We report low temperature magnetotransport measurements on a high mobility (µ = 325 000 cm 2 /V sec) 2D electron system on a H-terminated Si(111) surface. We observe the integral quantum Hall effect at all filling factors ν ≤ 6 and find that ν = 2 develops in an unusually narrow temperature range. An extended, exclusively even numerator, fractional quantum Hall hierarchy occurs surrounding ν = 3/2, consistent with two-fold valley-degenerate composite fermions (CFs). We determine activation energies and estimate the CF mass.

Using the discrete ±J bond distribution for the Sherrington-Kirkpatrick spin glass, all ground states for the entire ensemble of the bond disorder are enumerated. Although the combinatorial complexity of the enumeration severely restricts attainable system sizes, here N ≤ 9, some remarkably intricate patterns found in previous studies already emerge. The analysis of the exact ground state frequencies suggests a direct construction of their probability density function. Against expectations, the result suggests that its highly skewed appearance for finite N evolves logarithmically slow towards a Gaussian distribution. The Sherrington-Kirkpatrick (SK) model [1] of glassy behavior in magnetic materials has provided a conceptual framework for the effect of disorder and frustration that are observed in systems ranging from materials [2] to combinatorial optimization and learning [3]. It's conceptual simplicity is expressed through the Hamiltonianin which all pairs of binary Ising spin-variables σ i = ±1 are mutually connected through a bond matrix J i,j , which is symmetric and whose entries are random variables drawn from a distribution P (J) of zero mean and unit variance. We note that this Hamiltonian possesses a local "gauge"-invariance under the transformation ofat any site i and the bonds to all its adjacent sites j [4]. The SK model has reached significant prominence because, despite of its apparent simplicity, its solution proved surprisingly difficult, revealing an amazing degree of complexity in its structure [3]. While it is solvable in principle, many of its features have not been derived yet. One such feature concerns the probability density function (PDF) of its ground state energies. Being an extreme element of the energy spectrum, the distribution of e 0 is not necessarily normal but instead may follow a highly skewed "extreme-value statistics" as can be derived for the Random Energy Model [5]. If the energies within that spectrum are uncorrelated, it can be shown that the PDF for e 0 is among one of only a few universal functions. This extreme-value statistics of the ground states has been pointed out in Ref.[5] and has received considerable attention recently [6,7,8,9]. For instance, if the sum for H in Eq. (1) were over a large number of * Electronic address: sboettc@emory.edu † Electronic address: tkott@bucknell.edu independent terms, H would be Gaussian distributed. In such a spectrum, the probability of finding H → −∞ decays faster than any power, and ground states e 0 should be distributed according to a Gumbel PDF, [5]with m = 1, here generalized to the case where m refers to the m-th lowest extreme value [7]. In a spin glass the individual terms in Eq. (1) are not independent variables and deviations from any universal behavior may be expected. In particular, these deviations should become strongest when all spin variables are mutually interconnected such as here in the SK model, but may be less so for sparse graphs, such as low-dimensional lattices. (Although it should be noted that sparsely...

Low-field magnetotransport measurements on a high-mobility ͑ = 110, 000 cm 2 / Vs͒ two-dimensional electron system on a H-terminated Si͑111͒ surface reveal a sixfold valley degeneracy with a valley splitting Յ0.1 K. The zero-field resistivity xx displays strong temperature dependence for 0.07Յ T Յ 25 K as predicted for a system with high degeneracy and large mass. We present a method for using the low-field Hall coefficient to probe intervalley momentum transfer ͑valley drag͒. The relaxation rate is consistent with Fermiliquid theory but a small residual drag as T → 0 remains unexplained. Two-dimensional electron systems ͑2DESs͒ with additional discrete degrees of freedom ͑e.g., spin, valleys, subbands, and multiple charge layers͒ have attracted recent interest due to the role of such variables in transport and in the formation of novel ground states in the quantized Hall regime. In particular, systems with conduction-band valley degeneracy display a rich parameter space for observing and controlling 2DES behavior. 1 Among multivalley systems, electrons on the ͑111͒ surface of silicon are especially notable because effective-mass theory predicts the conduction band to be sixfold degenerate, yielding a total degeneracy ͑spinϫ valley͒ of 12 in the absence of a magnetic field ͑B͒. Previous investigations of Si͑111͒ transport using metaloxide-semiconductor field-effect transistor ͑MOSFETs͒ with peak mobilities Ϸ 4000 cm 2 / Vs observed a valley degeneracy g v of 2 or 6, with the reduced degeneracy attributed to oxide-induced surface strain. 2,3Here we report transport data on a hydrogen-terminated Si͑111͒ surface ͑H-Si͑111͒͒ with very high mobility ͑ = 110, 000 cm 2 / Vs at temperature T = 70 mK and carrier density n s = 6.7ϫ 10 11 cm −2 ͒ with clear sixfold valley degeneracy, indicated by the periodicity of Shubnikov-de Haas ͑SdH͒ oscillations, isotropic low-B transport, and strong T dependence of the longitudinal resistivity xx , consistent with a large g v . 4 In addition, we present a method for using the reduced Hall coefficient r H ϵ xy / ͑B / en s ͒ in the B → 0 limit as a probe of valley-valley interactions, using a drag model of intervalley momentum transfer in multivalley 2DESs. We find that the Hall coefficient ͑and thus, by our model, the intervalley drag͒ becomes strongly suppressed at low temperatures ͑T Շ 5 K͒; furthermore, although the T dependence of the drag is roughly quadratic as expected from Fermi-liquid theory, a small residual drag in the T → 0 limit remains unexplained.To create and probe a high-mobility electron system on a bare surface, we fabricate a device similar to a four wire MOSFET, with the critical difference that we replace the Si-SiO 2 interface with a H-Si͑111͒ surface adjacent to a vacuum cavity. 5 The main processing enhancements in the device discussed here relative to our prior samples are a higher resistivity Si͑111͒ substrate ͑ ϳ 10 k⍀-cm͒ and final H-termination and bonding performed in an oxygen-free ͑Ͻ1 ppm͒ environment. 6 The resulting device has a very high mobility wh...