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Physical review. B./Physical review. B

Thermal effects on the Wigner localization and Friedel oscillations in many-electron nanowires

Ilkka Kylänpää, Fabio Cavaliere, Niccolò Traverso Ziani, Maura Sassetti, E. Räsänen

Published Sep 13, 2016• 29 citations
Publisher

Abstract

Thermal effects on the total charge density are studied for a one-dimensional correlated quantum dot by means of the path integral Monte Carlo method. The competition between Friedel and Wigner oscillations at zero temperature is driven by the ratio between the interaction of electronic strength and the kinetic energy of electrons. At the onset of the formation of a Wigner molecule, we show that thermal enhancement of Wigner oscillations occurs in a range of temperatures, which can be observed in the electron density. We further show that low-temperature Friedel oscillations may change to Wigner oscillations upon an increase in the temperature.

DOI
10.1103/physrevb.94.115417

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Thermal effects on the total charge density are studied for a one-dimensional correlated quantum dot by means of the path integral Monte Carlo method. The competition between Friedel and Wigner oscillations at zero temperature is driven by the ratio between the interaction of electronic strength and the kinetic energy of electrons. At the onset of the formation of a Wigner molecule, we show that thermal enhancement of Wigner oscillations occurs in a range of temperatures, which can be observed in the electron density. We further show that low-temperature Friedel oscillations may change to Wigner oscillations upon an increase in the temperature.
Motivated by a recent experiment (Pecker et al 2013 Nat. Phys. 9 576), we study the stability, with respect to thermal effects, of Friedel and Wigner density fluctuations for two electrons trapped in a one-dimensional quantum dot. Diagonalizing the system exactly, the finite-temperature average electron density is computed. While the weak and strong interaction regimes display a Friedel oscillation or a Wigner molecule state at zero temperature, which as expected smear and melt as the temperature increases, a peculiar thermal enhancement of Wigner correlations in the intermediate interaction regime is found. We demonstrate that this effect is due to the presence of two different characteristic temperature scales: T(F), dictating the smearing of Friedel oscillations, and T(W), smoothing Wigner oscillations. In the early Wigner molecule regime, for intermediate interactions, T(F) < T(W) leading to the enhancement of the visibility of Wigner oscillations. These results complement those obtained within the Luttinger liquid picture, valid for larger numbers of particles.
The temperature-induced emergence of Wigner correlations over finite-size effects in a strongly interacting one-dimensional quantum dot is studied in the framework of the spin coherent Luttinger liquid. We demonstrate that, for temperatures comparable with the zero mode spin excitations, Friedel oscillations are suppressed by the thermal fluctuations of higher spin modes. On the other hand, the Wigner oscillations, sensitive to the charge mode only, are stable and become more visible. This behavior has been proved to be robust both in the thermal electron density and in the linear conductance in the presence of a scanning tunnel microscope tip. The latter probe is not directly proportional to the electron density and may confirm the above phenomena with complementary and additional information.
We explore the role of electron correlation in quasi-one-dimensional quantum wires as the range of the interaction potential is changed and their thickness is varied by performing exact quantum Monte Carlo simulations at various electronic densities. In the case of unscreened interactions with a long-range 1/x1/x1/x tail there is a crossover from a liquid to a quasi-Wigner crystal state as the density decreases. When this interaction is screened, quasi-long-range order is prevented from forming, although a significant correlation with 4kF4{k}_{F}4kF​ periodicity is still present at low densities. At even lower electron concentration, exchange is suppressed and the electrons behave like spinless fermions. Finally, we study the effect of electron correlations in the double quantum wire experiment [Steinberg et al., Phys. Rev. B 73, 113307 (2006)] by introducing an accurate model for the screening in the experiment and explicitly including the finite length of the system in our simulations. We find that decreasing the electron density continuously drives the system from a liquid to a state with quite strong 4kF4{k}_{F}4kF​ correlations. This crossover takes place around $22\text{ }\ensuremath{\mu}{\text{m}}^{\ensuremath{-}1}$, near the density where the electron localization occurs in the experiment. The charge and spin velocities are also in good agreement with the experimental findings in the proximity of the crossover. We argue that correlation effects play an important role at the onset of the localization transition.
We study Friedel oscillations and screening effects of the impurity potential in the Hubbard model. Electronic correlations are accounted for by solving the real-space dynamical mean-field theory equations using the continuous-time quantum Monte Carlo simulations at finite temperatures and using a homogeneous self-energy approximation with the numerical renormalization group at zero temperature. We find that in the Fermi-liquid phase both the amplitudes of Friedel oscillations and the screening charge decrease with increasing the interaction and follow the behavior of the Fermi-liquid renormalization factor. Inside the Mott insulator regime, the Friedel oscillations are absent but the residual screening charge remains finite.
Abstract Friedel and Wigner oscillations are well known phenomena occurring in quantum systems. Specifically, in a system composed by N confined fermions, the former are characterized by the presence of N / 2 peaks in the density distributions, whereas the last by N peaks. Here, we consider N = 2 fermions harmonically confined in one-dimensional quantum dots. It is known that the transition from the Friedel to the Wigner oscillations is induced by the increment of interaction between the fermions. The increment of temperature, on the other hand, acts on eliminating the oscillations. In this context, by employing a time-dependent density-functional theory formalism, we here obtain the emergence of Wigner oscillations in a model which simulates a real time cooling process.
The effects of a long range electronic potential on a one dimensional chain of spinless fermions are investigated by numerical techniques and analytic calculations. Due to a competition between the 2kF oscillations in the density and the log divergence of the long wavelength part of the Coulomb potential, the metallic character of the system is enhanced at intermediate (and up to quite large) lengthscales. We found that this quasi-metallic regime is not of the Luttinger Liquid type, as evidenced by strong deviations from predictions of conformal field theory and in agreement with the picture of a (very weakly pinned) Wigner crystal. When the strength of the Coulomb interaction is substantially increased, we observe a smooth cross-over to a strongly localized charge density wave.