  We construct the Einstein-axions AdS black hole from Born-Infeld
electrodynamics. Various DC transport coefficients of the dual boundary theory
are computed. The DC electric conductivity depends on the temperature, which is
a novel property comparing to that in RN-AdS black hole. The DC electric
conductivity are positive at zero temperature while the thermal conductivity
vanishes, which implies that the dual system is an electrical metal but thermal
insulator. The effects of Born-Infeld parameter on the transport coefficients
are analyzed. Finally, we study the AC electric conductivity from Born-Infeld
electrodynamics with momentum dissipation. For weak momentum dissipation, the
low frequency behavior satisfies the standard Drude formula and the electric
transport is coherent for various correction parameter. While for stronger
momentum dissipation, the modified Drude formula is applied and we observe a
crossover from coherent to incoherent phase. Moreover, the Born-Infeld
correction amplifies the incoherent behavior. Finally, we study the non-linear
conductivity in probe limit and compare our results with those observed in
(i)DBI model.
