One-dimensional Quantum Dot Research Articles

Entanglement Properties of the Two-Electron Quasi-One Dimensional Gaussian Quantum Dot

We analyze the entanglement characteristics of the quasi one-dimensional quantum dot containing two Coulombically interacting electrons in an inverted Gaussian potential. The linear entropy of the lowest energy states is calculated in the whole range of the effective interaction strength g for different parameters of the longitudinal potential and the lateral radius of the quantum dot. We employ the configuration interaction method with complex-coordinate rotation, since the considered states become autoionizing resonances at the interaction strength above the critical value gth. We study the dependence of the linear entropy on the parameters of the quantum dot and discuss how the stability properties of the system are characterized by the entanglement between the electrons.

Two-Electron Resonances in Quasi-One Dimensional Quantum Dots with Gaussian Confinement

We consider a quasi one-dimensional quantum dot composed of two Coulombically interacting electrons confined in a Gaussian trap. Apart from bound states, the system exhibits resonances that are related to the autoionization process. Employing the complex-coordinate rotation method, we determine the resonance widths and energies and discuss their dependence on the longitudinal confinement potential and the lateral radius of the quantum dot. The stability properties of the system are discussed.

Thermally enhanced Wigner oscillations in two-electron 1D quantum dots

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: TF, dictating the smearing of Friedel oscillations, and TW, smoothing Wigner oscillations. In the early Wigner molecule regime, for intermediate interactions, TF < TW 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.

Screening effect on the exciton mediated nonlinear optical susceptibility of semiconductor quantum dots.

We study the exciton contribution to the third-order optical susceptibility of one-dimensional semiconductor quantum dots and show that the screening of the electron-hole interaction has a strong influence on the nonlinear optical properties in the weak confinement regime. Based on a density matrix formulation, we estimate the spectrum of the third-order optical susceptibility and its contribution to the refraction index and absorption coefficient. In particular, we show that the multipeaked spectrum of the nonlinear susceptibility, which results from the hydrogenoid character of the exciton eigenstates for a purely Coulombian electron-hole coupling, is reverted towards a single peaked structure as the interaction becomes strongly screened, thus leading to a substantial enhancement of the nonlinear optical properties of semiconductor quantum dots.

Correlation functions for the detection of Wigner molecules in a one-channel Luttinger liquid quantum dot

In one-channel, finite-size Luttinger one-dimensional quantum dots, both Friedel oscillations and Wigner correlations induce oscillations in the electron density with the same wavelength, pinned at the same position. Therefore, observing such a property does not provide any hint about the formation of a Wigner molecule when electrons interact strongly and other tools must be employed to assess the formation of such correlated states. We compare here the behavior of three different correlation functions and demonstrate that the integrated two point correlation function, which represents the probability density of finding two particles at a given distance, is the only faithful estimator for the formation of a correlated Wigner molecule.

A theoretical analysis of the optical absorption properties in one-dimensional InAs/GaAs quantum dot superlattices

We present theoretical investigations of miniband structures and optical properties of InAs/GaAs one-dimensional quantum dot superlattices (1D-QDSLs). The calculation is based on the multi-band k·p theory, including the conduction and valence band mixing effects, the strain effect, and the piezoelectric effect; all three effects have periodic boundary conditions. We find that both the electronic and optical properties of the 1D-QDSLs show unique states which are different from those of well known single quantum dots (QDs) or quantum wires. We predict that the optical absorption spectra of the 1D-QDSLs strongly depend on the inter-dot spacing because of the inter-dot carrier coupling and changing strain states, which strongly influence the conduction and valence band potentials. The inter-miniband transitions form the absorption bands. Those absorption bands can be tuned from almost continuous (closely stacked QD case) to spike-like shape (almost isolated QD case) by changing the inter-dot spacing. The polarization of the lowest absorption peak for the 1D-QDSLs changes from being parallel to the stacking direction to being perpendicular to the stacking direction as the inter-dot spacing increases. In the case of closely stacked QDs, in-plane anisotropy, especially [110] and [11¯0] directions also depend on the inter-dot spacing. Our findings and predictions will provide an additional degree of freedom for the design of QD-based optoelectronic devices.

Back Cover: Spin textures of strongly correlated spin Hall quantum dots (Phys. Status Solidi RRL 12/2013)

When quantum confinement is applied to topological phases of matter, very interesting physics can emerge. Majorana fermions at the boundaries of topological superconductors are the most striking example. Another interesting system is a quantum dot defined into the edges of two-dimensional topological insulators. These edges represent a new state of matter, the helical Luttinger liquid, characterized by spin-momentum locking. In their work, Dolcetto et al. inspect the spin resolved charge density and the spin resolved density–density correlation functions of such quantum dots (see the Letter on pp. 1059–1063). The interplay between helicity and quantum confinement induced by magnetic barriers leads to strong oscillations in the spin resolved density even when Coulomb interaction is weak. The main finding is that when Coulomb interaction is strong, a peculiar spin texture emerges as signalled by the spin-resolved correlation functions. This crystal of spins is the counterpart of the charge Wigner crystal occurring in ordinary one-dimensional quantum dots.

Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by the scanning probe technique

We perform a numerical simulation of the mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps as a function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are compared with the original ones. This study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limiting case. We concentrate on large quantum dots for which strong electron–electron correlations appear. For circular dots the correlations lead to the formation of Wigner molecules that in the presence of a tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for a repulsive tip potential and overestimated for an attractive tip. In lower symmetry quantum dots Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of a tip. These charge densities are well resolved by the mapping. These single-electron islands appear in the laboratory frame provided that the classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.

Interaction and temperature effects on the pair correlation function of a strongly interacting 1D quantum dot

The pair correlation function of a strongly interacting one-dimensional quantum dot is evaluated analytically within the framework of the spin coherent Luttinger liquid model. The influence of electron interactions and temperature on the competition between finite-size effects and electronic correlations is analyzed, also in the regime of large numbers of particles. The development of Wigner molecule correlations is observed as interactions get stronger. The visibility of such signatures is enhanced for temperatures comparable with the spin excitation energy of the system due to a suppression of the uncorrelated Friedel contribution to the pair correlation function.

Carrier density dependences of anisotropic optical properties in closely stacked InAs/GaAs one-dimensional quantum dot superlattices

We theoretically study the carrier density dependences of optical properties of closely stacked InAs/GaAs one-dimensional quantum dot superlattices based on the eight-band k·p theory. We find that the phonon assisted carrier injection into the ground state of both conduction and valence minibands is possible for small interdot spacings. We also predict that optical gain and spontaneous emission spectra show strongly anisotropic characters and can be controlled between [001]-, [110]-, [11¯0]-polarization by injected carrier densities as well as interdot spacing. Our findings reveal interesting possibilities of quantum dot-based optoelectronic devices applications.

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

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.

Thermoelectric effects of a laterally coupled double-quantum-dot structure

We investigate the thermoelectric properties of a laterally coupled double-quantum-dot structure. For this structure, a one-dimensional quantum dot (QD) chain between two leads forms a main channel for electron transmission, and each QD in the chain laterally couples to an additional QD. It is found that at low temperature, similar insulating bands emerge around the antiresonant points in the electronic and thermal conductance spectra. And, the edges of the insulating bands become steep rapidly with the increase of QD numbers. What’s interesting is that striking thermoelectric effect exists in the energy region where the insulating bands appear. Furthermore, with the formation of the insulation bands, the magnitude of the Seebeck coefficient becomes stable, whereas the thermoelectric efficiency is increased. By plotting the Lorentz number spectrum, we observe that in such a structure, the Lorentz number strongly violates the Wiedemann-Franz law in the insulating-band region with its maximum at the point of antiresonance. When weak intradot Coulomb interaction is taken into account, the weakened thermoelectric effect can still be improved with the increase of QD numbers.

Temporal response and reflective behaviors in all-optical switch based on InAs/GaAs one-dimensional quantum-dot resonant photonic crystal

The temporal responses and the reflected digital signal behaviors of a novel InAs/GaAs one-dimensional quantum dot resonant photonic crystal (QD-RPC) with 400 periods of unit cell, consisting of an InAs quantum dot (QD) layer and other GaAs barrier layer, are theoretically investigated by using a transfer matrix method. We demonstrate that the stopband (resonant photonic band gap) has fast response and the Nyquist rate is up to 1.15THz centered at Bragg reflection wavelength 1242.3nm. The square-wave time series with the duration of 10ps reflected by the stopband is transmitted and the intensity of pump light utilized is only 0.32MW/cm2 when this structure acts as an all-optical switch for a given temperature 45K and relative size fluctuation 0.1%. In addition, the extinction ratios of this optical switch associated with temperatures and signal pulse durations are analyzed and discussed.

Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot

We evaluate the chemical potential of a one-dimensional quantum dot coupled to an atomic force microscope tip. The dot is described within the Luttinger liquid framework, and the conductance peak positions as a function of the tip location are calculated in the linear and non-linear transport regimes for an arbitrary number of particles. The differences between the chemical potential oscillations induced by the Friedel and Wigner terms are carefully analysed in the whole range of interaction strengths. It is shown that Friedel oscillations, unlike the Wigner ones, are sensitive probes for detecting excited spin states and collective spin density waves involved in the transport.

Signatures of Wigner correlations in the conductance of a one-dimensional quantum dot coupled to an AFM tip

The transport properties of an interacting one-dimensional quantum dot capacitively coupled to an atomic force microscope probe are investigated. The dot is described within a Luttinger liquid framework which captures both Friedel and Wigner oscillations. In the linear regime, we demonstrate that both the conductance peak position and height oscillate as the tip is scanned along the dot. A pronounced beating pattern in the conductance maximum is observed, connected to the oscillations of the electron density. Signatures of the effects induced by a Wigner molecule are clearly identified and their stability against the strength of Coulomb interactions are analyzed. While the oscillations of the peak position due to Wigner get enhanced at strong interactions, the peak height modulations are suppressed as interactions grow. Oscillations due to Friedel, on the other hand, are robust against interaction.

Crossover from strong to weak exciton confinement and third-harmonic generation on one-dimensional quantum dots

We study the effects of exciton confinement on the nonlinear optical susceptibility of one-dimensional quantum dots. We use a direct numerical diagonalization to obtain the eigenenergies and eigenstates of the discretized Hamiltonian representing an electron–hole pair confined by a semiparabolic potential and interacting with each other via a Coulomb potential. Density matrix perturbation theory is used to compute the nonlinear optical susceptibilities due to third-harmonic generation and the corresponding nonlinear corrections to the refractive index and absorption coefficient. These quantities are analyzed as a function of ratio between the confinement length L and the exciton Bohr radius a0. The Coulomb potential degrades the uniformity of the level separation. We show that this effect promotes the emergence of multiple resonance peaks in the third-harmonic generation spectrum. In the weak confinement regime β=L/a0≫1, the third-order susceptibility is shown to decay as 1/β8 due to the prevalence of the hydrogenoid character of the exciton eigenstates.

Coulomb blockade phenomenon in ultra-thin gold nanowires

Ultra-thin gold nanowires with uniform diameters of 2 nm and lengths of over 100 μm are synthesized via the reduction of gold(III) chloride in an oleylamine matrix. The gold nanowires, dispersed on an oxidized substrate, are top-contacted with metallic electrodes to manufacture back gated transistors. We investigate the transport properties in the fabricated devices as a function of the gate voltage, the bias voltage, and the temperature. The nonlinear current-bias voltage characteristics from 7 K up to 300 K are well described by the Coulomb blockade model in a nearly one-dimensional quantum dot array (which results from the gold nanowires’ thermal fragmentation into a granular material). Our results support a picture in which the electronic transport is governed by sequential tunneling at an applied bias above the global Coulomb blockade threshold, whereas in the Coulomb blockade regime, inelastic cotunneling is dominant up to 70 K, at which point it crosses over to activated behavior. The current dependence on the gate voltage that shows irregular oscillations is well explained by the superimposition of Coulomb oscillation patterns generated by each different dot in the one-dimensional array. We find that the competitive effects of excitation energy and stochastic Coulomb blockade balance the number of current peaks observed.

EXCITON-MEDIATED RAMAN SCATTERING IN ONE-DIMENSIONAL QUANTUM DOTS

The differential cross section (DCS) for exciton-mediated Raman scattering (EMRS) in one-dimensional semiconductor quantum dots is presented. The exciton states are considered as intermediate states in the Raman scattering process. The selection rules for the EMRS process are studied. The numerical results show that the contribution to DCS indicated by exciton is larger than that by electron. DCS of EMRS is larger when there is a bigger confinement potential frequency.

Extracting the density profile of an electronic wave function in a quantum dot

We use a model of a one-dimensional nanowire quantum dot to demonstrate the feasibility of a scanning probe microscope (SPM) imaging technique that can extract both the energy of an electron state and the amplitude of its wave function using a single instrument. This imaging technique can probe electrons that are buried beneath the surface of a low-dimensional semiconductor structure and provide valuable information for the design of quantum devices. A conducting SPM tip, acting as a movable gate, measures the energy of an electron state using Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wave function \ensuremath{\Psi}($x$) of the quantum state, changing the electron's energy by an amount proportional to $|{\ensuremath{\Psi}(x)|}^{2}$. By recording the change in energy as the SPM tip is moved along the length of the dot, the density profile of the electronic wave function can be found along the length of the quantum dot.

Rabi waves and Rabi wavepackets in one-dimensional quantum dot chain: Excitation, propagation, reflection

We theoretically investigate the spatial propagation of Rabi oscillations (Rabi waves) in one-dimensional inhomogeneous quantum dot (QD) chain. QD-chain is modeled by the set of two-level quantum systems with tunnel coupling between neighboring QDs. The space propagation of Rabi waves in the form of traveling waves and localized wave packets is considered. It is shown, that the propagation of Rabi waves is accompanied by the transfer of the inversion and quantum correlations along the QD-chain and by their reflection and mutual transformations at the spatial inhomogeneities of QE-chain. The effect is potentially applicable in quantum nanooptics and quantum informatics.