Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor ${\mathrm{UPt}}_3$

We study the emergence of odd-frequency superconducting pairing in ${\mathrm{UPt}}_3$. Starting from a tight-binding model accounting for the nonsymmorphic crystal symmetry of ${\mathrm{UPt}}_3$ and assuming an order parameter in the $E_{2u}$ representation, we demonstrate that odd-frequency pairing arises very generally, as soon as intersublattice hopping or spin-orbit coupling is present. We also show that in the low temperature superconducting $B$ phase, the presence of a chiral order parameter together with spin-orbit coupling, leads to additional odd-frequency pair amplitudes not present in the $A$ or $C$ phases. Furthermore, we show that a finite Kerr rotation in the $B$ phase is only present if odd-$\omega$ pairing also exists.

Figure 1

Schematic depiction of the locations of the U atoms in the $AB$-stacked hexagonal lattice of ${\mathrm{UPt}}_3$ with vectors in the basal plane labeled ${\mathbf{e}}_i$ and intersublattice vectors labeled ${\mathbf{r}}_i$.

Figure 2

(a) Fermi surface of ${\mathrm{UPt}}_3$ shown within the 3D Brillouin zone (hexagonal frame) plotted using the Hamiltonian in Eq. (1) with parameters $\left(t,t_z,t^{\prime },\alpha ,\mu \right)=\left(1,4,1,0,16\right)$ to reproduce the topology of the Fermi surface near the $\mathrm{\Gamma }$ point. (b) A 2D cross-section of the Fermi surface shown in (a) for $k_z=0$. (c) Same as (a) except using different parameters, $\left(t,t_z,t^{\prime },\alpha ,\mu \right)=\left(1,-4,1,2,12\right)$, to reproduce the topology of the Fermi surface at the $A$ point. (d) A 2D cross-section of the Fermi surface shown in (c) for $k_z=\pi$.