Majorana-Mediated Spin Transport in Kitaev Quantum Spin Liquids

We study the spin transport through the quantum spin liquid (QSL) by investigating the real-time and real-space dynamics of the Kitaev spin system with zigzag edges using the time-dependent Majorana mean-field theory. After the magnetic-field pulse is introduced to one of the edges, spin moments are excited in the opposite edge region although spin moments are never induced in the Kitaev QSL region. This unusual spin transport originates from the fact that the $S=1/2$ spins are fractionalized into the itinerant and localized Majorana fermions in the Kitaev system. Although both Majorana fermions are excited by the magnetic pulse, only the itinerant ones flow through the bulk regime without spin excitations, resulting in the spin transport in the Kitaev system despite the presence of a nonzero spin gap. We also demonstrate that this phenomenon can be observed in the system with small Heisenberg interactions using the exact diagonalization.

Figure 1

Kitaev model on a honeycomb lattice with zigzag edges. Red, blue, and green lines represent $x$, $y$, and $z$ bonds, respectively. Solid (open) circles represent spin-$1/2$ in the $A$ ($B$) sublattice. In this figure, four $z$ (green) bonds exist along the $\mathit{a}$ direction in the R region, namely, $L_R=4$.

Figure 2

Real-time dynamics of the Kitaev spin system with $L_a=50$ and $L_b=300$. The contour plot of $\mathrm{\Delta }{S}^z(x,t)$ on the plane of the time $t$ and the space $x$ in the system (a) without and (b) with the M (white) region where the QSL is realized without spin polarization between the L (left gray) and R (right gray) regions (see the top of the panels). The dashed lines represent $x=vt$ with the Majorana velocity $v$ (see text).

Figure 3

Real-time evolution of (a) $\mathrm{\Delta }\xi$ and (b) $\mathrm{\Delta }\eta$ of the Kitaev spin system with $L_a=50$ and $L_b=300$. The setup and parameters are the same as in Fig. 2.

Figure 4

Contour plots of $\mathrm{\Delta }{S}^z(x,t)$ in the 24-site cluster with $h_R=0.01J_K$ when (a) $(J_H/J_K,A)=(0,1)$, (b) (0.03,1), and (d) (0.03,5). The dashed lines represent $x=vt$ with the Majorana velocity $v$ (see text). (c) Time evolution of $\mathrm{\Delta }{S}^z$ at the right edge site $x_{\mathrm{RE}}$ with $A=1$.