Open Quantum Dots Research Articles

Fingerprints of transverse and longitudinal coupling between induced open quantum dots in the longitudinal magnetoconductance through antidot lattices

We propose numerical simulations of longitudinal magnetoconductance through a finite antidot lattice located inside an open quantum dot with a magnetic field applied perpendicular to the plane. The system is connected to reservoirs using quantum point contacts. We discuss the relationship between the longitudinal magnetoconductance and the generation of transversal couplings between the induced open quantum dots in the system. The system presents longitudinal magnetoconductance maps with crossovers (between transversal bands) and closings (longitudinal decoupling) of fundamental quantum states related to the open quantum dots induced by the antidot lattice. A relationship is observed between the distribution of antidots and the formed conductance bands, allowing a systematic follow up of the bands as a function of the applied magnetic field and quantum point-contact width. We observed a high conductance intensity [between $n$ and $(n+1)$ quantum of conductance, $n=1,2,\dots{}$] in the regions of crossover and closing of states. This suggests transversal couplings between the induced open quantum dots of the system that can be modulated by varying both the antidots potential and the quantum point-contact width. A new continuous channel (not expected) is induced by the variation in the contact width and generate Fano resonances in the conductance. These resonances can be manipulated by the applied magnetic field.

Modeling of open quantum dots and wave billiards using imaginary potentials for the source and the sink

A heuristic model for particle states and current flow in open ballistic two-dimensional (2D) quantum dots/wave billiards is proposed. The model makes use of complex potentials first introduced in phenomenological nuclear inelastic scattering theory (the optical model). Here we assume that external input and output leads connecting the system to the source and the drain regions may be represented by complex potentials. In this way, a current may be set up between the two ‘pseudo-leads’. Probability densities and current flows for an open quantum dot are analyzed here numerically and the results are compared with the microwave measurements used to emulate the system. The model is of conceptual as well as practical interest. In addition to quantum billiards, it may be used as a tool per se to analyze transport in classical wave analogues, such as microwave resonators, acoustic resonators, effects of leakage on such systems, etc.

Quasistationary Electron States for CdTe/ZnTe/CdTe Open Spherical Quantum Dots

The energy spectra of an electron in open spherical quantum dot (QD) within the effective mass approximation (EMA) and rectangular potential model is presented. Energy structure of quantum dots is important because of their possible applications in electronic and optoelectronic devices. For proper description and interpretation of tunneling processes knowledge of resonant states of quantum dots is necessary. Energy values depend on parameter like size of system and spatial composition. The lifetimes of the quasistationary states are computed within the framework of the scattering S-matrix method. It is shown how core radius and barrier thickness for the CdTe/ZnTe/CdTe example influence electron states and their lifetimes.

Periodic Scarred States in Open Quantum Dots as Evidence of Quantum Darwinism

Scanning gate microscopy (SGM) is used to image scar structures in an open quantum dot, which is created in an InAs quantum well by electron-beam lithography and wet etching. The scanned images demonstrate periodicities in magnetic field that correlate to those found in the conductance fluctuations. Simulations have shown that these magnetic transform images bear a strong resemblance to actual scars found in the dot that replicate through the modes in direct agreement with quantum Darwinism.

Open quantum dots in graphene: Scaling relativistic pointer states

Open quantum dots provide a window into the connection between quantum and classical physics, particularly through the decoherence theory, in which an important set of quantum states are not "washed out" through interaction with the environment–the pointer states provide connection to trapped classical orbits which remain stable in the dots. Graphene is a recently discovered material with highly unusual properties. This single layer, one atom thick, sheet of carbon has a unique bandstructure, governed by the Dirac equation, in which charge carriers imitate relativistic particles with zero rest mass. Here, an atomic orbital-based recursive Green's function method is used for studying the quantum transport. We study quantum fluctuations in graphene and bilayer graphene quantum dots with this recursive Green's function method. Finally, we examine the scaling of the domiant fluctuation frequency with dot size.

Transport through open quantum dots: Making semiclassics quantitative

We investigate electron transport through clean open quantum dots (quantum billiards). We present a semiclassical theory that allows to accurately reproduce quantum transport calculations. Quantitative agreement is reached for individual energy and magnetic field dependent elements of the scattering matrix. Two key ingredients are essential: (i) inclusion of pseudo-paths which have the topology of linked classical paths resulting from diffraction in addition to classical paths and (ii) a high-level approximation to diffractive scattering. Within this framework of the pseudo-path semiclassical approximation (PSCA), typical shortcomings of semiclassical theories such as violation of the anti-correlation between reflection and transmission and the overestimation of conductance fluctuations are overcome. Beyond its predictive capabilities the PSCA provides deeper insights into the quantum-to-classical crossover.

Phase readout of a charge qubit capacitively coupled to an open double quantum dot

We study the dynamics of a charge qubit that is capacitively coupled to an open double quantum dot. Depending on the qubit state, the transport through the open quantum dot may be resonant or off-resonant, such that the qubit affects the current through the open double dot. We relate the initial qubit state to the magnitude of an emerging transient current peak. The relation between these quantities enables the readout of not only the charge but also the phase of the qubit.

Entanglement generation through an open quantum dot: Exact two-electron scattering state in the Anderson model

We analytically study entanglement generation through an open quantum-dot system described by the two-lead Anderson model. We exactly obtain the transition rate between the nonentangled incident state in one lead and the outgoing spin-singlet state in the other lead. We find that only the spin-singlet state can transmit in the cotunneling process. To discuss such an entanglement property in the open quantum system, we construct the exact two-electron scattering state of the Anderson model. It is striking that the scattering state contains spin-singlet bound states induced by the Coulomb interaction. The bound state describes a scattering process in which the set of momenta is not conserved and hence, it is not in the form of a Bethe eigenstate.

RPA APPROACH TO NON-LINEAR TRANSPORT IN QUANTUM DOTS

An accurate theoretical treatment of electron-electron interactions in mesoscopic systems is available in very few cases and approximation schemes are developed in most of the applications, especially for many-level quantum dots. Here we present transport calculations within the random-phase approximation for the Coulomb interaction using the Keldysh Green's functions formalism. We describe the quantum dot systems by a tight-binding Hamiltonian. Our method is similar to the one used by Faleev and Stockman [Phys. Rev. B 66 085318 (2002)] in their study of the equilibrium properties of a homogeneous 2D electron gas. The important extension at the formal level is that we combine the RPA and the Keldysh formalism for studying non-linear transport properties of open quantum dots. Within the Keldysh formalism the polarization operator becomes a contour-ordered quantity that should be computed either from the non-interacting Green functions of the coupled quantum dot (the so-called G0W approximation) either self-consistently (GW approximation). We performed both non-selfconsistent and self-consistent calculations and compare the results. In particular we recover the Coulomb diamonds for interacting quantum dots and we discuss the charge sensing effects in parallel quantum dots.

Nonequilibrium charge transport in an interacting open system: Two-particle resonance and current asymmetry

We use Lippman-Schwinger scattering theory to study nonequilibrium electron transport through an interacting open quantum dot. The two-particle current is evaluated exactly while we use perturbation theory to calculate the current when the leads are Fermi liquids at different chemical potentials. We find an interesting two-particle resonance induced by the interaction and obtain criteria to observe it when a small bias is applied across the dot. Finally, for a system without spatial inversion symmetry we find that the two-particle current is quite different depending on whether the electrons are incident from the left lead or the right lead.

Relativistic Quantum Scars

The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.

Evolution of quasi-stationary states of an electron in an open spherical quantum dot

A theory of the evolution of spectral parameters of quasi-stationary states of an electron in an open spherical quantum dot is proposed in terms of the effective-mass and rectangular potential barrier model. The probability distribution functions (over the quasi-momentum or the energy) of electron location within the open quantum dot and their spectral characteristics, such as generalized resonance energies and generalized resonance widths, are introduced. It is demonstrated that, as the barrier layer thickness varies from zero to infinity, generalized resonance energies and the generalized resonance widths determined by the distribution function method satisfy the Heisenberg uncertainty principle, whereas the resonance energies and resonance widths determined from the poles of the scattering matrix for small thicknesses of the barrier layer do not obey this principle.

Critical and excess current through an open quantum dot: Temperature and magnetic-field dependence

We present measurements of temperature and magnetic-field dependence of the critical current and excess current in a carbon nanotube Josephson quantum dot junction. The junction is fabricated in a controlled environment which allows for extraction of the full critical current. The measurements are performed in the open quantum dot regime and fitted to theory with good qualitative agreement. We also show how to extract level spacing, level broadening, and charging energy of an open quantum dot from a bias spectroscopy plot.

Exact Scattering Eigenstates, Many-Body Bound States, and Nonequilibrium Current in an Open Quantum Dot System

We obtain an exact many-body scattering eigenstate in an open quantum dot system. The scattering state is not in the form of the Bethe eigenstate in the sense that the wave number set of the incoming plane wave is not conserved during the scattering and many-body bound states appear. By using the scattering state, we study the average nonequilibrium current through the quantum dot under a finite bias voltage. The current-voltage characteristics that we obtained by taking the two-body bound state into account is qualitatively similar to several known results.

The spectrum and properties of the scattering cross section of electrons in open spherical quantum dots

In the effective mass approximation in the model of rectangular potentials, the scattering cross section of electrons in an open spherical quantum dot is calculated for the first time. It is shown that, for such a nanosystem with a barrier of several monolayers, the experimental measurements of the scattering cross section allow adequate identification of the resonance energies and the widths of resonance states in the low-energy region of the quasi-stationary electron spectrum. It is also shown that, for an open spherical quantum dot with a low-strength potential barrier, the adequate spectral parameters of the quasi-stationary spectrum are the generalized resonance energies and widths determined via the probability of an electron being inside the quantum dot.

Observation of open quantum dot via low temperature scanning gate microscopy

Low temperature transport of a well-defined open-quantum dot has been studied via scanning gate microscopy (SGM). The open dot was fabricated on AlGaAs/GaAs heterostructure using trenches defined via electron beam lithography and a wet etching. The active size of the quantum cavity is approximately 1 μm × 1 μm. The SGM observation was performed at low temperature with a conductive piezolever, which is lifted up 50 nm above the surface with applied a negative voltage. During the scan of the tip, resistance across the dot is measured in a four-probe configuration and stored in a SPM controller synchronized with the position of the tip. The SGM response at zero-magnetic field shows a high resistance when the tip situates onto a line along the inlet and the outlet of the dot. The image could be understood as that the tip induced potential disturbs the current flow in the dot and it results in the increase of resistance. Such an image can be obtained even at more than 8 K, therefore this image would correspond to a classical transport. On the other hand, the image obtained at less than 2 K shows almost similar image as that observed at higher temperature. However, after subtracting the high temperature image as the back ground structure, which is achieved by a high pass filtering, conductance fluctuations are visualized in the low temperature image. These fluctuations would be attributed to a change of quantum interference condition as well as a manipulation of the wave-function confined in the open quantum dot.

Numerical study of the Coulomb blockade in an open quantum dot

Coulomb blockade in an open quantum dot connected to a bulk lead by a single-mode point contact is studied numerically by using the path-integral Monte Carlo method. We focus on the two-channel Kondo behavior of the capacitance of the dot, and study (1) logarithmic divergence for a wide range of tunneling strength and (2) channel anisotropy due to an in-plane magnetic field.

Two-electron bound states in a continuum in quantum dots

A bound state in a continuum (BIC) might appear in open quantum dots for the variation in the dot’s shape. By means of the equations of motion of the Green’s functions, we investigate the effect of strong intradot Coulomb interactions on that phenomenon within the framework of the impurity Anderson model. The equation that the imaginary part of the poles of the Green’s function equals zero yields the condition for BICs. As a result, we show that the Coulomb interactions replicate the single-electron BICs into two-electron ones.

Interference of ballistic electrons in an open quantum dot at high temperatures

The Aharonov-Bohm-type oscillations in the ballistic magnetoconductivity of an open quantum dot ∼1 μm in size created in the GaAs/AlGaAs heterostructure by local anode oxidation have been studied. The measurements have been performed at temperatures of 4.2 and 1.5 K, which are high enough to expect a considerable suppression of the oscillations with period h/e (in magnetic flux units). The magnetoconductivity oscillations with a period less than the quantum h/e with respect to the magnetic field are observed at 1.5 K. The explanation is proposed on the basis of the interference of the electrons moving along the time-reversed paths inscribed into the quantum dot that have their initial and final points at one of the contacts, i.e., corresponding to a period of h/2e.

Effect of strain and alloy composition inhomogeneity on the electronic and optical properties of III‐nitride semiconductors

AbstractUsing the empirical tight binding method with a sp3s* basis for the first neighbour interactions and only p–p interactions for the second neighbours, we calculated the optical properties near the fundamental gap of cubic GaxAl1–xN alloys for x<0.33 grown on a substrate whose lattice constant varies from the lattice constant of cubic AlN to GaN. We found that the spectra of the fully relaxed alloy have a tail with onset energy at the indirect gap of AlN and an edge at the direct gap of the alloy which follows the Vegard's law within 0.1 eV. The maximum of band gap for each alloy composition is found for a substrate with the lattice constant of the fully relaxed alloy. When the substrate composition is such that induces negative tetragonal strain on the alloy (εxx<0) the energy band gap is mainly affected by the alloy composition while for εxx>0 the alloy composition has a limited effect. The total effect of substrate and alloy composition in the calculated range on the band gap can be as much as 0.4 eV and is mainly due to the valence band shift as the conduction band is only slightly affected by the substrate or the alloy composition. This band gap change is adequate to explain the experimentally observed double photoluminescence peak of open quantum dots. The energy separation of the double peak is 0.1 eV and one peak can be attributed to the tetragonically strained wetting layer and the other to the fully relaxed quantum dots. Furthermore the present results can be used to estimate any possible stoichiometric inhomogeneity and help design structures with specific energies for the pair of peaks. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)