Evidence of pair-density wave in doping Kitaev spin liquid on the honeycomb lattice

TL;DR

This study demonstrates the emergence of a pair-density wave as the dominant superconducting order in a doped Kitaev spin liquid model on a honeycomb lattice, revealing novel intertwined charge and pairing correlations.

Contribution

It provides the first example of a pair-density wave as the leading superconducting order in a bipartite lattice within a doped Kitaev model, using density-matrix renormalization group calculations.

Findings

Light doping induces charge-density-wave correlations.

Superconducting correlations exhibit d-wave-like symmetry.

Pair-density wave is the dominant superconducting order.

Abstract

We study the effects of doping the Kitaev model on the honeycomb lattice where the spins interact via the bond-directional interaction $J_K$, which is known to have a quantum spin liquid as its exact ground state. The effect of hole doping is studied within the $t$-$J_K$ model on a three-leg cylinder using density-matrix renormalization group. Upon light doping, we find that the ground state of the system has quasi-long-range charge-density-wave correlations but short-range single-particle correlations. The dominant pairing channel is the even-parity superconducting pair-pair correlations with $d$-wave-like symmetry, which oscillate in sign as a function of separation with a period equal to that of the spin-density wave and two times the charge-density wave. Although these correlations fall rapidly (possibly exponentially) at long distances, this is never-the-less the first example where a pair-density wave is the strongest SC order on a bipartite lattice. Our results may be relevant to ${\rm Na_2IrO_3}$ and $\alpha$-${\rm RuCl_3}$ upon doping.