Figure 1

(Upper panel) The three dispersion relations for the bands of the underscreened Anderson lattice model in the normal state (schematic). The momentum $\underline{k}$ is taken to be along the $(1,1,1)$ direction. The upper [$E^{+}\left(\underline{k}\right)$] and lower [$E^{-}\left(\underline{k}\right)$] bands are comprised of $\alpha$ 5$f$ states hybridized with the conduction band. The band in the center marked by the red curve (open circles) is the unhybridized $\beta$ band. (Lower panel) The 5$f$ weights of the upper and lower hybridized bands ($|A_{\sigma }^{\pm }\left(\underline{k}\right){|}^2$) are plotted as functions of $\underline{k}$. The $\beta$ band has pure 5$f$ character.Reuse & Permissions

Figure 2

The $\alpha$ and $\beta$ components of the 5$f$ density of states per spin versus $\omega$ (solid lines), and $n_f^{\alpha }$ and $n_f^{\beta }$ electrons per spin (dashed lines) as functions of $\mu$, in which the Hartree-Fock energies of the 5$f$ orbitals have been kept constant. The simple cubic tight-binding density of states has been approximated by a semielliptical form.Reuse & Permissions

Figure 3

The interband susceptibility ${\chi }_f^{\alpha ,\beta \left(0\right)}\left(\underline{Q}\right)$ (solid line) and the sum of the intraband susceptibilities ${\chi }_f^{\alpha ,\alpha \left(0\right)}\left(\underline{Q}\right)+{\chi }_f^{\beta ,\beta \left(0\right)}\left(\underline{Q}\right)$ (dashed line) as functions of $\mu$, with fixed Hartree-Fock $f$ electron bands $E_{f,\sigma }^{\chi }\left(\underline{k}\right)$. The unhybridized $f$ and conduction-band dispersion relations have been described within a simple cubic tight-binding model.Reuse & Permissions

Figure 4

The temperature dependence of the gap parameter $|{\kappa }_{\underline{Q},\sigma }\left(T\right)|$ for a value of $J=0.128$ and $U=J$. This value of $J$ is comparable to the assumed value of 0.6 for the 5$f$ bandwidth due to direct f-f hopping.Reuse & Permissions

Figure 5

(Upper panel) A schematic close-up view of the dispersion relations (filled markers) for the bands with $\alpha$ character in the novel state and their 5$f$ $\alpha$ weights (unfilled markers). The wave vector $\underline{k}$ is directed along the $(1,1,1)$ direction. The position of the Fermi energy $\mu$ is marked by the arrow. The $\alpha$ intensities for the various branches of dispersion relations are indicated by symbols of the same type. (Lower panel) The dispersion relations for the bands with $\beta$ character and their 5$f$ $\beta$ weights are plotted as functions of $\underline{k}$.Reuse & Permissions

Figure 6

The dispersion relations for the 5$f$ $\alpha$ (black line) and 5$f$ $\beta$ (red line) electrons along the $(k,k,k)$ direction. The widths of the lines are proportional to their intensities. The Fermi energy $\mu$ is set at about 0.32 and is indicated by the horizontal line. The $\alpha$-dispersion relations shows the existence of a direct gap of the order of $2\left|V\right|\sim 0.2$ between the two branches. For other wave vectors, the $\alpha$ and $\beta$ branches follow similar dispersion relations; however, their degeneracy is lifted by a small energy of the order of ${\left|V\right|}^2$. Gaps at the Fermi energy are seen to occur at points which are connected by the commensurate nesting vector $\underline{Q}=(1,1,1)$. (Figure courtesy of T. Durakiewicz.)Reuse & Permissions

Figure 7

The combined $\alpha$ 5$f$ ${\rho }^{\alpha }\left(\omega \right)$ and conduction-band density of states for the ordered state as a function of $\omega$. The $\beta$ 5$f$ density of states ${\rho }^{\beta }\left(\omega \right)$ is also shown as a function of $\omega$. It seen that the gap structure associated with the novel ordering is highly asymmetric.Reuse & Permissions