Extended Data Fig. 1: Theoretical hallmarks of CB order.
a, Lowest band structure factor S1(k) at T=100 mK obtained by exact diagonalisation of a 8 site square lattice (Betts cluster) with periodic boundary conditions. It exhibits a dominant peak at quasi-momentum k = (π/a, π/a), which is a characteristic signature of CB order. A second strongly suppressed quasi-peak lies at k = (0, 0) (due to finite size effects), corresponding to a homogenous liquid without any density order. b, ∣S1(π/a, π/a)∣ (black) and ∣S1(0, 0)∣ (blue) are plotted versus temperature T. Up to T ≲ Tc = 420 mK, the structure factor signalling CB order remains at least twice as large as the structure factor for a homogeneous liquid. c, CB order parameter deduced from mean-field calculations as a function of the chemical potential μ and temperature (T = 4, 125, 247, 389, 450 mK in blue, violet, black, red and green respectively). The order parameter is given by the population difference ∣nA − nB∣ between two sub-lattices, A and B, of the square lattice. Below around 410 mK ∣nA − nB∣ is significant manifesting CB order.
