Fermionology in the Kondo-Heisenberg model: the case of CeCoIn$_{5}$

Fermi surface of heavy electron systems plays a fundamental role in understanding their variety of puzzling phenomena, for example, quantum criticality, strange metal behavior, unconventional superconductivity and even enigmatic phases with yet unknown order parameters. The spectroscopy measurement of typical heavy fermion superconductor CeCoIn$_{5}$ has demonstrated multi-Fermi surface structure, which has not been in detail studied theoretically in a model system like the Kondo-Heisenberg model. In this work, we make a step toward such an issue with revisiting the Kondo-Heisenberg model. It is surprising to find that the usual self-consistent calculation cannot reproduced the fermionology of the experimental observation of the system due to the unfounded sign binding between the hopping of the conduction electrons and the mean-field valence-bond order. To overcome such inconsistency, we assume that the sign binding should be relaxed and the mean-field valence-bond order can be considered as a free/fit parameter so as to meet with real-life experiments. Given the fermionology, the calculated effective mass enhancement, entropy, superfluid density and Knight shift are all in qualitative agreement with the experimental results of CeCoIn$_{5}$, which confirms our assumption. Our result supports a $d_{x^{2}-y^{2}}$-wave pairing structure in heavy fermion material CeCoIn$_{5}$. In addition, we have also provided the scanning tunneling microscopy (STM) spectra of the system, which is able to be tested by the present STM experiments.