  We propose a theoretical model for a gapless spin liquid phase that may have
been observed in a recent experiment on $\mathrm{H_3Li Ir_2 O_6}$. Despite the
insulating and non-magnetic nature of the material, the specific heat
coefficient $C/T \sim 1/\sqrt{T}$ in zero magnetic field and $C/T \sim T/
B^{3/2}$ with finite magnetic field $B$ have been observed. In addition, the
NMR relaxation rate shows $1/(T_1T) \sim (C/T)^2$. Motivated by the fact that
the interlayer/in-plane lattice parameters are reduced/elongated by the
hydrogen-intercalation of the parent compound $\mathrm{Li_2 Ir O_3}$, we
consider four layers of the Kitaev honeycomb lattice model with additional
interlayer exchange interactions. It is shown that the resulting spin liquid
excitations reside mostly in the top and bottom layers of such a layered
structure and possess a quartic dispersion. In an applied magnetic field, each
quartic mode is split into four Majorana cones with the velocity $v \sim
B^{3/4}$. We suggest that the spin liquid phase in these "defect" layers,
placed between different stacking patterns of the honeycomb layers, can explain
the major phenomenology of the experiment, which can be taken as evidence that
the Kitaev interaction plays the primary role in the formation of a quantum
spin liquid in this material.
