Unconventional orbital ordering and emergent dimensional reduction in fulleride superconductors

Nonlocal order parameters in space-time are proposed to characterize the unconventional orbital-selective conducting state in fulleride superconductors, called the Jahn-Teller metal. In previous works, it has been argued that this state can be interpreted as a spontaneous orbital-selective Mott state, in which the electrons in two of the three $t_{1u}$ molecular orbitals are localized, while those in the third one are metallic. Here, based on the realistic band structure for fullerides, we provide a systematic study of nonlocal order parameters and characterize the Jahn-Teller metal, for which there exists no one-body local order parameter in contrast to conventional orderings. It is shown that the Mottness, or integer filling nature for each orbital due to strong correlation effects, is a relevant feature of the present orbital order. The local orbital moment thus vanishes and the static distortion associated with a conventional orbital moment is absent. Transport characteristics are also investigated, and it is found that the dimensionality is effectively reduced from three to two at low energies, while the cubic nature is recovered at high energies. This accounts for the high upper critical field observed in the superconducting state of the fcc fullerides inside the Jahn-Teller metal regime.

Figure 1

Schematic illustration of the SOSM state in the fcc fullerides $A_3{\mathrm{C}}_{60}$. Three $t_{1u}$ orbitals are schematically drawn for two fullerene molecules. The orange colored atoms represent the alkali metal $A$. A part of this figure is reproduced from Ref. [33].

Figure 2

(a)–(c) Single particle spectra for the fulleride ${\mathrm{Rb}}_3{\mathrm{C}}_{60}$ without orbital ordering. (a) bare band dispersion and (b1)–(b3) orbital-resolved spectra $A_{\gamma =x,y,z}(\mathit{k},\omega )$. The spectrally decomposed orbital moment $\mathcal{M}(\mathit{k},\omega )$ is plotted in (c). (d)–(f) are plots similar to (a)–(c), but for the SOSM state. The parameter $\tilde{U}$ is chosen as $\tilde{U}=0.1$ eV and the broadening factor as $\eta =8\mathrm{meV}$. The path in momentum space connects the points $\mathrm{\Gamma }(0,0,0)\to X(0,1,0)\to U(\frac{1}{4},1,\frac{1}{4})\to \mathrm{\Gamma }(1,1,1)$, $\mathrm{\Gamma }(0,0,0)\to L(\frac{1}{2},\frac{1}{2},\frac{1}{2})\to K(\frac{3}{4},\frac{3}{4},0)\to W(1,\frac{1}{2},0)\to X(1,0,0)$ where the coordinates for the symmetric points in $\mathit{k}$ space are shown with the unit $\pi /a$.

Figure 3

Wave vector integrated orbital-dependent spectra for (a) the normal metal and (b) the SOSM state. The spectrum with only the $z$ orbital considered is shown in panel (c).

Figure 4

Spatially-local and frequency-dependent orbital ordered moment on the real axis.

Figure 5

Frequency dependence of the optical conductivities ${\sigma }_{xx}$, ${\sigma }_{yy}$, and ${\sigma }_{zz}$ for (a),(b) the SOSM state $[{\mathrm{\Sigma }}_{x,y}\left(\mathrm{\Omega }\right)={\tilde{U}}^2/\mathrm{\Omega }$, ${\mathrm{\Sigma }}_z\left(\mathrm{\Omega }\right)=0]$ and (c),(d) the system with static mean fields $[{\mathrm{\Sigma }}_{x,y}\left(\mathrm{\Omega }\right)=\tilde{U}$, ${\mathrm{\Sigma }}_z\left(\mathrm{\Omega }\right)=0]$. The damping parameter and effective Coulomb interaction are chosen as $\mathrm{\Gamma }=15.6$ meV and $\tilde{U}=0.1$ eV. In (b),(d), the dotted lines show the value corresponding to the isotropic limit realized in the original cubic phase.

Figure 6

One-dimensional schematic illustrations for (left) orbital ordering (SOSM) in the half-filled three-orbital Hubbard model with antiferromagnetic Hund's coupling and (right) channel ordering in the half-filled two-channel Kondo lattice. The bottom panel shows the single-particle excitation energy having both metallic and insulating bands.

Figure 7

Spatially-local and frequency-dependent orbital ordered moment on the imaginary axis.