Quantum Theory of Lee-Naughton-Lebed's Angular Effect in Strong Electric Fields

Some time ago, Kobayashi et al. experimentally studied the so-called Lee-Naughton-Lebed's (LNL) angular effect in strong electric fields [K. Kobayashi, M. Saito, E. Omichi, and T. Osada, Phys. Rev. Lett. \textbf{96}, 126601 (2006)]. They found that strong electric fields split the LNL conductivity maxima in $\alpha$-(ET)$_2$-based organic conductor and hypothetically introduced the corresponding equation for conductivity. In this Letter, for the first time we suggest quantum mechanical theory of the LNL angular oscillations in moderately strong electric fields. In particular, we demonstrate that the obtained by us approximate theoretical formula coincides with the hypothetical one and well describes the above mentioned experiments.