Gapless excitations in field-induced Kitaev spin liquids with line defects

The field-induced Kitaev spin liquid is a strongly correlated topological phase which may have been realized in the layered material $\alpha$-RuCl$_3$. It is characterized by the presence of gapped non- Abelian anyon excitations in the bulk and gapless chiral Majorana modes at the edges. In this work we show that gapless one-dimensional modes can also survive in the bulk of the Kitaev spin liquid when they are bound to line defects at which the exchange interaction falls below a critical value. Treating the weak interaction at the line defect within a mean-field approximation, we determine the critical interaction strength as a function of the external magnetic field. In the gapless regime, we use the low-energy effective field theory to calculate the spin-lattice relaxation rate for a spin near the defect. We discuss the relevance of these results to nuclear magnetic resonance experiments that claimed to have observed gapless excitations in the putative spin liquid phase of $\alpha$-RuCl$_3$.