Possible quantum hall effect in the two-dimensional organic conductor, ${\tau }$-(EDO-S, S-DMEDT-TTF)${_{2}}$(AuBr${_{2}}$)${_{1+y}}$ in the two-Fermi surface system

In the two-dimensional organic conductor, $\tau $-(EDO-$S$,$S$-DMEDT-TTF)$_{2}$(AuBr$_{2})_{1+y}$, we have observed Shubnikov de Hass oscillations with Landau level down to $n = 1$ (quantum limit), and found Hall resistance plateau above 35 Tesla.($n = 1$). This plateau might be interpreted as a new quantum Hall effect (QHE), realized by two 2D Fermi surfaces (FS). Since the areas and effective masses are, 0.66%(1.6 $m_{0})$ and 6.1%(3.5-5.2 $m_{0})$ of the first Brillouin zone, the large FS can play the role of electron reservoir for the small FS. This explains the plateau structure in Hall effect. To confirm that two series of oscillations are associated with really thermodynamic phenomena, we performed torque and Shubnikov de Haas studies. Key words. Two-dimensional organic conductor, quantum Hall effect.