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arXiv:1309.2762 · New Journal of Physics

Temperature-induced emergence of Wigner correlations in a STM-probed one-dimensional quantum dot

Niccolò Traverso Ziani, Fabio Cavaliere, Maura Sassetti

Published Jun 4, 2013• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/15/6/063002

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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.
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.
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.
Explicit predictions for scanning tunneling microscopy (STM) on interacting one-dimensional electron systems are made using the Luttinger liquid formalism. The STM current changes with the distance from an impurity or boundary in a characteristic way, which reveals the spin-charge separation and the interaction strength in the system. The current exhibits Friedel-like oscillations, but also carries additional modulated behavior as a function of voltage and distance, which shows the spin-charge separation in real space. Moreover, very close to the boundary the current is strongly reduced, which is an indication of the interaction strength in the system.
We study the effect of temperature on the ability of a qubit probe to distinguish between different phases in strongly correlated systems. Now to this end, we investigate a spin-1/2 Heisenberg XXZ chain coupled to a qubit probe via a pure dephasing interaction. At zero temperature, as reported previously, the decoherence dynamics exhibit different behavior in the gapped and gapless phases of the chain, with characteristic strong oscillations in the gapped phase and monotonic decay in the gapless phase. These oscillations decay much more slowly than expected with rising temperature in the gapped phase and their remnants are still visible at infinite temperature. In the gapless phase at low temperatures, using Luttinger liquid theory, we predict that the coherence exhibits asymptotic exponential decay in time, with the decay rate sensitive to the sign of the anisotropy parameter. We conclude that probe dynamics continue to carry information about the chain even at finite, reasonably small temperatures, positioning qubit probes as sensitive and robust detectors for quantum phases of correlated spin systems.
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.
Coherent interconnects between gate-defined silicon quantum processing units are essential for scalable quantum computation and long-range entanglement. We argue that one-dimensional electron channels formed in the silicon quantum well of a Si/SiGe heterostructure exhibit strong Coulomb interactions and realize strongly interacting Luttinger liquid physics. At low electron densities, the system enters a Wigner regime characterized by dominant 4kF correlations; increasing the electron density leads to a crossover from the Wigner regime to a Friedel regime with dominant 2kF correlations. We support these results through large-scale density matrix renormalization group (DMRG) simulations of the interacting ground state under both screened and unscreened Coulomb potentials. We propose experimental signatures of the Wigner-Friedel crossover via charge transport and charge sensing in both zero- and high-magnetic field limits. We also analyze the impact of short-range correlated disorder - including random alloy fluctuations and valley splitting variations - and identify that the Wigner-Friedel crossover remains robust until disorder levels of about 400 micro eV. Finally, we show that the Wigner regime enables long-range capacitive coupling between quantum dots across the interconnect, suggesting a route to create long-range entanglement between solid-state qubits. Our results position silicon interconnects as a platform for studying Luttinger liquid physics and for enabling architectures supporting nonlocal quantum error correction and quantum simulation.