Stabilizing Z2 fluxes in Kitaev spin liquids (KSLs) is crucial for both characterizing candidate materials and identifying Ising anyons. In this study, we investigate the effects of spin-S magnetic impurities embedded in the spin-1/2 KSL. Utilizing exact diagonalization and density matrix renormalization group methods, we examine the impurity magnetization and ground-state flux sector with varying impurity coupling and spin size. Our findings reveal that impurity magnetization exhibits an integer/half-integer spin dependence, which aligns with analytical predictions, and a flux-sector transition from bound-flux to zero-flux occurs at low coupling strengths, independent of the impurity spin. Notably, for spin-3/2 impurities, we observe a reentrant bound-flux sector, which remains stable under magnetic fields. By considering fermionic representations of our spin Hamiltonian, we provide phenomenological explanations for the transitions. Our results suggest a novel way of binding a flux in KSLs, beyond the proposals of vacancies or Kondo impurities.

The Yao-Lee (YL) model is an example of exactly solvable spin-orbital models that are generalizations of the original Kitaev honeycomb model with extra local orbital degrees of freedom. Similar to the Kitaev model, both spin and orbital degrees of freedom are effectively represented using sets of three-flavored Majorana fermions. The YL model exhibits a quantum spin liquid ground state with gapped and immobile Z2 fluxes and three-fold degenerate itinerant Majorana fermions. Our work demonstrated that by introducing different time-reversal symmetry (TRS) breaking fields one can split the degeneracy of Majorana fermions and close the gap for some of the bands, thus changing its topology. We calculated a comprehensive topological phase diagram for the YL model by considering various combinations of TRS breaking fields. This investigation revealed the emergence of distinct topological regions, each separated by nodal lines, signifying an evolution in the model's topological properties. We also investigated the impact of vacancies in the system. Our findings revealed that while vacancies modify the low-energy spectrum of the model, their presence has a limited impact on the topological properties of the model, at least for small enough concentrations.

We study the spectroscopic signatures of vacancy-induced Majorana zero modes of the Kitaev spin liquid in the inelastic STM setup. When a clean Kitaev spin liquid is placed between the tip and the substrate, the tunneling barrier involves the flux-excitation gap that leads to a zero-response region. However, in the presence of  vacancies, a quasi-zero-energy peak appears in the flux-gap region, and its characteristic voltage and intensity are increased with vacancy concentrations, which can be attributed to the localized nature of vacancy-induced Majorana zero modes. The presence of these Majorana zero modes also makes the single-fermion van Hove singularity visible in the STM response, which represents the energy scale of fractionalized Majorana fermions in the Kitaev spin liquid.

Motivated by the emergence of this plethora of 4d and 5d transition metal Kitaev materials and by the fact that some level of disorder is inevitable in real materials, we study how the Kitaev spin liquid responds to various forms of disorder, such as vacancies, impurities, and bond randomness. We argue that the presence of the quenched disorder can lead to the Anderson localization of Majorana fermions and the appearance of Lifshitz tails, and that the disorder effects on the low-energy Majorana modes can be detected in thermal transport. While we find that both the site disorder and the bond randomness suppress the longitudinal thermal conductivity, the low-energy localization is stronger in the case of the site disorder.

We study the two-dimensional kagome-ice model derived from a pyrochlore lattice with second- and third-neighbor interactions. The canted moments align along the local ⟨111⟩ axes of the pyrochlore and respond to both in-plane and out-of-plane external fields. We find that the combination of further-neighbor interactions together with the external fields introduces a rich phase diagram with different spin textures. Close to the phase boundaries, metastable “snake” domains emerge with extremely long relaxation time. Our kinetic Monte Carlo analysis of the magnetic-field quench process from saturated state shows unusually slow dynamics. Although the interior spins are almost frozen in snake domains, the spins on the edge are free to fluctuate locally, leading to frequent creation and annihilation of monopole-antimonopole bound states. 

We present numerical studies of dipolar spin ice in the presence of a magnetic field slightly tilted away from the [111] axis. We find a first-order transition from a kagome ice to a q = X state when the external field is tilted toward the [11-2] direction. This is consistent with the anomalous critical scattering previously observed in the neutron scattering experiment on the spin ice material Ho2Ti2O7 in a tilted field [T. Fennell et al., Nat. Phys. 3, 566 (2007)]. We show that this ordering originates from the antiferromagnetic alignment of spin chains on the kagome planes. Our result captures the features observed in the experiments and points to the importance of the dipolar interaction in determining ordered states in the spin ice materials.