Fig. 4: Temperature Dependence of QPI Signature of a PDW.
From: Scattering interference signature of a pair density wave state in the cuprate pseudogap phase
a–f. Measured QPI signature \(\Lambda ({{{{{\boldsymbol{q}}}}}},20\,{{{{{\rm{meV}}}}}})\) for Bi2Sr2CaDyCu2O8 (doping level p ≈ 0.08) at temperatures T = (a) 0.1Tc, (b) 0.4Tc, (c) 0.8Tc, (d) Tc, (e) 1.25Tc, and (f) 1.5Tc. g–j. Predicted QPI signature \({\Lambda }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{q}}}}}},20\,{{{{{\rm{meV}}}}}})\) of 8\({a}_{0}\) PDW state that coexists with DSC state at temperatures T = (g) 0.01t, (h) 0.02t, (i) 0.04t, and (j) 0.05t. Theoretically, it is assumed that the short-range discommensurate nature of the charge order, as seen in the experiments56, will lead to reduced intensity of the density wave Bragg peaks compared to the long-range PDW driven charge order obtained in our mean-field analysis. Accordingly, the non-dispersing charge order Bragg peaks at wavevectors q = ±nQp, n = 0, 1, 2, …,7, in PDW+DSC state and q = ±n(2Qp), n = 0, 1, 2, 3, in the pure PDW state are suppressed by a factor of 100 in \({\Lambda }_{{{{{{\rm{P}}}}}}}\left({{{{{\boldsymbol{q}}}}}},20\,{{{{{\rm{meV}}}}}}\right)\), which helps in highlighting much weaker wavevectors emerging from impurity scattering. \({\Lambda }_{{{{{{\rm{P}}}}}}}\left({{{{{\boldsymbol{q}}}}}},20\,{{{{{\rm{meV}}}}}}\right)\) is computed for unidirectional PDW in a 56×56 lattice and symmetrized for plotting. Features at q ≈ (±1/4, ±1/4)2π/a0 extending in nodal directions are labeled by a red arrow. k–l. Predicted \({\Lambda }_{{{{{{\rm{P}}}}}}}({{{{{\boldsymbol{q}}}}}}, 20\,{{{{{\rm{ meV}}}}}})\) of pure 8\({a}_{0}\) PDW state at temperatures T = (k) 0.085t and (l) 0.09t. Measured \(\Lambda ({{{{{\boldsymbol{q}}}}}},20\,{{{{{\rm{meV}}}}}})\) in (a–f) for T = 0.1Tc ~ 1.5Tc are in good agreement with the simulation results in (g–l). The length of the arc-like feature (indicated by blue curves) subtending (±1, ±1)\(2{{{{{\rm{\pi }}}}}}/{a}_{0}\) increases from PDW+DSC to pure PDW state, which is a key feature of charge order driven by PDW. The intensity of \(\Lambda ({{{{{\boldsymbol{q}}}}}},20\,{{{{{\rm{meV}}}}}})\) and \({\Lambda }_{{{{{{\rm{P}}}}}}}\left({{{{{\boldsymbol{q}}}}}},20\,{{{{{\rm{meV}}}}}}\right)\) decreases as the temperature increases.
