Is SmB$_6$ a failed superconductor? --- Part II: a microscopic model

Heavy fermion materials provide a natural playground for extending our current understanding of topological phases of matter in the presence of strong correlations. In this talk, we would like to present a microscopic model of failed superconductivity in heavy fermion systems and its application to SmB$_6$. The essential part of the microscopic model is a Majorana representation of impurities in the Kondo lattices. We demonstrate a composite order parameter in this model cannot sustain stable supercurrent. In the mean-field level, we show a gapless Majorana Fermi sea emerges and is decoupled from impurities. We observe mirror symmetry protected surface states coexist with a bulk gapless Majorana Fermi sea. We establish the existence of a gapless Majorana Fermi sea may potentially resolve mysterious issues of quantum oscillation measurements in SmB$_6$. This work is done in collaboration with Onur Erten, Piers Coleman and Alexei M. Tsvelik.