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

Pair-density wave (PDW) is a novel superconducting (SC) state in which the SC order parameter varies periodically in real space such that its spatial average vanishes. Whether the PDW state can be induced by doping certain quantum spin liquid (QSL) remains an open question. We study the effects of doping the Kitaev spin liquid on honeycomb lattice using density-matrix renormalization group. The effect of hole doping is studied within the t-JK model on a three-leg cylinder where the spins interact via the bond-directional interaction JK. 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 correlation with d-wave-like symmetry, which oscillates 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 at long distances, this is never-the-less the first example where a PDW is the strongest SC order on a bipartite lattice.