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Abstract
We study the effects of doping the Kitaev model on the honeycomb lattice where the spins interact via the bond-directional interaction JK, which is known to have a quantum spin liquid as its exact ground state. The effect of hole doping is studied within the t-JK 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.
Highlights
The pair-density wave (PDW) is a superconducting (SC) state in which the order parameter varies periodically in space in such a way that its spatial average vanishes[1,2]
Intense interest in a somewhat different sort of PDW state has emerged due to recent discoveries in underdoped cuprate superconductors, where a direct observation of PDW has been made experimentally via local Cooper pair tunneling and scanning tunneling microscopy in Bi2Sr2CaCu2O8+x5–7, as well as the dynamical inter-layer decoupling observed in 1/8 hole-doped La2BaCuO48,9
While similar in having oscillatory SC order and associated K = 2Q charge-density wave (CDW) order, this PDW is conjectured to be stable in zero magnetic field, have an ordering vector that is independent of H, and can either have no associated magnetic order, or possibly have spin-density wave order (SDW) with the same ordering vector Q
Summary
The pair-density wave (PDW) is a superconducting (SC) state in which the order parameter varies periodically in space in such a way that its spatial average vanishes[1,2]. Much is known about the properties of the PDW state[1,2,10] there are very few microscopic models, which are shown to have PDW ground states. These include the one-dimensional (1D) Kondo-Heisenberg model with 1D electron gas coupled to a spin chain[11], the extended two-leg Hubbard–Heisenberg model[12], and strong coupling limit of the Holstein–Hubbard Model[13,14]. There is no evidence of PDW ordering found in more standard models even with second neighbor interactions[17,18,19,20]
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