The L-H transition leads to a substantial reduction in transport levels in tokamaks and stellarators, improving the plasma confinement in such devices. After the transition, the plasma is in a high-confinement regime characterized by steep density and temperature gradients, with a large radial electric field at the plasma edge. In this paper, we show that, on using an ExB wave transport model on a test particle, such large electric fields can produce shearless transport barriers (STBs), which are related to the presence of non-monotonic sheared profiles, preventing almost all the chaotic flux at the plasma edge. The behavior of these barriers enables us to investigate the properties of the L-H transition as a function of the intensity of the electrostatic fluctuations and the depth of the typical radial electric field well-like profile, developed at plasma edge during the transition. We found that, as the radial electric field well depth increases, the shearless edge transport barrier becomes more resistant to perturbations and that, eventually, an improved plasma confinement regime is accessed. In this sense, we found results consistent with the experimental observations. In particular, the transition curve in the parameter plane associated with the STB has a fractal structure, thanks to the non-integrable nature of the associated Hamiltonian.