# Chemical potential of Cooper pairs

Consider a BCS Hamiltonian with an additional term that reads: $i\mu c_k^+c_{-k}^+ + H.c$. What is the meaning of $\mu$? How one can write this term in real space, and does this term show up in the Richardson's pairing Hamiltonian? Thanks.

• This is just another pairing term and $\mu$ is part of the superconducting order parameter. – Meng Cheng Jun 20 '15 at 0:22
• That is certainly the case. Does that term have a representation in real space? – danport Jun 20 '15 at 0:48
• Sure, just as the usual pairing term. I assume you are talking about spin-1/2 (singlet pairing), and let me assume $\mu$ is a constant. The real space form is just $i\mu c_{\mathbf{r}\uparrow}^\dagger c_{\mathbf{r}\downarrow}^\dagger+h.c.$ – Meng Cheng Jun 20 '15 at 1:16