High quality epitaxial Sr 2 IrO 4 thin films with various thicknesses (9-300 nm) have been grown on SrTiO 3 (001) substrates, and their electric transport properties have been investigated. All samples showed the expected insulating behavior with a strong resistivity dependence on film thickness, that can be as large as three orders of magnitude at low temperature. A close examination of the transport data revealed interesting crossover behaviors for the conduction mechanism upon variation of thickness and temperature. While Mott variable range hopping (VRH) dominated the transport for films thinner than 85 nm, high temperature (>200 K) thermal activation behavior was observed for films with large thickness (≥85 nm), which was followed by a crossover from Mott to Efros-Shklovskii (ES) VRH in the low temperature range. This low temperature crossover from Mott to ES VRH indicates the presence of a Coulomb gap (~3 meV).Our results demonstrate the competing and tunable conduction in Sr 2 IrO 4 thin films, which in turn would be helpful for understanding the insulating nature related to strong spin-orbitalcoupling of the 5d iridates. In recent years, oxides with the 5d-element Ir have been established as a fertile ground for studying new physics arising from the large relativistic spin-orbit-coupling (SOC) [1][2][3]. So far, a variety of exotic properties related to the strong SOC such as intriguing insulating behavior [3][4][5][6][7][8][9][10] In addition to the newly raised controversy on the insulating nature of SIO, the conduction mechanism of the insulating state has been a long-standing issue. In an early work, variable range hopping (VRH) conduction was reported in single crystalline SIO [3]. A recent study also focusing on SIO single crystals revealed that the conduction well follows the thermal activation mechanism with an energy gap of Δ~107 meV perfectly matching the value of optical measurements [1,12]. Further investigations of the same group showed a VRH dominated conduction in doped SIO even though the doping content was small [19,20]. In Ba 2 IrO 4 (BIO), although it highly resembles SIO in terms of structural and electronic properties, good VRH conduction was observed in the whole measured temperature (T) range. Moreover this type of conduction is robust against carrier doping [6], which is very different from the SIO case. In fact, a close examination of the conduction mechanism in SIO and BIO can provide some more interesting details. While the doped SIO shows 3-dimentional (3D) VRH conduction [19,20] [19], which could probably be related to the SOC. These show intriguing conduction behavior in the single layered iridates, pointing to a rather poor understanding of the conduction mechanism in SIO. Moreover, this issue became even more puzzling in the case of SIO thin films, in which the thermal activation model was frequently used to determine the energy gap of SIO, although a linear fit on a plot of lnρ-1/T is questionable [21,22]. Therefore, it is of high interest and actuality to compreh...