We study the holographic phase transition of superconductor dual to a Lifshitz black brane probed by an anisotropic scalar field in the probe limit in Hoȓava-Lifshitz gravity. With the use of numerical and analytical method, we investigate how the critical temperature of the condensation is affected by the Lifshitz exponent z, α−correction term in the action as well as the dimensions of the gravity. We also numerically explore the condensation of the dual operator and optical conductivity of the holographic system. Various interesting properties of the holographic condensation affected by the parameters of model are discussed. * Electronic address:

We analytically obtain a new charged Lifshitz solution by adding a non-relativistic Maxwell field in Hořava-Lifshitz gravity. The black hole exhibits an anisotropic scaling between space and time (Lifshitz scaling) in the UV limit, while in the IR limit, the Lorentz invariance is approximately recovered. We introduce the probed Lorentz-violation fermions into the background and holographically investigate the spectral properties of the dual fermionic operator. The Lorentz-violation of the fermions will enhance the peak and correspond larger fermi momentum, which compensates the non-relativistic bulk effect of the dynamical exponent (z). For a fixed z, when the Lorentzviolation of fermions increases to a critical value, the behavior of the low energy excitation goes from a non-Fermi liquid type to a Fermi liquid type, which implies a kind of phase transition. * Electronic address: