Henrique J. P. Freire

Friedel oscillations in one-dimensional metals: From Luttinger's theorem to the Luttinger liquid

Abstract Charge density and magnetization density profiles of one-dimensional metals are investigated by two complementary many-body methods: numerically exact (Lanczos) diagonalization, and the Bethe–Ansatz local-density approximation with and without a simple self-interaction correction. Depending on the magnetization of the system, local approximations reproduce different Fourier components of the exact Friedel oscillations.

Hysteretic resistance spikes in quantum hall ferromagnets without domains.

We use spin-density-functional theory to study recently reported hysteretic magnetoresistance rho(xx) spikes in Mn-based 2D electron gases [Phys. Rev. Lett. 89, 266802 (2002)10.1103/PhysRevLett.89.266802]. We find hysteresis loops in our calculated Landau fan diagrams and total energies signaling quantum Hall ferromagnet phase transitions. Spin-dependent exchange-correlation effects are crucial to stabilize the relevant magnetic phases arising from distinct symmetry-broken excited- and ground-state solutions of the Kohn-Sham equations. Besides hysteretic spikes in rho(xx), we predict hysteretic dips in the Hall resistance rho(xy). Our theory, without domain walls, satisfactorily explains the recent data.

Simple implementation of complex functionals: Scaled self-consistency

We explore and compare three approximate schemes allowing simple implementation of complex density functionals by making use of self-consistent implementation of simpler functionals: (i) post-local-density approximation (LDA) evaluation of complex functionals at the LDA densities (or those of other simple functionals) (ii) application of a global scaling factor to the potential of the simple functional, and (iii) application of a local scaling factor to that potential. Option (i) is a common choice in density-functional calculations. Option (ii) was recently proposed by Cafiero and Gonzalez [Phys. Rev. A 71, 042505 (2005)]. We here put their proposal on a more rigorous basis, by deriving it, and explaining why it works, directly from the theorems of density-functional theory. Option (iii) is proposed here for the first time. We provide detailed comparisons of the three approaches among each other and with fully self-consistent implementations for Hartree, local-density, generalized-gradient, self-interaction corrected, and meta-generalized-gradient approximations, for atoms, ions, quantum wells, and model Hamiltonians. Scaled approaches turn out to be, on average, better than post approaches, and unlike these also provide corrections to eigenvalues and orbitals. Scaled self-consistency thus opens the possibility of efficient and reliable implementation of density functionals of hitherto unprecedented complexity.

Shubnikov-de Haas Oscillations in Digital Magnetic Heterostructures

In this paper we theoretically investigate the magnetic-field and temperature dependence of the Shubnikov-de Haas oscillations in group II-VI modulation-doped Digital Magnetic Heterostructures. We self-consistently solve the effective-mass Schrodinger equation within the Hartree approximation and calculate the electronic structure and the magneto-transport properties. Our results show i) a shift of the Shubnikov-de Haas minima to lower magnetic fields with increasing temperature, and ii) an anomalous oscillation which develops when two opposite Landau levels cross near the Fermi energy. Both of these are consistent with recent magneto-transport measurements in such heterostructures.

Density-Functional Theory in External Electric and Magnetic Fields

Density-functional theory (DFT) is one of the most widely used quantum mechanical approaches for calculating the structure and properties of matter on an atomic scale. It is nowadays routinely applied for calculating physical and chemical properties of molecules that are too large to be treatable by wave-function-based methods. The problem of determining the many-body wave function of a real system rapidly becomes prohibitively complex (1). Methods such as configuration interaction (CI) expansions, coupled cluster (CC) techniques or Moller–Plesset (MP) perturbation theory thus become harder and harder to apply. Computational complexity here is related to questions such as how many atoms there are in the molecule, how many electrons each atom contributes, how many basis functions are required to adequately describe these electrons, how many competing minima there are in the potential-energy surface determining the molecular geometry, and whether any additional external fields are present. The description of the many-body wave function in CI, CC and MP techniques depends sensitively on these questions, and becomes very difficult for systems with more than a few electrons.