Cluster Decomposition Principle in the BCS Superconducting State

by 樋口 雅彦
In a lot of first-principle calculations including the density functional theory for the superconductor (SC-DFT), the abnormal density is chosen as the order parameter of the SS. And, many experimental results, especially the critical temperature, can be explained quantitatively well by these calculations so far.
On the other hand, it has been pointed out in the previous work [J. Phys. Soc. Jpn. 86, 064704 (2017)] that the abnormal density can be an order parameter of the SS only if the cluster decomposition principle holds. However, unfortunately, the cluster decomposition principle has not been confirmed in the SS. Within our knowledge, it has not been well argued even in the BCS-SS. The above-mentioned successes of the SC-DFT calculations seem to be merely empirical successes.
In this work, the cluster decomposition principle is proven true in the BCS-SS by utilizing the second-order reduced density matrix (RDM2) of the BCS-SS. This work first gives a theoretical guarantee of choosing the abnormal density as the order parameter of the SS.