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Physical review. B, Condensed matter

Conduction in correlated one-dimensional electronic systems

Shubha Tewari

Published Sep 15, 1992• 11 citations
Publisher

Abstract

Motivated by the observation of periodic conductance oscillations in narrow channels, we study finite one-dimensional electronic systems with the following interactions: (i) an exactly solvable 1/${\mathit{x}}^{2}$ potential and (ii) the Coulomb potential with a cutoff, 1/ \ensuremath{\surd}${\mathit{x}}^{2}$+${\mathrm{\ensuremath{\delta}}}^{2}$ . The study of the 1/${\mathit{x}}^{2}$ model shows that at T=0, d〈N〉/d\ensuremath{\mu} exhibits sharp peaks as a function of chemical potential \ensuremath{\mu}, where 〈N〉 is the average number of particles in the channel. At finite temperatures, the peaks are broadened, but their spacings remain unchanged. We establish that the peaks are equally spaced for a model whose many-particle ground-state energy is quadratic in N, the particle number. We discuss our results for the ground-state energy of the Coulomb potential obtained from a Monte Carlo simulation at T=0 in this context.

DOI
10.1103/physrevb.46.7782

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Motivated by the observation of periodic conductance oscillations in narrow channels, we study finite one-dimensional electronic systems with the following interactions: (i) an exactly solvable 1/x2{\mathit{x}}^{2}x2 potential and (ii) the Coulomb potential with a cutoff, 1/ \ensuremath{\surd}x2{\mathit{x}}^{2}x2+\ensuremathδ2{\mathrm{\ensuremath{\delta}}}^{2}\ensuremathδ2 . The study of the 1/x2{\mathit{x}}^{2}x2 model shows that at T=0, d〈N〉/d\ensuremath{\mu} exhibits sharp peaks as a function of chemical potential \ensuremath{\mu}, where 〈N〉 is the average number of particles in the channel. At finite temperatures, the peaks are broadened, but their spacings remain unchanged. We establish that the peaks are equally spaced for a model whose many-particle ground-state energy is quadratic in N, the particle number. We discuss our results for the ground-state energy of the Coulomb potential obtained from a Monte Carlo simulation at T=0 in this context.
We study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter bbb $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.
We present a two band fermion model consisting of a subband of conduction electrons and a subband of local electron pairs interacting via interband interactions. The model is solved in one dimension by means of the Bethe ansatz for an empty subband of local electron pairs. The ground state energy, the chemical potential, the critical exponents, describing the asymptotic behavior of correlation functions at long distances, the effective electron transport mass have been calculated numerically for an arbitrary density of conduction electrons.
Several recent results concerning frequency dependent and nonlinear transport of one-dimensional correlated electrons are reviewed. The frequency dependent conductance of a Luttinger liquid is discussed. For zero-range interaction the conductance is similar to that of a non-interacting ideal quantum wire, with a renormalized zero-frequency limit. For a screened Coulomb potential, the conductance as a function of the frequency shows features of the elementary excitations. They can be simulated in terms of a capacitance, an inductance and a resistance. The non-linear DC-conductance of the Luttinger liquid in presence of a tunnel barrier shows Coulomb blockade if the interaction is of finite range. The capacitance scales in the same way as for the system without the tunnel barrier. The linear DC-response of a tunnel barrier as a function of the frequency and the voltage of a monochromatic driving field shows oscillations which can be interpreted as signature of a frequency-induced depinning of a charge density wave.
Using a few electrons interacting via a U/r Coulomb repulsion on two dimensional L ×L square lattices with periodic boundary conditions and nearest neighbor hopping t, I review on results of systematic exact finite size numerical studies of the ground state as a function of the Coulomb energy to kinetic energy ratio rs=UL/(2t√πN). Studies of the persistent currents, of the magnetization, of the inter-particle spacing distributions, of a simple analytical ansatz converge towards the same conclusion: there is a new regime for intermediate values rs, where delocalized electrons co-exist with a solid Wigner molecule. The study of this new regime, first done in the presence of random potentials, is extended to the clean lattice limit. The results are consistent, for a finite size lattice, with a possibility proposed by Andreev and Lifshitz for the continuous thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles.
We investigate the effect of electron-electron interactions on the conductance of quasi one-dimensional systems without potential scattering. For a finite temperature or system length, the short-range interaction is not renormalized to 0, and it gives rise to a finite correction to the conductance if we calculate it using Kubo formula. We show that this correction can be absorbed into the renormalization of the chemical potential and that the properly defined conductance to be observed in the experiments is equal to that of non-interacting electrons.