Majorana correlations in the Kitaev model with ordered-flux structures

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.

Statistical properties of linear Majorana fermions

“…With the energy spectrum found in the expression (31) We also observed that when the parameter k increases, the mean energy U/N increases with an approximately linear behavior close to the origin, i. e., T = 0. However, when T increases, the behavior of the energy starts to be more distinct.…”

“…In particular, we believe that studying Majorana fermions can help us better understand the behavior of these relativistic particles. In fact, once we understand the behavior of these particles better, we are able to comprehensively understand some physical phenomena, e. g., the dynamic of quantum spin liquid which has been widely studied [31][32][33][34] to understand spin transports in quantum spin systems and are applied in spintronic contexts [35]. In addition, to understand the properties of Majorana's fermions allow us to know a little more about the thermodynamics associated with topological insulators and the Majorana's superconductivity [36], which can leads to semiconductor nanowires [37] and to a revolution in the industry of electrical devices [38].…”

Role of Majorana fermions in spin transport of anisotropic Kitaev model

“…On the other hand, since low-lying itinerant Majorana fermions does not induce magnetic excitations in the bulk, longrange spin transport is expected to be retained even in the presence of magnetic impurities. It is also interesting to examine Majorana correlations in the present system [50], which is beyond the scope of our study.…”