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Abstract

We study the effect of adding disorder to the Kitaev model on the hyperhoneycomb lattice, which hosts both gapped and gapless spin liquid phases with an emergent Z(2) gauge field. The latter has an unusual gapless spectrum of Majorana fermion excitations, with a co-dimension-two Fermi ring. We thus address the question of the interplay of topological physics and disorder by considering the properties of isolated single and pairs of vacancies. We show that near the vacancies, the local magnetic response to a field h(z) is parametrically enhanced in comparison to the pristine bulk. Unlike the previously studied case of the 2D honeycomb Kitaev model, the vacancies do not bind a flux of the Z(2) gauge field. In the gapped phase, an isolated vacancy gives rise to effectively free spin-half moments with a nonuniversal coupling to an external field. In the gapless phase, the low-field magnetization is suppressed parametrically to (-ln h(z))(-1/2) because of interactions with the surrounding spin liquid. We also show that a pair of vacancies is subject to a sublattice-dependent interaction on account of coupling through the bulk spin liquid, which is spatially anisotropic even when all Kitaev couplings have equal strength. This coupling is thus exponentially suppressed with distance in the gapped phase. In the gapless phase, two vacancies on the same (opposite) sublattice exhibit an enhanced (suppressed) low-field response, amounting to an effectively (anti-)ferromagnetic interaction.