Environmental effects on the tensile strength of chemically vapor deposited silicon carbide fibers

The room temperature and elevated temperature tensile strengths of commercially available chemically vapor-deposited (CVD) silicon carbide fibers were measured after 15 min heat treatment to 1600 C in various environments. These environments included oxygen, air, argon and nitrogen at one atmosphere and vacuum at 10/9 atmosphere. Two types of fibers were examined which differed in the SiC content of their carbon-rich coatings. Threshold temperature for fiber strength degradation was observed to be dependent on the as-received fiber-flaw structure, on the environment and on the coating. Fractographic analyses and flexural strength measurements indicate that tensile strength losses were caused by surface degradation. Oxidation of the surface coating is suggested as one possible degradation mechanism. The SiC fibers containing the higher percentage of SiC near the surface of the carbon-rich coating show better strength retention and higher elevated temperature strength

Composite fermions in bands with N-fold rotational symmetry

We study the effect of band anisotropy with discrete rotational symmetry $C_N$ (where $N\ge 2$) in the quantum Hall regime of two-dimensional electron systems. We focus on the composite Fermi liquid (CFL) at half filling of the lowest Landau level. We find that the magnitude of anisotropy transferred to the composite fermions decreases very rapidly with $N$. We demonstrate this by performing density matrix normalization group calculations on the CFL, and comparing the anisotropy of the composite fermion Fermi contour with that of the (non-interacting) electron Fermi contour at zero magnetic field. We also show that the effective interaction between the electrons after projecting into a single Landau level is much less anisotropic than the band, a fact which does not depend on filling and thus has implications for other quantum Hall states as well. Our results confirm experimental observations on anisotropic bands with warped Fermi contours, where the only detectable effect on the composite Fermi contour is an elliptical distortion ($N = 2$).Comment: 6 pages + bibliography, 5 figure

Connection between Fermi contours of zero-field electrons and ν=12\nu=\frac12 composite fermions in two-dimensional systems

We investigate the relation between the Fermi sea (FS) of zero-field carriers in two-dimensional systems and the FS of the corresponding composite fermions which emerge in a high magnetic field at filling $\nu = \frac{1}{2}$, as the kinetic energy dispersion is varied. We study cases both with and without rotational symmetry, and find that there is generally no straightforward relation between the geometric shapes and topologies of the two FSs. In particular, we show analytically that the composite Fermi liquid (CFL) is completely insensitive to a wide range of changes to the zero-field dispersion which preserve rotational symmetry, including ones that break the zero-field FS into multiple disconnected pieces. In the absence of rotational symmetry, we show that the notion of `valley pseudospin' in many-valley systems is generically not transferred to the CFL, in agreement with experimental observations. We also discuss how a rotationally symmetric band structure can induce a reordering of the Landau levels, opening interesting possibilities of observing higher-Landau-level physics in the high-field regime.Comment: 7 pages + references, 7 figures. Added many-body DMRG calculatio

Geometry of flux attachment in anisotropic fractional quantum Hall states

Fractional quantum Hall (FQH) states are known to possess an internal metric degree of freedom that allows them to minimize their energy when contrasting geometries are present in the problem (e.g., electron band mass and dielectric tensor). We investigate the internal metric of several incompressible FQH states by probing its response to band mass anisotropy using infinite DMRG simulations on a cylinder geometry. We test and apply a method to extract the internal metric of a FQH state from its guiding center structure factor. We find that the response to band mass anisotropy is approximately the same for states in the same Jain sequence, but changes substantially between different sequences. We provide a theoretical explanation of the observed behavior of primary states at filling $\nu = 1/m$ in terms of a minimal microscopic model of flux attachment.Comment: 12 pages including references, 14 figure

Effects of large disorder on the Hofstadter butterfly

Motivated by the recent experiments on periodically modulated, two dimensional electron systems placed in large transversal magnetic fields, we investigate the interplay between the effects of disorder and periodic potentials in the integer quantum Hall regime. In particular, we study the case where disorder is larger than the periodic modulation, but both are small enough that Landau level mixing is negligible. In this limit, the self-consistent Born approximation is inadequate. We carry extensive numerical calculations to understand the relevant physics in the lowest Landau level, such as the spectrum and nature (localized or extended) of the wave functions. Based on our results, we propose a qualitative explanation of the new features uncovered recently in transport measurements.Comment: 15 pages, 13 figures, several pictures have been shrunk to comply with the size requirement

Hopping Conduction in Uniaxially Stressed Si:B near the Insulator-Metal Transition

Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal scaling curve. For large values of the argument, the scaling function is well fit by the exponentially activated form associated with variable range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence of the prefactor, corresponding to the T-dependence of the critical curve, has been determined reliably for this system, and is proportional to the square-root of T. We show explicitly that nevlecting the prefactor leads to substantial errors in the determination of the scaling parameters and the critical exponents derived from them. The conductivity is not consistent with Mott variable-range hopping in the critical region nor does it obey this form for any range of the parameters. Instead, for smaller argument of the scaling function, the conductivity of Si:B is well fit by an exponential form with exponent 0.31 related to the critical exponents of the system at the metal- insulator transition.Comment: 13 pages, 6 figure

Search for Ferromagnetism in doped semiconductors in the absence of transition metal ions

In contrast to semiconductors doped with transition metal magnetic elements, which become ferromagnetic at temperatures below ~ 100K, semiconductors doped with non-magnetic ions (e.g. silicon doped with phosphorous) have not shown evidence of ferromagnetism down to millikelvin temperatures. This is despite the fact that for low densities the system is expected to be well modeled by the Hubbard model, which is predicted to have a ferromagnetic ground state at T=0 on 2- or 3-dimensional bipartite lattices in the limit of strong correlation near half-filling. We examine the impurity band formed by hydrogenic centers in semiconductors at low densities, and show that it is described by a generalized Hubbard model which has, in addition to strong electron-electron interaction and disorder, an intrinsic electron-hole asymmetry. With the help of mean field methods as well as exact diagonalization of clusters around half filling, we can establish the existence of a ferromagnetic ground state, at least on the nanoscale, which is more robust than that found in the standard Hubbard model. This ferromagnetism is most clearly seen in a regime inaccessible to bulk systems, but attainable in quantum dots and 2D heterostructures. We present extensive numerical results for small systems that demonstrate the occurrence of high-spin ground states in both periodic and positionally disordered 2D systems. We consider how properties of real doped semiconductors, such as positional disorder and electron-hole asymmetry, affect the ground state spin of small 2D systems. We also discuss the relationship between this work and diluted magnetic semiconductors, such as Ga_(1-x)Mn_(x)As, which though disordered, show ferromagnetism at relatively high temperatures.Comment: 47 page

Long-range order versus random-singlet phases in quantum antiferromagnetic systems with quenched disorder

The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to long-range order that is stable unless either the order parameter or the spatial dimensionality exceeds a critical value. The instability of this fixed point corresponds to the system entering a random-singlet phase. The stabilization of long-range order is due to quantum fluctuations, whose role in determining the phase diagram is discussed.Comment: 5 pp., REVTeX, epsf, 3 eps figs, final version as published, including erratu