Short Quantum Wire Research Articles

Self-induction and magnetic effects in electron transport through a photon cavity

We explore higher order dynamical effects in the transport through a two-dimensional nanoscale electron system embedded in a three-dimensional far-infrared photon cavity. The nanoscale system is considered to be a short quantum wire with a single circular quantum dot defined in a GaAs heterostructure. The whole system, the external leads and the central system are placed in a constant perpendicular magnetic field. The Coulomb interaction of the electrons, the para- and diamagnetic electron-photon interactions are all treated by a numerically exact diagonalization using step-wise truncations of the appropriate many-body Fock spaces. We focus on the difference in transport properties between a description within an electric dipole approximation and a description including all higher order terms in a single photon mode model. We find small effects mostly caused by an electrical quadrupole and a magnetic dipole terms that depend strongly on the polarization of the cavity field with respect to the transport direction and the photon energy. When the polarization is aligned along the transport direction we find indications of a weak self-induction that we analyze and compare to the classical counterpart, and the self-energy contribution of high-order interaction terms to the states the electrons cascade through on their way through the system. Like expected the electron-photon interaction is well described in the dipole approximation when it is augmented by the lowest order diamagnetic part for a nanoscale system in a cavity in an external magnetic field.

Lifetimes of confined optical phonons and the shape of a Raman peak in disordered nanoparticles. II. Numerical treatment

Disorder-induced broadening of optical vibrational eigenmodes in nanoparticles of nonpolar crystals is studied numerically. The methods previously used to treat phonons in defectless particles are adjusted for numerical evaluation of the disordered problem. Imperfections in the form of Gaussian and binary disorders as well as surface irregularities are investigated thoroughly in a wide range of impurity concentrations and disorder strengths. For dilute and weak point-like impurities the regimes of separated and overlapped phonon levels are obtained and the behavior of the linewidth predicted theoretically is confirmed, the crossover scale falls into the actual range of several nanometers. These notions survive for strong dilute impurities, as well. Regimes and crossovers predicted by theory are checked and identified, and minor discrepancies are discussed. To mention a few of them: slower than in theory increasing of the linewidth with the phonon quantum number for weak disorder and only qualitative agreement between theory and numerics for resonant broadening in strong dilute disorder. The novel phenomena discovered numerically are: "mesoscopic smearing" of distribution function in the ensemble of identical disordered particles, inflection of the linewidth dependence on the impurity concentration for light "dense" binary impurities, and position-dependent capability of strong impurity to catch the phonon. It is shown that surface irregularities contribute to the phonon linewidth less than the volume disorder, and their rate reveals faster decay with increasing of the particle size. It is argued that the results of present research are applicable also for quantum dots and short quantum wires.

Oscillations in electron transport caused by multiple resonances in a quantum dot-QED system in the steady-state regime

We model the electron transport current as the photon energy is swept through several resonances of a multi-level quantum dot, embedded in a short quantum wire, coupled to photon cavity. We use a Markovian quantum master equation appropriate for the long-time evolution and include the electron-electron and both the para- and the diamagnetic electron-photon interactions via diagonalization in a truncated many-body Fock space. Tuning the photon energy, several anti-crossings caused by Rabi-splitting in the energy spectrum of the quantum dot system are found. The strength of the Rabi-splittings and the photon-exchange between the resonant states depend on the polarization of the cavity photon field. We observe oscillations of the charge in the system and several resonant transport current peaks for the photon energies corresponding to the resonances in the steady-state regime.

Cavity‐Photon‐Induced High‐Order Transitions between Ground States of Quantum Dots

AbstractIt is shown that quantum electromagnetic transitions to high orders are essential to describe the time‐dependent path of a nanoscale electron system in a Coulomb blockade regime when coupled to external leads and placed in a 3D rectangular photon cavity. The electronic system consists of two quantum dots embedded asymmetrically in a short quantum wire. The two lowest in energy spin degenerate electron states are mostly localized in each dot with only a tiny probability in the other dot. In the presence of the leads, a slow high‐order transition between the ground states of the two quantum dots is identified. The Fourier power spectrum for photon–photon correlations in the steady state shows a Fano type of resonance for the frequency of the slow transition. Full account is taken of the geometry of the multilevel electronic system, and the electron–electron Coulomb interactions together with the para‐ and diamagnetic electron–photon interactions are treated with step‐wise exact numerical diagonalization and truncation of appropriate many‐body Fock spaces. The matrix elements for all interactions are computed analytically or numerically exactly.

Photon-Mediated Thermoelectric and Heat Currents through a Resonant Quantum Wire-Cavity System

We theoretically consider a short quantum wire, which on both ends is connected to leads that have different temperatures. The quantum wire is assumed to be coupled to a cavity with a single-photon mode. We calculate the heat and thermoelectric currents in the quantum wire under the effect of the photon field. In the absence of the photon field, a plateau in the thermoelectric current is observed due to the thermal smearing at a high temperature gradient. In the presence of the resonance photon field, when the energy spacing between the lowest states of the quantum wire is approximately equal to the photon energy, a suppression in thermoelectric current and negativity in the heat current are seen due to the dressed electron-photon states. It is also found that the cavity with high photon energy has more influence on the thermoelectric current at a high temperature gradient.

Current correlations for the transport of interacting electrons through parallel quantum dots in a photon cavity

We calculate the current correlations for the steady-state electron transport through multi-level parallel quantum dots embedded in a short quantum wire, that is placed in a non-perfect photon cavity. We account for the electron–electron Coulomb interaction, and the para- and diamagnetic electron–photon interactions with a stepwise scheme of configuration interactions and truncation of the many-body Fock spaces. In the spectral density of the temporal current–current correlations we identify all the transitions, radiative and non-radiative, active in the system in order to maintain the steady state. We observe strong signs of two types of Rabi oscillations.

Electroluminescence Caused by the Transport of Interacting Electrons through Parallel Quantum Dots in a Photon Cavity

AbstractWe show that a Rabi‐splitting of the states of strongly interacting electrons in parallel quantum dots embedded in a short quantum wire placed in a photon cavity can be produced by either the para‐ or the dia‐magnetic electron‐photon interactions when the geometry of the system is properly accounted for and the photon field is tuned close to a resonance with the electron system. We use these two resonances to explore the electroluminescence caused by the transport of electrons through the one‐ and two‐electron ground states of the system and their corresponding conventional and vacuum electroluminescense as the central system is opened up by coupling it to external leads acting as electron reservoirs. Our analysis indicates that high‐order electron‐photon processes are necessary to adequately construct the cavity‐photon dressed electron states needed to describe both types of electroluminescence.

Interference Effects in a Tunable Quantum Point Contact Integrated with an Electronic Cavity

We show experimentally how quantum interference can be produced using an integrated quantum system comprising an arch-shaped short quantum wire (or quantum point contact, QPC) of 1D electrons and a reflector forming an electronic cavity. On tuning the coupling between the QPC and the electronic cavity, fine oscillations are observed when the arch QPC is operated in the quasi-1D regime. These oscillations correspond to interference between the 1D states and a state which is similar to the Fabry-Perot state and suppressed by a small transverse magnetic field of 60mT. Tuning the reflector, we find a peak in resistance which follows the behavior expected for a Fano resonance. We suggest that this is an interesting example of a Fano resonance in an open system which corresponds to interference at or near the Ohmic contacts due to a directly propagating, reflected discrete path and the continuum states of the cavity corresponding to multiple scattering. Remarkably, the Fano factor shows an oscillatory behavior taking peaks for each fine oscillation, thus, confirming coupling between the discrete and continuum states. The results indicate that such a simple quantum device can be used as building blocks to create more complex integrated quantum circuits for possible applications ranging from quantum-information processing to realizing the fundamentals of complex quantum systems.

Nonlinear spectra of spinons and holons in short GaAs quantum wires.

One-dimensional electronic fluids are peculiar conducting systems, where the fundamental role of interactions leads to exotic, emergent phenomena, such as spin-charge (spinon-holon) separation. The distinct low-energy properties of these 1D metals are successfully described within the theory of linear Luttinger liquids, but the challenging task of describing their high-energy nonlinear properties has long remained elusive. Recently, novel theoretical approaches accounting for nonlinearity have been developed, yet the rich phenomenology that they predict remains barely explored experimentally. Here, we probe the nonlinear spectral characteristics of short GaAs quantum wires by tunnelling spectroscopy, using an advanced device consisting of 6000 wires. We find evidence for the existence of an inverted (spinon) shadow band in the main region of the particle sector, one of the central predictions of the new nonlinear theories. A (holon) band with reduced effective mass is clearly visible in the particle sector at high energies.

Spectral characteristics of the coherent dynamics of the order parameter in superconducting nanorods

Within the density-matrix formalism based on the Bogoliubov-de Gennes equations approach we investigate the dynamics of the non-equilibrium BCS pairing induced by a sudden change of the coupling constant in quasi-1D and quasi-0D samples. We demonstrate that two different dynamical regimes of the amplitude of the BCS gap can be distinguished: an initially damped oscillation in the case of short quantum wires and purely irregular dynamics in the case of nanorods.

Coupled Collective and Rabi Oscillations Triggered by Electron Transport through a Photon Cavity

We show how the switching-on of an electron transport through a system of two parallel quantum dots embedded in a short quantum wire in a photon cavity can trigger coupled Rabi and collective electron-photon oscillations. We select the initial state of the system to be an eigenstate of the closed system containing two Coulomb interacting electrons with possibly few photons of a single cavity mode. The many-level quantum dots are described by a continuous potential. The Coulomb interaction and the para- and dia-magnetic electron-photon interactions are treated by exact diagonalization in a truncated Fock-space. To identify the collective modes the results are compared for an open and a closed system with respect to the coupling to external electron reservoirs, or leads. We demonstrate that the vacuum Rabi oscillations can be seen in transport quantities as the current in and out of the system.

Interaction-induced backscattering in short quantum wires

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

Excitation of collective modes in a quantum flute

We use a generalized master equation (GME) formalism to describe the nonequilibrium time-dependent transport of Coulomb interacting electrons through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire is modulated by out-of-phase time-dependent potentials that simulate a turnstile device. We explore this setup by keeping the contact with one lead at a fixed location at one end of the wire, whereas the contact with the other lead is placed on various sites along the length of the wire. We study the propagation of sinusoidal and rectangular pulses. We find that the current profiles in both leads depend not only on the shape of the pulses, but also on the position of the second contact. The current reflects standing waves created by the contact potentials, like in a wind musical instrument (for example, a flute), but occurring on the background of the equilibrium charge distribution. The number of electrons in our quantum ``flute'' device varies between two and three. We find that for rectangular pulses the currents in the leads may flow against the bias for short time intervals, due to the higher harmonics of the charge response. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. The system (leads plus sample wire) is described by a lattice model.

Generalized Master equation approach to mesoscopic time-dependent transport

We use a generalized Master equation (GME) formalism to describe the non-equilibrium time-dependent transport through a short quantum wire connected to semi-infinite biased leads. The contact strength between the leads and the wire are modulated by out-of-phase time-dependent functions which simulate a turnstile device. One lead is fixed at one end of the sample whereas the other lead has a variable placement. The system is described by a lattice model. We find that the currents in both leads depend on the placement of the second lead. In the rather small bias regime we obtain transient currents flowing against the bias for short time intervals. The GME is solved numerically in small time steps without resorting to the traditional Markov and rotating wave approximations. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method.

Computations of the optical transitions and absorption spectra in a set of realistic, elongated InAs/GaAs quantum boxes having a Gaussian distribution

InAs/GaAs quantum dots (QDs) grown by various methods do not have the same dimensions in the three axes. This paper reports on expressions for computations of the optical transitions and absorption spectra of InAs/GaAs QDs that have a square base and the variation of the height is Gaussian. The dots were considered to be elongated quantum boxes with square bases having finite potentials at the boundaries. The results are in excellent agreement with reported experimental data of photoluminescence and absorption. The expressions could be successfully applied to short quantum wires.

The formation of bound states and the conductance modulation on 0.7 anomaly in a quantum wire

The electron transport in a short quasi-1D quantum wire is studied. In addition to the conductance quantization, several resonances are observed. Two of the resonances appear as extra plateaus below 2e2/h. A gate voltage offset is used to tune the local potential of the quantum wire. A robust resonance is seen and the resonances evolve continuously with respect to the offset. The conductance has opposite responses to temperature in successive regions of gate voltage Vg. In the source-drain bias spectroscopy, two more conductance peaks are observed in addition to the Zero-Bias-Anomaly. The locations of the extra peaks evolve with respect to Vg showing a pattern similar to that in a quantum dot. We suggest that a bound state forms in the quantum wire. The prominent 0.7 anomaly in our quantum wire is recognized as the residue of conductance resonance.

The potential of split-gate transistors as one-dimensional electron waveguides revealed through the testing and analysis of yield and reproducibility

We study the yield and reproducibility of quantized conductance in short one-dimensional quantum wires in split-gate transistors. In order to get an unambiguous assessment, more than 500 split gates have been fabricated and tested at 1.4 K. The study clearly shows that the devices are too sensitive to the inherent dopant structures and to variations of processing. The limitations of split gates also have been revealed through the fluctuations of the pinch-off voltage and the characteristics of the first quantized plateau.

Conductance of short quantum wires with sharp boundaries

The conductance of short ballistic wires with boundaries, whose curvature radius is comparable to the electron wavelength, is investigated. It is found that, in such wires, no conductance quantization takes place. Instead, pronounced interference effects are observed. These effects are related to the Fabry-Perot interference by the wire edges and with the mesoscopic interference caused by the coherent scattering of electrons by the wire edges and by the impurities located in the near-wire regions of the 2D electron gas.

Growth, Structural, and Optical Properties of Self-Assembled (In,Ga)As Quantum Posts on GaAs

Self-assembled quantum dots embedded in semiconductor heterostructures have proved to be a rich system for exploring the physics of three dimensionally confined charges and excitons. We present here a novel structure, which allows adjusting the level of confinement between 3D and 2D for electrons and holes, respectively. The quantum post consists of a quantum dot connected to a short quantum wire. The molecular beam epitaxy deposition of these self-assembled structures is discussed, and their structural and chemical compositions are presented. Their optical properties measured by photoluminescence are compared to an eight-band strain-dependent k.p model incorporating detailed structure and alloy composition. The calculations show electron delocalization in the quantum wire part of the quantum post and hole localization in the strain-induced regions at the ends of the quantum post. The quantum post offers the possibility of controlling the dipole moment in the structure and opens up new means for tuning the intra-subband transitions by controlling its dimensions.

Magneto‐subbands in spin–orbit coupled quantum wires with anisotropic 2‐D harmonic potential

AbstractThe spin states of electrons in a perpendicular magnetic field (B) are studied with the introduction of anisotropic harmonic confinement and spin–orbit coupling (SOC) (both Dresselhaus and Rashba interactions). The effective g ‐factors, as well as B ‐dependence of subbands, are numerically calculated for GaAs and their dependence on confinement strength and degree of anisotropy is estimated. This model is in good agreement with previous reports [PRB 72, 155410 (2005) and so on] in the isotropic limit and weak SOC, indicating its usefulness for slightly deformed quantum dots and short quantum wire. However, dispersion caused by mixing of spin states imposes limitations when SOC and confinement are comparable. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)