Molecular Pairing and Fully Gapped Superconductivity in Yb-doped ${\mathrm{CeCoIn}}_5$

The recent observation of fully gapped superconductivity in Yb doped ${\mathrm{CeCoIn}}_5$ poses a paradox, for the disappearance of nodes suggests that they are accidental, yet $d$-wave symmetry with protected nodes is well established by experiment. Here, we show that composite pairing provides a natural resolution: in this scenario, Yb doping drives a Lifshitz transition of the nodal Fermi surface, forming a fully gapped $d$-wave molecular superfluid of composite pairs. The $T^4$ dependence of the penetration depth associated with the sound mode of this condensate is in accordance with observation.

Figure 1

Schematic phase diagram for the ${\mathrm{Yb}}_x{\mathrm{Ce}}_{1-x}{\mathrm{CoIn}}_5$. For $x<x_{-}$ ($x_{-}\approx 0.2$) the temperature dependence of London penetration depth $\mathrm{\Delta }\lambda \sim T-T^2$, consistent with nodal $d$-wave superconductivity in clean and dirty limits, respectively. However, for $x>0.2$, the power law of the $\mathrm{\Delta }\lambda$ exceeds 2 and approaching values as high as 4 [3]. This is incompatible with nodal $d$-wave superconductivity and suggests a fully gapped state. We argue that in the gapless phase, Cooper pairs and composite pairs coexist, whereas in the fully gapped phase, only the composite pairs are present. As a function of Yb doping, the chemical potential increases and the nodes of the order parameter move to the corners of the Brillouin zone and annihilate. We predict that upon further doping, there is a re-entrant transition at $x=x_{+}$ to a second gapless phase. Upon even further doping, there might be a third transition to a normal state at $x_s$ since superconductivity has been only observed up to $x\le 0.65$.

Figure 2

Schematic heavy fermion band structure. Ce Kondo lattice is holelike whereas Yb Kondo lattice is electronlike. Thus, upon Yb doping, the chemical potential increases and the character of the heavy fermion band structure transforms from being holelike to being electronlike.

Figure 3

Temperature dependence of the London penetration depth. For $T<{\omega }_p$, the $\mathrm{\Delta }\lambda (T)$ is exponentially suppressed, whereas it crosses over to $T^4$ for $T>{\omega }_p$.