.4, (c) 0.5, and (d) 0.7 at n = 0.8. Insets magnify the atomic excitation regime.

Figure 5.  The area of the molecular peak A_peak (pink dotted line) and the square of the pairing gap Δ² (green solid line) as a function of t at n = 0.8.

Figure 6.  S(q = [π/2,π/2],ω) as a function of ω for n = 1.0 (black solid line), n = 0.8 (red dashed line), and n = 0.6 (blue dotted line) at t/U = 0.4.

Figure 7.  Sound speed c_s as a function of t at n = 0.8. Inset: 〈vF2〉 versus t.

Figure 8.  Color maps of S(q,ω) for (a) n = 0.6 and (b) n = 0.4 with t/U = 0.4.

Figure 9.  (a) c_s and (b) 〈vF2〉 as functions of n for t/U = 0.4 (solid line), 0.5 (dashed line), and 0.7 (dotted line). Inset to (a): the corresponding Δ as a function of n.