Particles with electric charge q ≤ 10−3 e and masses in the range 1-100 MeV/c 2 are not excluded by present experiments. An experiment uniquely suited to the production and detection of such "millicharged" particles has been carried out at SLAC. This experiment is sensitive to the infrequent excitation and ionization of matter expected from the passage of such a particle. Analysis of the data rules out a region of mass and charge, establishing, for example, a 95%-confidence upper limit on electric charge of 4.1×10−5 e for millicharged particles of mass 1 MeV/c 2 and 5.8×10 −4 e for mass 100 MeV/c 2 .PACS numbers: 14.80.-j, 95.35.+dThe quantization of electric charge is an empirically well-supported idea. Of the numerous searches for fractional charge carried out thus far, none has provided conclusive evidence for charge non-quantization. The current bounds on the proton-electron charge difference [1] and the neutron charge [2], of order 10−21 e, lend strong support to the notion that charge quantization is a fundamental principle. However, the Standard Model with three generations of quarks and leptons does not impose charge quantization. In order to enforce quantization of charge, physics beyond the Standard Model is necessary [3]. This observation has stimulated inquiry into mechanisms whereby charge quantization (and perhaps even charge conservation) might be violated [4]. Particles with small fractional charge (q < ∼ 10 −2 e) appear as a natural consequence of many of these mechanisms. There has been interest in the possibility of a small, nonzero electric charge for the neutrino [5], and the possibility that particles with small fractional charge account for a portion of the dark matter in the universe [6]. Additionally, a noteworthy model has been proposed wherein certain particles could exhibit apparent fractional charge without violating charge quantization [7]. Several authors have investigated constraints, imposed by laboratory experiments and by astrophysical and cosmological arguments, on the existence of (free) fractionally charged particles [8]. They point out that there remains a large domain in mass and charge (10

We studied the Shubnikov-de Haas (SdH) oscillations in high-mobility Si-MOS samples over a wide range of carrier densities n ≃ (1 − 50) × 10 11 cm −2 , which includes the vicinity of the apparent metal-insulator transition in two dimensions (2D MIT). Using a novel technique of measuring the SdH oscillations in superimposed and independently controlled parallel and perpendicular magnetic fields, we determined the spin susceptibility χ * , the effective mass m * , and the g * -factor for mobile electrons. These quantities increase gradually with decreasing density; near the 2D MIT, we observed enhancement of χ * by a factor of ∼ 4.7.71. 30.+h, 73.40.Qv, 71.27.+a Many two-dimensional (2D) systems exhibit an apparent metal-insulator transition (MIT) at low temperatures as the electron density n is decreased below a critical density n c (for reviews see, e.g., Refs. [1][2][3]). The phenomena of the MIT and 'metallic' conductivity in 2D attract a great deal of interest, because it addresses a fundamental problem of the ground state of strongly correlated electron systems. The strength of electron-electron interactions is characterized by the ratio r s of the Coulomb interaction energy to the Fermi energy ǫ F . The 2D MIT is observed in Si MOSFETs at n c ∼ 1 × 10 11 cm −2 , which corresponds to r s ∼ 8 (for 2D electrons in (100)-Si, r s = 2.63 10 12 cm −2 /n).In the theory of electron liquid, the electron effective mass m * , the g * -factor, and the spin susceptibility χ * ∝ g * m * are renormalized depending on r s [4]. Though the quantitative theoretical results [5][6][7] vary considerably, all of them suggest enhancement of χ * , m * and g * with r s . Earlier experiments [8][9][10][11] have shown growth of m * and g * m * at relatively small r s values, pointing to a ferromagnetic type of interactions in the explored range 1 < ∼ r s < 6.5. Potentially, strong interactions might drive an electron system towards ferromagnetic instability [4]. Moreover, it has been suggested that the 'metallic' behavior in 2D is accompanied by a tendency to a ferromagnetic instability [12]. Thus, in relation to the still open question of the origin of the 2D MIT, direct measurements of these quantities in the dilute regime near the 2D MIT are crucial.In this Letter, we report the direct measurements of χ * , m * , and hence g * over a wide range of carrier densities (1 ≤ r s ≤ 8.4), which extends for the first time down to and across the 2D MIT. The data were obtained by a novel technique of measuring the interference pattern of Shubnikov-de Haas (SdH) oscillations in crossed magnetic fields. The conventional technique of measuring g * m * in tilted magnetic fields [8,10] is not applicable when the Zeeman energy is greater than the cyclotron energy [13]. The crossed field technique removes this restriction and allows us to extend measurements over the wider range of r s . We find that for small r s , the g * m *values increase slowly in agreement with the earlier data by Fang and Stiles [8] and Okamoto et al. [10]. For larger valu...

Pudalov et al. Reply: In a recent Letter [1] we studied the magnetoresistance (MR) in strong inplane fields for Si-MOSFET samples with different mobilities. We found that the field of the MR saturation B sat is strongly sample dependent, being different by a factor of up to 2 for different samples at a given density of mobile electrons. In subsequent studies [2], a similar observation was reported for a single sample, cooled down at different gate voltage values. Based on these results, we highlighted in Ref.[1] the role of sample-specific localized states (''disorder'') in the strong-field MR, and concluded that the field at which the MR saturates does not reflect spin polarization of mobile carriers solely.In the preceding Comment to our Letter, Dolgopolov and Gold [3] (DG) attempt to explain the experimentally observed sample dependence of the B sat field. For the twodimensional (2D) case, they apply a two-fluid model, which is known for the 3D Anderson-Mott transition, with the aim to calculate a disorder-dependent field of complete spin polarization B c . DG do not calculate the MR, but implicitly identify B c with B sat , thus using the assumption which was questioned in Ref. [1].The density of electrons n, which is plotted on the X axis of Fig. 2 of Ref.[1], is deduced from the period of Shubnikov-de Haas (SdH) oscillations, as stated in our paper. The oscillations in the 2D case have a frequency equal to n SdH =n h where n h is the density of flux quanta, and n SdH is the density of those electrons which participate in cyclotron motion and occupy the Landau levels.In order to explain our observation of the disorderdependent B sat , DG suggest to deduce the density of extended states n ext by subtracting the density of singly occupied localized states n so from the density n n SdH . The relation n ext n SdH ÿ n so were automatically fulfilled if all electrons (localized and extended) would participate in the SdH effect. However, it can be questioned whether this is the case, and the DG model does not answer this question. The ''reduced'' quantity n ext is further used in order to obtain a reduced field B c of the complete spin polarization of extended states. To calculate the reduced B c value, DG take into account a constant density of states F . But in their model, F has to be reduced for lower lying states and the shift in B c might have an opposite sign. Definitely, the behavior of localized states in magnetic field in the Hubbard model with strong onsite interaction requires a more thorough consideration.We note that in order to explain the observed changes in

We report on magnetotransport studies of the unusual two-dimensional metallic phase in high mobility Si-MOS structures. We have observed that the magnetic field applied in the 2D plane suppresses the metallic state, causing the resistivity to increase dramatically by more than 30 times. Over the total existence range of the metallic state, we have found three distinct types of the magnetoresistance, related to the corresponding quantum corrections to the conductivity. Our data suggest that the unusual metallic state is a consequence of both spin-and Coulomb-interaction effects.Typeset using REVT E X 1