Magnon Bose-Einstein Condensation and Superconductivity in a Frustrated Kondo Lattice

Magnetically frustrated Kondo lattices are considered to be one of the most promising platforms for the realization of novel types of metallic quantum criticality. Motivated by the recent experiments on the heavy fermion compounds with a nonmagnetic valence bond solid (VBS) ground state of the localized spins, such as YbAl₃C₃, we study a one-dimensional two-leg spin ladder model with a VBS ground state doped with itinerant fermions. Using field theory techniques and precise density matrix renormalization group calculations, we provide a solution of the model as a function of the Kondo coupling and magnetic field. We demonstrate that the magnetic field-driven transition to an easy-plane antiferromagnet (known as magnon Bose-Einstein condensation (BEC) in the insulating limit) is stable in the presence of a Fermi sea and its universality class is unchanged, while the critical field decreases as a function of Kondo coupling. We also find that spin fluctuations in the VBS phase can drive unconventional superconducting correlations. Finally, we argue that, depending on the filling of conduction electrons, the magnon BEC transition can remain stable in a metal also in dimensions two and three.