| Summary: | 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 a dominant quasi-long-range charge-density-wave correlations but short-range single-particle correlations. In the pairing channel, the even-parity superconducting correlation is dominant 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 (possibly exponentially) at long distances, this is never-the-less the example where a pair-density wave is the leading instability in the pairing channel on the honeycomb lattice.
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