Identification of a Kitaev quantum spin liquid by magnetic field angle dependence

Abstract

Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments.

Field-angle dependence of thermal Hall conductivity in a magnetically ordered Kitaev-Heisenberg system

“…( 1) is invariant under these operations. Moreover, the invariance is retained even with the Γ and Γ interactions [56]. With respect to the thermal Hall conductivity, κ ab should be unchanged by the C 3 rotation around the c axis, but it changes its sign under the C 2 rotation around the b axis.…”

“…If the magnetic field is applied along the b direction, the Hamiltonian is unchanged under the C 2 rotation around b axis. Therefore, κ ab should be zero in the presence of the magnetic field parallel to b or its equivalent directions when a magnetic order does not occur [43,56,73].…”

“…In particular, the half-quantized plateau has been observed in the thermal Hall conductivity [41][42][43][44], which offers convincing evidence for the emergence of Majorana fermions and the presence of a Majorana chiral edge mode. Triggered by these experimental results, magnetic-field effects on the Kitaev-related systems have been studied theoretically [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. Moreover, classical phase diagrams of the Kitaev-Heisenberg and Kitaev-Γ models under the magnetic field were obtained by the mean-field (MF) approach and Monte Carlo simulations [25][26][27][28]60].…”

“…In the phase diagrams, an applied magnetic field stabilizes various ordered states, including noncollinear and noncoplanar configurations. Stimulated by the recent experimental results on the field-angle dependence of the thermal Hall conductivity [43], the thermal Hall effect for various field directions has been examined in the Kitaev models with additional interactions in the Majorana fermion representation [48,54,56] and spin-wave theory [27,46,47,55,61]. However, details on the field-angle dependence of magnetic excitations and thermal Hall conductivity remain unclear in the Kitaev-related models.…”

Phase Diagrams of Kitaev Models for Arbitrary Magnetic-Field Orientations

“…[63] has addressed this issue and also the magnetic field effects perturbatively, yet assuming a KSL GS. In this respect, it is crucial to clarify the effect of large Γ ∼ |K| [64,65] as well as arbitrary magnetic field orientations and strengths to understand the validity of existing results based on the putative F Kitaev GS. Naturally, an unbiased method is needed where the ordered phases and the fractional phases are treated on equal footing.…”