Vacancies in the Kitaev quantum spin liquids on the 3D hyper-honeycomb lattice

TL;DR

This paper investigates how vacancies affect the magnetic and topological properties of the 3D hyper-honeycomb Kitaev quantum spin liquid, revealing unique local responses and interactions influenced by the gapless or gapped phases.

Contribution

It provides a detailed analysis of vacancy effects in the 3D Kitaev model, including local magnetic responses and interactions, highlighting differences from the 2D case and the role of topological phases.

Findings

Vacancies enhance local magnetic response near them.

In the gapped phase, vacancies behave like free spin-half moments.

In the gapless phase, low-field magnetization is suppressed as (-ln h_z)^(-1/2).

Abstract

We study the effect of adding disorder to the exactly solvable Kitaev model on the hyper-honeycomb lattice, which hosts both gapped and gapless spin liquid phases with an emergent $\mathbb{Z}_2$ 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 pair 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 $\mathbb{Z}_2$ gauge field. In the gapped phase, an isolated vacancy gives rise to effectively free spin-half moments with a non-universal 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.