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In this paper, "Fractionalized Fermi Liquids" by T. Senthil, Subir Sachdev and Matthias Vojta, the authors state in the last paragraph on page 2, "the pairing of the spinons and the condensation of $B_{1,2}$ implies that the resulting phase also has pairing of the conduction electrons, and is a superconductor." Can anyone prove it?

They are considering the Kondo-Heisenberg model on a triangular lattice and the Hamiltonian is given by eq(1) \begin{equation} H = -\sum_{j,j'} t(j,j')c^{\dagger}_{j\sigma}c_{j'\sigma} + \frac{1}{2}\sum_j J_k(j) S_j\cdot c^{\dagger}_{j\sigma}\tau_{\sigma\sigma'}c_{j\sigma'} +\sum_{j<j'}j_H(j,j')S_j\cdot S_{j'}. \end{equation} $t(j,j')$ is for hopping, $J_K$ for Kondo interaction, and $J_H$ for Heisenberg interaction. The order parameters are $B_1 = f^{\dagger}_{\sigma}c_{\sigma}$,$B_2 = \epsilon^{\sigma \sigma'} f_{\sigma}c_{\sigma'}$, and $ D = \epsilon^{\sigma \sigma'} f_{\sigma}f_{\sigma'}$. Here, $f_{j\sigma}$ comes from the pseudo-fermion representation of the spin operator $S_j = f^{\dagger}_{j\sigma}\tau_{\sigma\sigma'}f_{j\sigma'}/2$.

In fact, can anyone show $\langle B_{1i} \rangle \langle B_{1j} \rangle D_{ij} \propto \langle \epsilon^{\sigma \sigma'} c_{i\sigma}c_{j\sigma'} \rangle$ ?

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  • $\begingroup$ The problem is solved by myself. Use Green's functions. $\endgroup$ – DKS Nov 2 '14 at 7:41
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Well, there have several papers on this issue, e.g. PRB 86 4526. I have also studied this Hamiltonian in my paper arXiv:1410.6261. In my opinion, the RVB pairing induces the pairing of conduction electrons via the nonvanishing Kondo screening. To my surprise, such SC state is able to fit the experimental data of the heavy fermion superconductor CeCoIn5.[The fermi surface measured by ARPES, the entropy and London penetration depth.]

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  • $\begingroup$ Why do you call it surprising? $\endgroup$ – DKS Dec 27 '14 at 8:20
  • $\begingroup$ Because other models cannot reproduce the observed Fermi surface and my model can. Besides, our model gives results consistent with quantum osillation experiment, specific heat measurement and penetration depth experiment. $\endgroup$ – seeandwalk Jan 15 '15 at 11:06

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