Out-of-plane thermopower of strongly correlated layered systems: An application to Bi 2 ( Sr , La ) 2 CaCu 2 O 8 + δ

We calculate the out-of-plane thermopower in a quasi-two-dimensional system and argue that this quantity is an effective probe of the asymmetry of the single-particle spectral function. We find that the temperature and doping dependence of the out-of-plane thermopower in ${\text{Bi}}_{2}{(\text{Sr},\text{La})}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ single crystals is broadly consistent with the behavior of the spectral function determined from angle resolved photoemission spectroscopy and tunneling experiments. We also investigate the relationship between out-of-plane thermopower and entropy in a quasi-two-dimensional material. We present experimental evidence that at moderate temperatures, there is a qualitative correspondence between the out-of-plane thermopower in ${\text{Bi}}_{2}{(\text{Sr},\text{La})}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ and the entropy obtained from specific-heat measurements. Finally, we argue that the derivative of the entropy with respect to particle number may be the more appropriate quantity to compare with the thermopower rather than the entropy per particle.