ϵ 0 0.1 0.2 0.5 0.9 0.99 m $^{2}$L2 AdS = 0 14 . 6 13 . 9 13 . 2 11 . 3 9 . 0 8 . 6 m $^{2}$L2 AdS = − 1 13 . 8 13 . 2 12 . 6 10 . 8 8 . 6 8 . 2 m $^{2}$L2 AdS = − 2 12 . 9 12 . 4 11 . 9 10 . 3 8 . 4 8 . 1 infinity when the frequency approaches zero. In Fig. 5 we present the ratio ω$_{g}$/ T$_{c}$ as a function of the balance parameter with fixed values m $^{2}$L2 AdS = 0 − 1 and − 2, which shows that the ratio ω$_{g}$/ T$_{C}$ almost linear decreases with the increase of the balance constant. From Figs. 4, 5 and table II, we find that the ratio of the gap fre quency in conductivity ω$_{g}$ to the critical temperature T$_{c}$ in this black hole reduces to Cai’s result ω$_{g}$/ T$_{c}$ ≈ 13 [36] found in the Hoˇrava-Lifshitz black hole with the condition of the detai led balance for small ϵ , while it tends to the Horowitz-Roberts relation ω$_{g}$/ T$_{c}$ ≈ 8 as ϵ → 1. Our result provides a bridge between the two kind of the relations. V. CONCLUSIONS The behavior of the holographic superconductors in the Hoˇr ava-Lifshitz gravity has been investi- gated in this manuscript by introducing a complex scalar fiel d and a Maxwell field in a planar black- hole background. We first present a detailed analysis of the c ondensation of the operator O + by the numerical and analytical methods for the Hoˇrava-Lifshitz black hole without the condition of the de- tailed balance. We obtain consistent analytical result with that obtained numerically by selecting the appropriate matching point. It is found that, as the parameter of the detailed balance ϵ increases with fixed mass of the scalar field m , the condensation gap becomes smaller, corresponding to the larger critical temperature, which means that the scalar hair can be formed easier for the larger ϵ . And it is shown that, for the same ϵ , the condensation gap becomes larger if m 2 becomes less negative, which means that it is harder for the scalar hair to form as the mass of the scalar field becomes larger. We then studied the electrical conductivity in the Hoˇrava-Li fshitz black-hole background and find that the ratio of the gap frequency in conductivity to the critical temperature, ω$_{g}$/ T$_{c}$ , almost linear decreases with the increase of the balance constant. For ϵ = 0 the ratio reduces to Cai’s result ω$_{g}$/ T$_{c}$ ≈ 13 [36] found in a Hoˇrava-Lifshitz black hole with the condition of the detailed balance, while as ϵ → 1 it 12 TABLE II: The ratio ω$_{g}$/ T$_{c}$ for di ff erent values of the constant ϵ with m $^{2}$L2 AdS = 0 , − 1 and − 2.