Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness

The activation gaps for fractional quantum Hall states at filling fractions $\nu=n/(2n+1)$ are computed for heterojunction, square quantum well, as well as parabolic quantum well geometries, using an interaction potential calculated from a self-consistent electronic structure calculation in the local density approximation. The finite thickness is estimated to make $\sim$30% correction to the gap in the heterojunction geometry for typical parameters, which accounts for roughly half of the discrepancy between the experiment and theoretical gaps computed for a pure two dimensional system. Certain model interactions are also considered. It is found that the activation energies behave qualitatively differently depending on whether the interaction is of longer or shorter range than the Coulomb interaction; there are indications that fractional Hall states close to the Fermi sea are destabilized for the latter.Comment: 32 pages, 13 figure

Number of adaptive steps to a local fitness peak

We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean. If the mean is finite, all the walk length cumulants grow with the sequence length but approach a constant otherwise. Experimental implications of our analytical results are also discussed

Band Structure of the Fractional Quantum Hall Effect

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.Comment: 10 page

Composite-fermionization of bosons in rapidly rotating atomic traps

The non-perturbative effect of interaction can sometimes make interacting bosons behave as though they were free fermions. The system of neutral bosons in a rapidly rotating atomic trap is equivalent to charged bosons coupled to a magnetic field, which has opened up the possibility of fractional quantum Hall effect for bosons interacting with a short range interaction. Motivated by the composite fermion theory of the fractional Hall effect of electrons, we test the idea that the interacting bosons map into non-interacting spinless fermions carrying one vortex each, by comparing wave functions incorporating this physics with exact wave functions available for systems containing up to 12 bosons. We study here the analogy between interacting bosons at filling factors $\nu=n/(n+1)$ with non-interacting fermions at $\nu^*=n$ for the ground state as well as the low-energy excited states and find that it provides a good account of the behavior for small $n$, but interactions between fermions become increasingly important with $n$. At $\nu=1$, which is obtained in the limit $n\rightarrow \infty$, the fermionization appears to overcompensate for the repulsive interaction between bosons, producing an {\em attractive} interactions between fermions, as evidenced by a pairing of fermions here.Comment: 8 pages, 3 figures. Submitted to Phys. Rev.

Estimation of minority carrier diffusion lengths in InP/GaAs solar cells

Minority carrier diffusion length is one of the most important parameters affecting the solar cell performance. An attempt is made to estimate the minority carrier diffusion lengths is the emitter and base of InP/GaAs heteroepitaxial solar cells. The PC-1D computer model was used to simulate the experimental cell results measured at NASA Lewis under AMO (air mass zero) spectrum at 25 C. A 16 nm hole diffusion length in the emitter and a 0.42 micron electron diffusion length in the base gave very good agreement with the I-V curve. The effect of varying minority carrier diffusion lengths on cell short current, open circuit voltage, and efficiency was studied. It is also observed that the front surface recombination velocity has very little influence on the cell performance. The poor output of heteroepitaxial cells is caused primarily by the large number of dislocations generated at the interfaces that propagate through the bulk indium phosphide layers. Cell efficiency as a function of dislocation density was calculated and the effect of improved emitter bulk properties on cell efficiency is presented. It is found that cells with over 16 percent efficiencies should be possible, provided the dislocation density is below 10(exp 6)/sq cm

Leveling transparency via situated intermediary learning objectives (SILOs)

When designers set out to create a mathematics learning activity, they have a fair sense of its objectives: students will understand a concept and master relevant procedural skills. In reform-oriented activities, students first engage in concrete situations, wherein they achieve situated, intermediary learning objectives (SILOs), and only then they rearticulate their solutions formally. We define SILOs as heuristics learners devise to accommodate contingencies in an evolving problem space, e.g., monitoring and repairing manipulable structures so that they model with fidelity a source situation. Students achieve SILOs through problem-solving with media, instructors orient toward SILOs via discursive solicitation, and designers articulate SILOs via analyzing implementation data. We describe the emergence of three SILOs in developing the activity Giant Steps for Algebra. Whereas the notion of SILOs emerged spontaneously as a framework to organize a system of practice, i.e. our collaborative design, it aligns with phenomenological theory of knowledge as instrumented action

Reconstructing the electron in a fractionalized quantum fluid

The low energy physics of the fractional Hall liquid is described in terms quasiparticles that are qualitatively distinct from electrons. We show, however, that a long-lived electron-like quasiparticle also exists in the excitation spectrum: the state obtained by the application of an electron creation operator to a fractional quantum Hall ground state has a non-zero overlap with a complex, high energy bound state containing an odd number of composite-fermion quasiparticles. The electron annihilation operator similarly couples to a bound complex of composite-fermion holes. We predict that these bound states can be observed through a conductance resonance in experiments involving a tunneling of an external electron into the fractional quantum Hall liquid. A comment is made on the origin of the breakdown of the Fermi liquid paradigm in the fractional hall liquid.Comment: 5 pages, 2 figure

Comparative modeling of InP solar cell structures

The comparative modeling of p(+)n and n(+)p indium phosphide solar cell structures is studied using a numerical program PC-1D. The optimal design study has predicted that the p(+)n structure offers improved cell efficiencies as compared to n(+)p structure, due to higher open-circuit voltage. The various cell material and process parameters to achieve the maximum cell efficiencies are reported. The effect of some of the cell parameters on InP cell I-V characteristics was studied. The available radiation resistance data on n(+)p and p(+)p InP solar cells are also critically discussed

Tunable Electron Interactions and Fractional Quantum Hall States in Graphene

The recent discovery of fractional quantum Hall states in graphene raises the question of whether the physics of graphene and its bilayer offers any advantages over GaAs-based materials in exploring strongly-correlated states of two-dimensional electrons. Here we propose a method to continuously tune the effective electron interactions in graphene and its bilayer by the dielectric environment of the sample. Using this method, the charge gaps of prominent FQH states, including \nu=1/3 or \nu=5/2 states, can be increased several times, or reduced all the way to zero. The tunability of the interactions can be used to realize and stabilize various strongly correlated phases in the FQH regime, and to explore the transitions between them.Comment: 4.2 pages, 5 figure