Effect of NdB6 addition on densification and properties of ZrB2

This paper reports on the effect of NdB₆ addition on densification and properties of ZrB₂. NdB₆ powder (2.5,5 and 10wt.%) was added to ZrB₂ powder and consolidated by hot pressing. It was found that NdB₆ addition assisted in densification of ZrB₂ at lower hot pressing temperature of 1750°C. Formation of solid solution was observed at the interface of ZrB₂ and NdB₆ phases. Hardness was found to be slightly increased by 2.5wt.% NdB₆ addition but decreased by 5 and 10% NdB₆ addition. Fracture toughness of composite is found to be higher than the monolithic ceramic. It was found that composite samples have excellent oxidation resistance at 900°C in air

Masses of composite fermions carrying two and four flux quanta: Differences and similarities

This study provides a theoretical rationalization for the intriguing experimental observation regarding the equality of the normalized masses of composite fermions carrying two and four flux quanta, and also demonstrates that the mass of the latter type of composite fermion has a substantial filling factor dependence in the filling factor range $4/17 > \nu > 1/5$, in agreement with experiment, originating from the relatively strong inter-composite fermion interactions here.Comment: 5 pages, 2 figure

Nonresonant inelastic light scattering in the Hubbard model

Inelastic light scattering from electrons is a symmetry-selective probe of the charge dynamics within correlated materials. Many measurements have been made on correlated insulators, and recent exact solutions in large dimensions explain a number of anomalous features found in experiments. Here we focus on the correlated metal, as described by the Hubbard model away from half filling. We can determine the B1g Raman response and the inelastic X-ray scattering along the Brillouin zone diagonal exactly in the large dimensional limit. We find a number of interesting features in the light scattering response which should be able to be seen in correlated metals such as the heavy fermions.Comment: 9 pages, 7 figures, typeset with ReVTe

Hamiltonian Theory of the FQHE: Conserving Approximation for Incompressible Fractions

A microscopic Hamiltonian theory of the FQHE developed by Shankar and the present author based on the fermionic Chern-Simons approach has recently been quite successful in calculating gaps and finite tempertature properties in Fractional Quantum Hall states. Initially proposed as a small-$q$ theory, it was subsequently extended by Shankar to form an algebraically consistent theory for all $q$ in the lowest Landau level. Such a theory is amenable to a conserving approximation in which the constraints have vanishing correlators and decouple from physical response functions. Properties of the incompressible fractions are explored in this conserving approximation, including the magnetoexciton dispersions and the evolution of the small-$q$ structure factor as \nu\to\half. Finally, a formalism capable of dealing with a nonuniform ground state charge density is developed and used to show how the correct fractional value of the quasiparticle charge emerges from the theory.Comment: 15 pages, 2 eps figure

Edge reconstructions in fractional quantum Hall systems

Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations are present. We present a {\it microscopic} calculation of the edge states in the fractional quantum Hall systems at various filling factors using the extended Hamiltonian theory of the fractional quantum Hall effect. We find that at $\nu=1/3$ the quantum Hall edge undergoes a reconstruction as the background potential softens, whereas quantum Hall edges at higher filling factors, such as $\nu=2/5, 3/7$, are robust against reconstruction. We present the results for the dependence of the edge states on various system parameters such as temperature, functional form and range of electron-electron interactions, and the confining potential. Our results have implications for the tunneling experiments into the edge of a fractional quantum Hall system.Comment: 11 pages, 9 figures; minor typos corrected; added 2 reference

Hamiltonian Theory of the Composite Fermion Wigner Crystal

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $\nu=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table

Hamiltonian theory of gaps, masses and polarization in quantum Hall states: full disclosure

I furnish details of the hamiltonian theory of the FQHE developed with Murthy for the infrared, which I subsequently extended to all distances and apply it to Jain fractions \nu = p/(2ps + 1). The explicit operator description in terms of the CF allows one to answer quantitative and qualitative issues, some of which cannot even be posed otherwise. I compute activation gaps for several potentials, exhibit their particle hole symmetry, the profiles of charge density in states with a quasiparticles or hole, (all in closed form) and compare to results from trial wavefunctions and exact diagonalization. The Hartree-Fock approximation is used since much of the nonperturbative physics is built in at tree level. I compare the gaps to experiment and comment on the rough equality of normalized masses near half and quarter filling. I compute the critical fields at which the Hall system will jump from one quantized value of polarization to another, and the polarization and relaxation rates for half filling as a function of temperature and propose a Korringa like law. After providing some plausibility arguments, I explore the possibility of describing several magnetic phenomena in dirty systems with an effective potential, by extracting a free parameter describing the potential from one data point and then using it to predict all the others from that sample. This works to the accuracy typical of this theory (10 -20 percent). I explain why the CF behaves like free particle in some magnetic experiments when it is not, what exactly the CF is made of, what one means by its dipole moment, and how the comparison of theory to experiment must be modified to fit the peculiarities of the quantized Hall problem

Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions

A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the $\nu=1/3$, 2/5, and 3/7 gapped fractions, and find approximate agreement with numerical results. I also analyse the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 2/5 and 3/7, and it is shown that the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state, cannot be described as a simple quantum ferromagnet.Comment: 18 pages, 18 encapsulated ps figure

Spin-pairing instabilities at the coincidence of two Landau levels

The effect of interactions near the coincidence of two Landau levels with opposite spins at filling factor 1/2 is investigated. By mapping to Composite Fermions it is shown that the fluctuations of the gauge field induces an effective attractive Fermion interaction. This can lead to a spin-singlet ground state that is separated from the excited states by a gap. The magnitude of the gap is evaluated. The results are consistent with the recently observed half-polarized states in the FQHE at a fixed filling factor. It is suggested that similar anomalies exist for other spin configurations in degenerate spin-up and spin-down Landau levels. An experiment for testing the spin-singlet state is proposed.Comment: to be published in Physical Review