We have studied the temperature dependence of resistivity, p, for a two-dimensional electron system in silicon at low electron densities n, 10 cm, near the metal-insulator transition. The resistivity was empirically found to scale with a single parameter Tp, which approaches zero at some critical electron density n, and increases as a power To oc~n,n,~with P = 1.6 6 0.1 both in metallic (n,) n,) and insulating (n, (n) regions. This dependence was found to be sample independent. We have also studied the diagonal resistivity at Landau-level filling factor v =-,where the system is known to be in a true metallic state at high magnetic field and in an insulating state at low magnetic field. The temperature dependencies of resistivity at B = 0 and at v =were found to be identical. These behaviors suggest a true metal-insulator transition in the two-dimensional electron system in silicon at B = 0, in contrast with the well-known scaling theory.

We have studied the resistivity of a two-dimensional electron system in silicon in the temperature range 200 mK < T < 7.5 K at zero magnetic eld at low electron densities, when the electron system is in the insulating regime. Our results show that at an intermediate temperature range, = 0 exp (T0=T) 1 2 ] for at least four orders of magnitude up to 3 10 9 . This behavior is consistent with the existence of a Coulomb gap. Near the metal/insulator transition, the prefactor was found to be 0 h=e 2 , and resistivity scales with temperature. For very low electron densities, ns, the prefactor diminishes with diminishing ns. A comparison with the theory shows that a speci c set of conditions are necessary to observe the behavior of resistivity consistent with the existence of the Coulomb gap.At su ciently low temperatures (T), in disordered systems such as semiconductors, transport occurs by phonon-assisted tunneling to states nearby in energy. The tunneling distance to a state within k B T of the Fermi energy (E F ) increases with decreasing temperature (here k B is the Boltzmann constant). This transport process has been labeled variable-range hopping (VRH) and is characterized by resistivity of the form (T ) = 0 exp (T 0 =T ) x ;(1) where T 0 is some characteristic temperature. Mott 1] derived this law by assuming a constant density of states (DOS) at the Fermi energy and found in two dimensions that x = 1 3 . This is a single-particle picture which ignores the Coulomb interaction. Efros and Shklovskii 2] have argued that the Coulomb interaction between localized electrons creates a gap, the so-called \Coulomb gap", in the density of states near the Fermi energy. This is manifested by a resistivity of the form of Eq. (1) with x = 1 2 , which is universal for both two-and three-dimensional (2D and 3D) electronic systems.In 1986, Timp, Fowler, Hartstein, and Butcher (TFHB) 3] examined the conductivity as a function of temperature and electric eld in sodium-doped silicon metal-oxide-semiconductor eld-e ect transistors (MOSFET's) and found no evidence of the Coulomb gap. More recently, Coulomb gap behavior has been observed in relatively low-mobility GaAs/AlGaAs heterostructures 4,5]. In this paper, we report experimental studies of the temperature dependence of resistivity of high-mobility silicon MOSFET's. Our experimental data follows the form of Eq. (1) with x = 1 2 for a range of parameters such as temperature and 2D electron density n s . This behavior is consistent with the existence of the Coulomb gap. We believe di erences between our results and those of TFHB are due to di erences between parameter spaces examined in each case.

We report experimental studies of disorder-induced transitions between quantum-Hall, metallic, and insulating states in a very dilute two-dimensional electron system in silicon at a magnetic field corresponding to Landau level filling factor ν = 1. At low disorder, the lowest extended state at ν = 1 is below the Fermi energy so that the system is in the quantum Hall state.Out data show that with increasing disorder (but at constant electron density and magnetic field), the extended state does not disappear but floats up in energy so that the system becomes insulating. As the extended state crosses the Fermi energy, the conductivity σ xx ∼ e 2 /2h has temperature dependence characteristic of a metallic system. PACS 73.40. Hm, 73.40.Qv, 71.30.+h Typeset using REVT E X 1