Odd-Parity Triplet Pair Induced by Hund’s Rule Coupling

We discuss microscopic aspects of the odd-parity triplet pair in orbital degenerate systems. From the concept of off-diagonal long-range order, a pair state is unambiguously defined as the eigenstate with the maximum eigenvalue of a pair correlation function. Performing this scheme by a numerical technique, we clarify that the odd-parity triplet pair occurs as an out-of-phase combination of local triplets induced by Hund’s rule coupling for the lattice including two sites in the unit cell.

Figure 1

(a) Two-dimensional square and (b) honeycomb lattices. Thin lines in (a) denote an eight-site cluster, while in (b), they indicate an eight-site cluster composed of four unit cells including two sites, 1 and 2. Thick arrows define vectors ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$.

Figure 2

Schematic views for wave functions of (a) odd-parity and (b) even-parity triplet pairs in the honeycomb lattice.

Figure 3

(a) Ground-state phase diagram for eight-site honeycomb lattice with $n=0.75$. Note that the region for $J>U^{\prime }$ is unphysical. (b) Maximum and second maximum eigenvalues of $P$ as a function of $U^{\prime }-J$ in the FM phase. Coefficients of the odd- and even-parity triplet pair correlation functions for (c) $\mathbf{a}=(0,0)$, (d) $\mathbf{a}={\mathbf{a}}_1$, (e) $\mathbf{a}={\mathbf{a}}_2$, and (f) $\mathbf{a}={\mathbf{a}}_1+{\mathbf{a}}_2$, for $U^{\prime }-J=1$.