Correlation-driven $d$-wave superconductivity in Anderson lattice model: Two gaps

Superconductivity in heavy-fermion systems has an unconventional nature and is considered to originate from the universal features of the electronic structure. Here, the Anderson lattice model is studied by means of the full variational Gutzwiller wave function incorporating nonlocal effects of the on-site interaction. We show that the $d$-wave superconducting ground state can be driven solely by interelectronic correlations. The proposed microscopic mechanism leads to a multigap superconductivity with the dominant contribution due to $f$ electrons and in the $d_{x^2-y^2}$-wave channel. Our results rationalize several important observations for ${\mathrm{CeCoIn}}_5$.

Figure 1

Phase diagram on total band filling-hybridization magnitude plane, with the dominant, $d_{x^2-y^2}$-wave superconducting order parameter for $f$ electrons, ${\mathrm{\Delta }}_{\mathrm{G};1,0}^{ff}$ (see main text). The dashed lines mark the selected $f$-state isovalents. The vertical dotted line marks the non-BCS region defined by the gain in the kinetic energy $\mathrm{\Delta }{E}_{\mathrm{kin}}>0$ in the SC state. For the selected point, $n=1.8,\left|V\right|/\left|t\right|=0.65$, we show in the inset that SC appears with the increasing $f\text{−}f$ interaction.

Figure 2

Values of the SC gaps vs $d$-wave angular dependence on the Fermi surface $\left(E_F\right)$ for selected parameters $n=1.8$ and $\left|V\right|/\left|t\right|=0.65$. The larger gap, ${\mathrm{\Delta }}_1$, has the predominant $d_{x^2-y^2}$ character. Inset: A quarter of the Brillouin zone with the absolute value of the resultant SC gaps.

Figure 3

(a) Effective SC-gap components with the dominant $d_{x^2-y^2}$-wave $f\text{−}f$ part. Components with ${\mathrm{\Delta }}_{\mathbf{i}\mathbf{j}}^{\alpha \beta }/{\mathrm{\Delta }}_{1,0}^{ff}<5\%$ are not included. (b) Condensation energy for SC state in the consecutive orders of the diagrammatic expansion. In both plots, $n=1.8$.

Figure 4

(a) Condensation energy $\mathrm{\Delta }E$ for the selected $n$. (b) Kinetic energy difference $\mathrm{\Delta }{E}_{\mathrm{kin}}$ between normal and SC states. The case with $\mathrm{\Delta }{E}_{\mathrm{kin}}>0$ is opposite to that predicted by the BCS theory.