Zero-magnetic-field collective insulator phase in a dilute 2D electron system

Abstract

We report on a collective low temperature metal-insulator transition which develops in a dilute 2D electron system in Si at zero magnetic field, below a critical carrier density ris 10'^ cm-^. In the insulator phase, the dc conduction is thermally activated and exhibits a sharp threshold as a function of electric field. The collective insulator state at zero field shows many of the features attributed to the pinned Wigner solid. We have also observed a trend from a collective to a single-particle insulator state with decreasing electron density and/or increasing disorder. PACS numbers: 73.40.Qv, 71.55.Jv, 71.30.+h In the limit of zero temperature, the dilute twodimensional electron (2DE) system is expected to become an insulator in the presence of disorder [1]. Various theoretical models for this insulating state have been proposed ranging from Anderson's single-particle localization (SPL) [1] to collective phases like the pinned Wigner solid (WS) [2], and the pinned charge density wave (CDW) [3]. Pioneering work [4] on low mobility Si samples revealed features indicative of a collective glassy state in high magnetic fields. The search for an electron ordered state in a quantizing magnetic field has recently led to the experimental observation of metal-insulator (MI) transitions in high mobility samples: GaAs-AlGaAs [5] heterostructures and Si-MOSFET's [6][7][8]. In these samples, reentrant MI transitions in a magnetic field were observed around fractional (mainly 1/5 in GaAs) and integer (1 and 2 in Si) filling factors. However, the realization of the "true" Wigner solid at zero magnetic field in GaAs would require an unrealistically dilute electron system since the critical density for quantum melting at T -0 [9] (also known as "cold melting") is very low, i.e., Ticm ~ 3 X 10^ cm~^. In contrast, the cold melting density in (100) Si should be at least 20 x larger, due to the larger effective mass (m* = 0.197ne) and lower dielectric constant {n = 7.7) which increases the ratio of the electron-electron interaction energy [{nnsY^'^e^/K\ to the kinetic energy {nrish'^/2m*) [8]. Therefore, a zerofield collective electron solid (ES) is more likely to be observed in high mobility Si inversion layers. There has not been, to our knowledge, any observation of the collective ES (and, in particular, the pinned Wigner solid) and its quantum melting at zero magnetic field in 2D. In our earlier work [6,8], there is an indication, however, that the insulating phase does not disappear as iif -> 0 but rather shifts to lower density and has features similar to those of the reentrant MI transitions in a magnetic field.In this Letter, we present experimental evidence for the collective character of the low temperature metalinsulator transition at zero field in Si MOSFET's with weak disorder. The data show a trend from a collective to a single-particle insulator state with decreasing density and/or increasing disorder. We compare our data on nonlinear dc transport, activation energy, and threshold electric field with the available...

Phase diagram of the two-dimensional quantum electron freezing with external impurities

“…1 by stars. The r sc and n i dependence ͑at a fixed dϭ5a B ͒ of the experimental points are in agreement with our calculations, although the range of impurity concentration of the samples of Pudalov et al 2 are rather limited.…”

“…The presence of impurities at a setback distance dϭ5a B (Ӎ100 Å) shifts the solid-liquid transition in a pure system from r sc Ӎ37 to r sc Ӎ8.5, consistent with the recent experiments of Pudalov et al 2 Finally, we present the phase diagram of a 2D electron system with impurities in Fig. 1.…”

“…Impurity distance against the critical density r sc at which the solid-liquid transition occurs is shown for fixed impurity concentration n i . In the experiments of Pudalov et al 2 three samples of differing mobilities ͑impurity concentrations͒ were used. Assuming that the observed peak mobilities are proportional to n i and carrying out an analysis similar to that given by Gold 12 we infer that the samples of Pudalov et al 2 have critical densities n c ϭ8.9ϫ10 10 cm Ϫ2 , 9.7ϫ10 10 cm Ϫ2 , and 10 10 cm Ϫ2 .…”

“…Typically there are dopants located at some distance d ͑setback distance͒ away from the quantum well. To confront experiment with theory, we have performed a quantum Monte Carlo simulation 5 that includes the impurity effects and the Coulomb interaction on the electron solid-fluid transition with parameters appropriate for the Si-MOSFET system investigated by Pudalov et al 2 Good agreement with the experimental results is found. A key element in this calculation is the difference of the electron fluid and solid response to the effect of external impurities.…”

“…Here r s ϭ1/ͱ na B where a B ϭប 2 ⑀/m*e 2 is the Bohr radius, n is the density, m* ͑0.2 m e for Si-MOSFET's͒ is the effective mass, and ⑀ ͑7.7 for Si-MOSFET's͒ is the dielectric constant. Pudalov et al 2 reported observation of a solid-fluid transition in Si-MOSFET's near r s ϭ10. The experimental systems are not perfect.…”