Resolving the order parameter of High-T$_{c}$ Superconductors through quantum pumping spectroscopy

Abstract

The order parameter of High-T$_{c}$ superconductors through a series of experiments has been quite conclusively demonstrated to not be of the normal $s-wave$ type. It is either a pure $d_{x^{2}-y^{2}}$-wave type or a mixture of a $d_{x^{2}-y^{2}}-wave$ with a small imaginary $s-wave$ or $d_{xy}-wave$ component. In this work a distinction is brought out among the four types, i.e., $s- wave$, $d_{x^{2}-y^{2}}- wave$, $d_{x^{2}-y^{2}}+is - wave$ and $d_{x^{2}-y^{2}}+id_{xy}- wave$ types with the help of quantum pumping spectroscopy. This involves a normal metal double barrier structure in contact with a High-T$_{c}$ superconductor. The pumped current, heat and noise show different characteristics with change in order parameter revealing quite easily the differences among these.