The anomalous conducting phase that has been shown to exist in zero field in dilute two-dimensional electron systems in silicon MOSFETs is driven into a strongly insulating state by a magnetic field of about 20 kOe applied parallel to the plane. The data suggest that in the limit of T -> 0 the conducting phase is suppressed by an arbitrarily weak magnetic field. We call attention to striking similarities to magnetic field-induced superconductor-insulator transitions

In a series of recent experiments, Kravchenko and colleagues 1,2 observed unexpectedly that a two-dimensional electron gas in zero magnetic field can be a conductor. The two-dimensionality was imposed by confining the electron gas to move laterally at the interface between two semiconductors. The observation of a conductor in two dimensions (2D) is surprising as the conventional theory of metals precludes the presence of a metallic state at zero temperature in 2D 3. Nonetheless, there are now several experiments confirming the existence of the new conducting phase in a dilute two-dimensional electron gas in zero magnetic field 4-7. Here we argue based on an analysis of the experiments and general theoretical grounds that this phase is a zero-temperature superconductor with an inhomogeneous charge density. While the specific details differ as the semiconductor that confines the 2D electron gas is changed, several key similarities 1,2,4-7 exist among the reported observations of the transition to the conducting state: 1) the existence of a critical electron or hole density, n c , above which the conducting phase appears, 2) a characteristic temperature, typically on the order of half the Fermi temperature, T F , below which the resistivity on the conducting side decreases, 3) critical scaling, indicative of a quantum critical point, in the vicinity of the insulator-conducting phase transition, 4) non-linear current-voltage (I-V) curves that exhibit a symmetry around the I-V curve at criticality, and 5) suppression of the conducting phase by a magnetic field. In Si metal-oxide-field-effect-transistors (MOSFET's) samples 1 , temperature (T) and electric field (E) scaling have made it possible to extract the dynamical and correlation length exponents, z and ν, respectively. By fitting the resis-tivity measurements to functions of the form, ρ(T, n) = f 1 (|δ|/T b) and ρ(E, n) = f 2 (|δ|/E a), with n, the electron density, b = 1/zν, a = 1/[(z + 1)ν], and δ = (n − n c)/n c , Kravchenko and colleagues 1 found that ν = 1.5 and z = 0.8. Analogous scaling occurs in GaAs 5 but only in the most disordered samples. This indicates that the underlying transition in the clean system is first order, whereas in the presence of disorder, it becomes second order and critical scaling applies. Three postulates anchor the conventional theory of metals 3 : 1) Fermi liquid theory accurately describes the low-temperature physics of conventional clean metals, 2) the classical and quantum corrections to the conductivity are additive 8 as the system size increases, and 3) the logarithmic derivative (β) of the dimensionless conductance with respect to the system size is a continuous mono-tonic single-valued function as the strength of the disorder is increased from weak to strong. From (2) and (3) it follows 3,8 that β is always negative in two dimensions. Hence, as the system size increases, the conductance decreases and insulating behavior necessarily obtains in two dimensions. The general applicability of the scaling analysis rests firmly o...

We report a remarkable symmetry between the resistivity and conductivity on opposite sides of the B = 0 metal-insulator transition in a two-dimensional electron gas in high-mobility silicon MOSFET's. This symmetry implies that the transport mechanisms on the two sides are related.Within the scaling theory of localization [1] developed for non-interacting electrons, no metallic phase exists in two dimensions in the absence of a magnetic field and no metal-insulator transition is therefore possible. Contrary to this expectation, several recent experiments [2,3,4] have given clear indication of a metal-insulator transition in zero magnetic field in a two-dimensional electron gas in high-mobility silicon metal-oxide-semiconductor fieldeffect transistors (MOSFET's). Measurements in samples equipped both with aluminum [2,4] and polysilicon [3] gates have demonstrated that the 2D gas of electrons exhibits behavior that is characteristic of a true phase transition: the resistivity scales with temperature [2,3] and electric field [4] with a single parameter that approaches zero at a critical electron density n c . The nature of this unexpected transition and the physical mechanism that drives it are not understood.In GaAs/AlGaAs heterostructures, Shahar et al.[5] have recently found a direct and simple relation between the longitudinal resistivity in the magnetic fieldinduced insulating phase and the neighboring quantum Hall liquid (QHL) phase: ρ xx (∆ν) = 1/ρ xx (−∆ν). Here ∆ν = ν − ν c , and ν c is the critical filling factor for the ν = 1 QHL-insulator transition; the relation also holds for the fractional ν = 1/3 QHL-insulator transition when mapped [6] onto the ν = 1 QHL-insulator transition of composite Fermions. Shahar et al.[5] point out that this remarkable symmetry indicates a close relation between the conduction mechanisms in the two phases.In this paper, we report a similar symmetry near the critical electron density for the B = 0 metal-insulator transition in the 2D electron gas in high mobility silicon MOSFET's. Over a range of temperature 0.3 K < T <

The response to a parallel magnetic field of the very dilute insulating two-dimensional system of electrons in silicon metal-oxide-semiconductor field-effect transistors is dramatic and similar to that found on the conducting side of the metal-insulator transition: there is a large initial increase in resistivity with increasing field, followed by saturation to a value that is approximately constant above a characteristic magnetic field of about 1 T. This is unexpected behavior in an insulator that exhibits Efros-Shklovskii variable-range hopping in zero field, and appears to be a general feature of very dilute electron systems. ͓S0163-1829͑99͒50932-6͔Until quite recently, it was believed that all twodimensional systems of electrons ͑or holes͒ are necessarily localized in the absence of a magnetic field in the limit of zero temperature. This conclusion was based on the scaling theory for noninteracting electrons of Abrahams et al., 1 was further confirmed theoretically for weakly interacting electrons, 2,3 and received experimental confirmation in a number of materials, including thin films 4 and ͑high-density͒ silicon metal-oxide-semiconductor field-effect transistors ͑MOSFET's͒. 5,6 In the last several years, however, measurements in very dilute two-dimensional systems have provided evidence of a transition from insulating to conducting behavior with increasing electron ͑hole͒ density above some low critical value on the order of 10 9 -10 11 cm Ϫ2 . 7-13 At these very low densities the energy of electron-electron interactions exceeds the Fermi energy by an order of magnitude or more, and correlations thus provide the dominant energy in the problem. Dilute, strongly interacting two-dimensional systems are currently the focus of intense theoretical interest, and have elicited a spate of theoretical attempts to account for the presence and nature of the unexpected conducting phase.One of the most interesting characteristics of the conducting phase is its dramatic response to a magnetic field applied parallel to the plane of the two-dimensional system. For example, the resistivity of very high-mobility silicon MOS-FET's increases by almost three orders of magnitude with increasing field, saturating to a new value in fields above ϳ2 -3 T. 14,15 A similar effect was observed in p-GaAs/Al x Ga 1Ϫx As heterostructures 11 confirming that this giant positive magnetoresistance is a general property of dilute conducting two-dimensional ͑2D͒ systems. 16 In Ref. 17, it was reported that the metal-insulator transition in Si MOSFET's shifts toward higher electron densities in a parallel magnetic field of the order of a few T, while at higher magnetic fields, the effect saturates. We note that a parallel magnetic field couples only to the spins of the electrons and not to their orbital motion. Spins are thus known to play a crucial role, and it has been suggested that full alignment of the electrons results in the complete suppression of the anomalous conducting phase.In this paper we report that the response of the very dilut...

The suppression by a magnetic field of the anomalous H = 0 conducting phase in high-mobility silicon MOSFETs is independent of the angle between the field and the plane of the 2D electron system. In the presence of a parallel field large enough to fully quench the anomalous conducting phase, the behavior is similar to that of disordered GaAs/AlGaAs heterostructures: the system is insulating in zero (perpendicular) field and exhibits reentrant insulator-quantum Hall effect-insulator transitions as a function of perpendicular field. The results demonstrate that the suppression of the low-T phase is related only to the electrons' spin.PACS numbers: 71.30.+h, 73.40.Qv, 73.40.Hm According to the one-parameter scaling theory of localization for non-interacting electrons [1], a twodimensional electron system (2DES) is always insulating at sufficiently large length scales (i.e., in the limit of zero temperature) in the absence of a magnetic field. In high-mobility silicon metal-oxide-semiconductor field-effect transistors (MOSFETs), however, a metalinsulator transition has been observed at a critical electron density, n c ∼ 10 11 cm −2 , and a H = 0 conducting phase has been shown to exist below 1 K [2]. Similar critical behavior has been reported in a p-type SiGe quantum well [3] and in the hole gas in GaAs/AlGaAs heterostructures [4,5]. At low carrier densities, the interaction energy in these systems is more than an order of magnitude larger than the Fermi energy, so that one does not expect the non-interacting theory of localization [1] to be applicable in its simplest form.In a disordered 2DES, Khmel'nitskii [6] predicted that the extended states that exist at the centers of each Landau level in large perpendicular magnetic fields should "float" up in energy as H ⊥ → 0, leading to an insulating phase at H = 0. Consistent with this expectation, insulating behavior has been observed in low-density, strongly disordered 2DES in GaAs/AlGaAs heterostructures [7,8]. In contrast, the low-density 2DES in highmobility Si MOSFETs exhibits quite different behavior. As H ⊥ → 0, the extended states shift upward from the centers of the Landau levels [9], as expected. However, instead of "floating" up indefinitely with decreasing magnetic field, the states apparently combine at the Fermi level [9,10], giving rise to anomalous field dependence of ρ xx in small magnetic fields first reported in Ref. [11] and shown in the inset to Fig. 1. This behavior is a puzzle, and its physical origin has remained unclear.We have recently shown that the anomalous lowdensity/low-temperature conducting phase in silicon MOSFETs is suppressed by a magnetic field applied parallel to the 2D plane of the electrons [12,13]: as shown in Fig. 2 in Ref. [12], the resistivity increases by several orders of magnitude as the parallel magnetic field is increased to H || ∼ 20 kOe, above which it saturates to a value that is approximately independent of magnetic field. This prompted us to suggest that the enigmatic behavior in small perpendicular fields is ass...