Successive Majorana Topological Transitions Driven by a Magnetic Field in the Kitaev Model

TL;DR

This paper investigates topological quantum phase transitions in the Kitaev honeycomb model under a magnetic field, revealing successive Majorana fermion spectrum changes and topological shifts with potential experimental signatures.

Contribution

It uncovers a new gapless phase driven by topological changes in Majorana spectra and analyzes the effects of magnetic field orientation on topological properties.

Findings

Identification of a gapless phase between two quantum spin liquids.

Topological change in Majorana spectrum via line node formation.

Reversal of thermal edge current due to Chern number sign change.

Abstract

We study quantum phase transitions in the honeycomb Kitaev model under a magnetic field, focusing on the topological nature of Majorana fermion excitations. We find a gapless phase between the low-field gapless quantum spin liquid and the high-field gapped forced-ferromagnetic state for the antiferromagnetic Kitaev model in the [001] field by using the Majorana mean-field theory, in conjunction with the exact diagonalization and the spin-wave theory supporting the validity of this approach. The transition between the two gapless phases is driven by a topological change of the Majorana spectrum --- line node formation interconnecting two Majorana cones. The peculiar change of the Majorana band topology is rationalized by a sign change of the effective Kitaev coupling by the magnetic field, which does not occur in the ferromagnetic Kitaev case. Upon tilting the magnetic field away from [001], the two gapless phases become gapped and topologically nontrivial, characterized by nonzero Chern numbers with different signs. The sign change of the Chern number leads to a reversal of the thermal edge current in the half-quantized thermal Hall effect.