Majorana correlations in the Kitaev model with ordered-flux structures

TL;DR

This paper investigates how different flux configurations in the Kitaev honeycomb model influence the behavior of Majorana fermions, revealing gapped, semi-Dirac, and power-law dispersions, with implications for controlling Majorana-based excitations.

Contribution

It introduces a detailed analysis of flux pattern effects on Majorana fermion dispersions and correlations, including the impact of randomness, extending understanding beyond the flux-free state.

Findings

Periodically arranged fluxes can induce gapped or semi-Dirac Majorana dispersions.

Flux disorder maintains power-law decay in Majorana correlations despite increased flux density.

Different flux configurations significantly alter the low-energy Majorana excitations.

Abstract

We study the effects of the flux configurations on the emergent Majorana fermions in the $S=1/2$ Kitaev model on a honeycomb lattice, where quantum spins are fractionalized into itinerant Majorana fermions and localized fluxes. A quantum spin liquid appears as the ground state of the Kitaev model in the flux-free sector, which has intensively been investigated so far. In this flux sector, the Majorana fermion system has linear dispersions and shows power law behavior in the Majorana correlations. On the other hand, periodically-arranged flux configurations yield low-energy excitations in the Majorana fermion system, which are distinctly different from those in the flux-free state. We find that one of the periodically arranged flux states results in the gapped Majorana dispersion and the exponential decay in the Majorana correlations. The Kitaev system with another flux configuration exhibits a semi-Dirac like dispersion, leading to the power law decay with a smaller power than that in the flux-free sector along symmetry axes. We also examine the effect of the randomness in the flux configurations and clarify that the Majorana density of states is filled by increasing the flux density, and power-law decay in the Majorana correlations remains. The present results could be important to control the motion of Majorana fermions, which carries the spin excitations, in the Kitaev candidate materials.