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arXiv:0810.5624 · Journal of Physics Condensed Matter

Effect of external electric field on the charge density waves in one-dimensional Hubbard superlattices

Jayeeta Chowdhury, S N Karmakar, Bibhas Bhattacharyya

Published Dec 1, 2008• 3 citations
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Abstract

We have studied the ground state of one-dimensional Hubbard superlattice structures with different unit-cell sizes in the presence of an electric field. A self-consistent Hartree-Fock approximation calculation is done in the weak- to intermediate-interaction regime. Studying the charge gap at the Fermi level and the charge density structure factor, we get an idea of how the charge modulation on the superlattice is governed by the competition between the electronic correlation and the external electric field.

DOI
10.1088/0953-8984/21/1/015302

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We have studied the ground state of one-dimensional Hubbard superlattice structures with different unit-cell sizes in the presence of an electric field. A self-consistent Hartree-Fock approximation calculation is done in the weak- to intermediate-interaction regime. Studying the charge gap at the Fermi level and the charge density structure factor, we get an idea of how the charge modulation on the superlattice is governed by the competition between the electronic correlation and the external electric field.
We discuss the interplay between electronic correlations and an underlying superlattice structure in determining the period of charge density waves (CDW's), by considering a one-dimensional Hubbard model with a repeated (nonrandom) pattern of repulsive (U>0)(U>0)(U>0) and free (U=0)(U=0)(U=0) sites. Density matrix renormalization group diagonalization of finite systems (up to 120 sites) is used to calculate the charge-density correlation function and structure factor in the ground state. The modulation period can still be predicted through effective Fermi wave vectors kF∗{k}_{F}^{*}kF∗​ and densities, and we have found that it is much more sensitive to electron (or hole) doping, both because of the narrow range of densities needed to go from q∗=0{q}^{*}=0q∗=0 to $\ensuremath{\pi}$, but also due to sharp $2{k}_{F}^{*}\ensuremath{-}4{k}_{F}^{*}$ transitions; these features render CDW's more versatile for actual applications in heterostructures than in homogeneous systems.
We have studied a one-dimensional Hubbard superlattice with different Coulomb correlations at alternating sites for a half-filled band. Mean field calculations based on the Hartree-Fock approximation together with a real space renormalization group technique were used to study the ground state of the system. The phase diagrams obtained in these approaches agree with each other from the weak to the intermediate coupling regime. The mean field results show very quick convergence with system size. The renormalization group results indicate a spatial modulation of local moments that was identified in some previous work. Also we have studied the magnetoconductance of such superlattices which reveals several interesting points.
The charge structure factor of the half-filled Hubbard superlattices with one on-site repulsive site and [Formula: see text] free sites per unit cell is investigated numerically. The behaviors of charge structure reveal a kind of even–odd [Formula: see text] disparity. For even [Formula: see text], we always observe a commensurate charge density wave (CDW). For odd [Formula: see text], we observe a commensurate–incommensurate CDW transition at a critical on-site repulsion around the particle–hole symmetric point. This transition results from the competition between the local charge correlations with odd distance and even distance.
We study the formation of charge density waves (CDW's) in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive (U>0)(U>0)(U>0) and free (U=0)(U=0)(U=0) sites. By means of Lanczos diagonalizations for the ground state, we calculate the charge structure factor. Our results show that while the superlattice structure affects the modulation of the charge density waves, the periodicity can still be predicted through an effective density. We also show that, for a fixed repulsive layer thickness, the periodicity of the CDW is an oscillatory function of the free layer thickness.
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In this thesis we focus on a systematic study of the ground state of the one-dimensional one-band Hubbard model in the Hartree-Fock approximation. Phases with non-uniform charge density and states with coexisting phases separated by a domain wall are included in the study. We calculate the full Hartree-Fock phase diagram for uniform and non-uniform phases, and we show that at particular electron densities the uniform phase is unstable to phase separation. Supercell calculations are carried out, and we use the computational minimisation procedure to calculate the Hartree-Fock energies for the self-consistent spin configurations. (author)