[en] A trial wave function Ψ(1, 2,..., N ) of an N electron system can always be written as the product of an antisymmetric Fermion factor F { z_ij } = Π _{i< j}z_ij , and a symmetric correlation factor G { z_ij }. F results from the Pauli principle, and G is caused by Coulomb interactions. One can represent G diagrammatically [1] by distributing N points on the circumference of a circle, and drawing appropriate lines representing correlation factors (cfs) z_ij between pairs. Here, of course, z_ij = z_i – z_j , where z_i is the complex coordinate of the i ^th electron. Laughlin correlations for the ν = 1/3 filled incompressible quantum liquid (IQL) state contain two cfs connecting each pair ( i,j ). For the Moore-Read state of the half-filled excited Landau level (LL), with ν = 2 + 1/2, the even value of N for the half-filled LL is partitioned into two subsets A and B , each containing N /2 electrons [2]. For any one partition ( A,B ), the contribution to G is given by G_AB = Π _{i< j∈A}z_ij ² Π _k<ι∈B z_kι ². The full G is equal to the symmetric sum of contributions G_AB over all possible partitions of N into two subsets of equal size. For Jain states at filling factor ν = p/q < 1/2, the value of the single particle angular momentum ι satisfies the equation 2 ι = ν^-1N - C_ν , with C_ν = q + 1 - p . The values of (2 ι, N ) define the function space of G { z_ij} , which must satisfy a number of conditions. For example, the highest power of any z_i cannot exceed 2 ι + 1 - N . In addition, the value of the total angular momentum L of the lowest correlated state must satisfy the equation L = ( N /2)(2 ι +1 - N ) - K_G , where K_G is the degree of the homogeneous polynomial generated by G . Knowing the values of L for IQL states (and for states containing a few quasielectrons or a few quasiholes) from Jain’s mean field CF picture allows one to determine K_G . The dependence of the pair pseudopotential V(L₂) on pair angular momentum L ₂ suggests a small number of correlation diagrams for a given value of the total angular momentum L . Correlation diagrams and correlation functions for the Jain state at ν = 2/5 and for the Moore-Read states will be presented as examples. The generalizations of the method of selecting G from small to larger systems will be discussed. (paper)

[en] The generalized longitudinal charge-spin susceptibility functions and the collective excitations of spin-polarized quantum structures are investigated within the framework of spin-dependent linear response theory. We evaluate the charge response and the longitudinal spin response to a general external disturbance. Exchange-correlation effects between electrons of spin σ and σ' are included by using spin-polarization dependent generalized local field factors. Both collective charge-density and spin-density excitations are examined. The present results are compared with the case of a spin-unpolarized system. In contrast to the result for an unpolarized system, the mixing of charge and spin responses results in coupled charge-spin excitations in the spin polarized system

[en] The coupling of spin waves with charge- and spin-density waves is shown to be induced by a spin-dependent interaction in a quantum well, which is spin polarized by a dc magnetic field at an angle θ to the symmetry axis. The mixing of the plasmonic and magnonic modes, which occurs for both intra- and intersubband transitions, depends on the coupling constant of the spin-spin interaction, the tilt angle θ, and the initial spin polarization ζ. (c) 1999 The American Physical Society

[en] The electronic properties of spin-symmetry-broken dilute magnetic semiconductor quantum wells are investigated self-consistently at zero temperature. The spin-split subband structure and carrier concentration of modulation-doped quantum wells are examined in the presence of a strong magnetic field. The effects of exchange and correlations of electrons are included in a local-spin-density-functional approximation. We demonstrate that exchange correlation of electrons decreases the spin-split subband energy but enhances the carrier density in a spin-polarized quantum well. We also observe that as the magnetic field increases, the concentration of spin-down (majority) electrons increases but that of spin-up (minority) electrons decreases. The effect of orbital quantization on the in-plane motion of electrons is also examined and shows a sawtoothlike variation in subband electron concentrations as the magnetic-field intensity increases. The latter variation is attributed to the presence of ionized donors acting as the electron reservoir, which is partially responsible for the formation of the integer quantum Hall plateaus. (c) 2000 The American Physical Society

[en] The subband levels of quantum wells grown in a periodic array form minibands whose bandwidth Δ depends on the probability of interlayer tunneling. In the presence of a strong magnetic field, this system of minibands can exhibit various Coulomb-interaction-driven spin polarization instabilities at an integral value of the filling factor ν. We investigate in particular the Hartree-Fock phase diagram in the case in which the n=0 spin-up and n=1 spin-down Landau levels are separated by an energy smaller than Δ. A spin-density-wave ground state is shown to occur at filling factor ν=2. (c) 2000 The American Physical Society