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We derive the dispersion of the elementary excitations in a two-component integer and fractional quantum Hall effect. We consider the fully polarized ground state and show the existence of both a magnetoroton mode and a low-lying Goldstone mode (GM). For the unpolarized ground state we derive the dispersion for both a density-density mode and a spin-wave mode both going to a finite value at small momentum q. We examine the extension of the charge-density-wave (CDW)-like ground state and fluidlike Laughlin state to multicomponents. We show that the latter has the lowest ground-state energy with a polarized ground state at filling factor ..nu.. = 1, (1/3), and (1/5) and unpolarized at ..nu.. = (2/5). Most important, the CDW predicts a polarized ground state at ..nu.. = (2/5) and would, therefore, show dissipation via the GM channel contrary to the Laughlin-like ground states. We have, therefore, a new experimental possibility for selecting the correct ground state from many of the recent interesting suggestions.

Using the recently proposed single-mode magneto-roton ansatz for the dynamic structure factor of a two-dimensional electron gas in a strong magnetic field and a weak-coupling memory-function expression for the conductivity, we calculate the ac and dc conductivity of such systems in the fractionally quantized Hall regime. The results suggest new experimental tests of these ideas.

Explicit trial wave functions are proposed for the ground state at all odd-denominator rational filling factors of the lowest Landau level of a two-dimensional electron gas. An exact sum rule valid for any isotropic state in the lowest Landau level is used to justify an approximation scheme in which the hierarchy of quantum Hall states is associated with a corresponding hierarchy of classical fluids. Results are given for the energy at many rational filling factors and for the pair-correlation function at ν=2 over 7.

We discuss the size dependence of small-system periodic-boundary-condition calculations of ground-state energies and excitation energies for two-dimensional electron systems in a strong magnetic field. The discussion is based on an examination of the Hartree-Fock approximation for a finite-size system. We find that finite-size-system calculations overestimate the magnitude of the ground-state energy and underestimate excitation energies, especially in the case of higher-orbital Landau levels. Numerical estimates of the finite-size corrections are given for 4-, 9-, and 16-electron systems.

We describe a unitary transformation which eliminates terms coupling states with differing numbers of doubly occupied sites from the Hamiltonian of the Hubbard model. The $S$ matrix for the transformation, and the transformed Hamiltonian, ${H}^{\ensuremath{'}}$, are generated by an iterative procedure which results in an expansion in powers of the hopping integral $t$ divided by the on-site energy $U$. For a half-filled band and in the space with no doubly occupied sites, ${H}^{\ensuremath{'}}$ is equivalent to a spin Hamiltonian. We discuss the implications of our results for ${H}^{\ensuremath{'}}$ on theories of high-temperature superconductivity.

Etude du plasma electronique a T=0 dans un champ magnetique intense, dans l'approximation de Hartree-Fock avec traitement exact de l'echange; etablissement du diagramme de phases et mise en evidence d'une serie de transitions de l'etat fondamental qui passe d'un etat d'onde de densite de charge a Q∥H a un etat a densite uniforme, puis a un reseau de Wigner de trous et finalement a un cristal de Wigner electronique

We present a theory for cyclotron resonance of a two-dimensional electron gas in a strong magnetic field, using a generalized single-mode approximation for the magnetoplasmons of the system. The effects of electron-electron interactions and band nonparabolicity are included. The consequences of nonparabolicity are qualitatively altered by electronic correlations. Mode crossings are found to occur for filling factors near 2.5. These crossings may be responsible for some unexplained cyclotron-resonance anomalies observed away from integral filling factors.

The ground-state wave function is investigated at strong magnetic field for a system that consists of two parallel two-dimensional electron systems, which are coupled by the Coulomb interaction. Ground-state wave functions for finite-size systems on a sphere are obtained numerically and compared with Jastrow-type wave functions at Landau-level filling factors \ensuremath{\nu}=1, (1/2, (2/5, and (1/3. It is shown that the layer separations at which Jastrow-type wave functions give a good approximation to the ground state are filling-factor dependent.

We design a bi-anisotropic metamaterial with topologically nontrivial photonic phase analogous to that found in topological insulators. The most intriguing manifestation of this phase is the presence of edge states insensitive to structural imperfections and disorder.

We perform a first principles calculation of the anomalous Hall effect in ferromagnetic bcc Fe. Our theory identifies an intrinsic contribution to the anomalous Hall conductivity and relates it to the k-space Berry phase of occupied Bloch states. The theory is able to account for both dc and magneto-optical Hall conductivities with no adjustable parameters., Comment: 4 pages, 6 figures, author list corrected

We present a theory of the anomalous Hall effect in ferromagnetic (Mn,III)V semiconductors. Our theory relates the anomalous Hall conductance of a homogeneous ferromagnet to the Berry phase acquired by a quasiparticle wavefunction upon traversing closed paths on the spin-split Fermi surface of a ferromagnetic state. It can be applied equally well to any itinerant electron ferromagnet. The quantitative agreement between our theory and experimental data in both (In,Mn)As and (Ga,Mn)As systems suggests that this disorder independent contribution to the anomalous Hall conductivity dominates in diluted magnetic semiconductors., Comment: 4 pages, 2 figures

The formula for the quantized Hall conductance in a two-dimensional electron gas is often derived by solving the Schr\"odinger equation for an electron in crossed electric and magnetic fields, and taking the expectation value of the current operator in its eigenstates. In this report we demonstrate explicitly, by using the Dirac equation, that there are no relativistic corrections to this expression, at least in the ideal case. This is true even if the drift velocity of the electrons approaches the speed of light or the Landau level splitting approaches the electron rest-mass energy and holds despite the appearance of a classical correction to the cyclotron frequency.

The signal in point contact spectroscopy contains information on the absolute strength of the electron-phonon interaction in a metal. In order to determine this strength, however, it is necessary to compare the strength of ohmic and non-ohmic parts of the current and to make some assumption concerning the shape of the contact. In this article we show that the usual assumption of a circular contact would lead to an underestimate of the electron-phonon coupling strength if the actual contact were of more irregular shape. This observation is quantified by explicit calculations for rectangular contacts.