One-electron spin-dependent transport in split-gate structures containing self-organized InAs quantum dots

The paper presents the results obtained in a study of electron transport in split-gate structures prepared from heterostructures with self-organizing InAs quantum dots situated close to a two-dimensional electron gas. Coulomb oscillations of current through InAs quantum dots depending on the voltage on the gate were observed. Coulomb current oscillations persisted up to about 20 K. The Coulomb energy ΔE _C = 12.5 meV corresponding to theoretical estimates for the p-states of quantum dots in our structures was determined.     

Single-electron spin-dependent transport in split-gate structures containing self-assembled quantum dots

Study of split-gate structures, in which self-assembled InAs quantum dots (QDs) are located near the region of 2D electron gas, has revealed Coulomb oscillations in the dependence of the tunnel current through a limited number of InAs QDs in a channel on the gate voltage, which correspond to the excited states of QDs with opposite spins. The Coulomb oscillations of the current were observed up to a temperature of ～20 K. The Coulomb energy ΔE _C was found to be 12.5 meV, a value corresponding to the theoretical estimates for p states of QDs in our experimental structures.     

Period of photoconductivity oscillations and charge dynamics of quantum dots in <Emphasis Type="Italic">p</Emphasis>–<Emphasis Type="Italic">i</Emphasis>–<Emphasis Type="Italic">n</Emphasis> GaAs/InAs/AlAs heterojunctions

Quantum oscillations of photoconductivity in p–i–n GaAs/InAs/AlAs quantum-dot heterojunctions have been studied. The dominating effect of the dynamics of charge accumulation of optically excited holes at quantum dots on the oscillation period and on the general evolution of the holes with a change in the illumination power has been shown within a simple electrostatic model. Investigation of the temperature dependence of the oscillating structure of the current–voltage characteristics has confirmed our interpretation.     

g-Factor Calculation in Small Quantum Dots

It is shown that the effective Lande splitting factor or g-factor of electrons localized on heterostructures such as small quantum dots is always formed as a difference of two values. The first of themrelates to thematerial of the dot itself and critically depends on its sizes and shape; the second one relates to the barriermaterial (surrounding matrix); therewith, the dependence on the latter does not disappear at any dot sizes. The known (k, p) Kane theory defining the renormalization of electron mass and g-factor in bulk semiconductors, is modified for small quantum dots with “incomplete” band structure. Specific calculations of the electron ground state energy and g-factor are performed for the covariant InAs/AlSb heterostructure not localizing holes and, hence, capable of forming pure one-electron states (prototypes of solid-state qubits).     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

1/<Emphasis Type="Italic">Q</Emphasis> expansion for the energy spectrum of quantum dots

A new method is proposed for calculating the energy spectrum and the wave functions of N-electron quantum dots with an arbitrary confining potential. The method consists in expansion with respect to a dimensionless quantum parameter 1/Q, which is expressed in terms of the ratio of the characteristic Coulomb energy of electron-electron interaction to the characteristic energy of one-particle transition in a confining potential. Two-electron quantum dots with a parabolic confining potential in an external magnetic field are considered. Strongly correlated states of the system and the spin rearrangement in a strong magnetic field are analyzed. Analytic expressions are obtained for the energy and the wave functions of the system. It is shown that restriction of the analysis only to the first three terms in the quantum-parameter expansion gives an accuracy of one percent when calculating the energy even for values of Q on the order of unity, i.e., for the presently implementable GaAs quantum dots. The expressions for energy obtained are in a good agreement with the experimental data for quantum dots in a perpendicular magnetic field.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Phononless hopping conduction in two-dimensional layers of quantum dots

Regularities are studied in charge transport due to the hopping conduction of holes along two-dimensional layers of Ge quantum dots in Si. It is shown that the temperature dependence of the conductivity obeys the Efros-Shklovskii law. It is found that the effective localization radius of charge carriers in quantum dots varies nonmonotonically upon filling quantum dots with holes, which is explained by the successive filling of electron shells. The preexponential factor of the hopping conductivity ceases to depend on temperature at low temperatures (T<10 K) and oscillates as the degree of filling quantum dots with holes varies, assuming values divisible by the conductance quantum e²/h. The results obtained indicate that a transition from phonon-assisted hopping conduction to phononless charge transfer occurs as the temperature decreases. The Coulomb interaction of localized charge carriers has a dominant role in these phononless processes.     

Electronic transport of a T-shaped double-quantum-dot system in the Coulomb blockade regime

We studied the electronic transport properties of a T-shaped double-quantum-dot system in the Coulomb blockade regime when the onsite Coulomb interaction parameters U ₁ and U ₂ have finite values in both component dots. Our analysis is done in the so-called beyond Hartree-Fock approximation that includes contributions related to both normal and mixed averages of various number-like operators in the system. We provide an analytic formula for the main’s dot Green function in the case of large onsite Coulomb interaction parameters (U ₁ = U ₂ → ∞), and find that with a good approximation, this limit is realized when the ratio U ₁/t = U ₂/t ≥ 30, t being the interdot electron tunneling between the two component dots of the structures. In the most general situation of the Coulomb blockade regime (U ₁ ≠ U ₂) the system conductivity presents two dips corresponding to the Fano-Kondo effect and the system’s shot noise and electronic current present a series of plateaus that should be visible in experimental setups.     

Coulomb deexcitation of muonic hydrogen within the quantum close-coupling method

The Coulomb deexcitation of muonic hydrogen in collisions with the hydrogen atom has been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The calculations of the l-averaged cross sections of the Coulomb deexcitation are performed for (μp)_n and (μd)_n atoms in the initial states with the principal quantum number n = 3–9 and at relative energies E = 0.1–100 eV. The obtained results for the n and E dependences of the Coulomb deexcitation cross sections drastically differ from the semiclassical results. An important contribution of the transitions with Δn > 1 to the total Coulomb deexcitation cross sections (up to ～37%) is predicted.     

Collective states in highly symmetric atomic configurations and single-photon traps

We study correlated states in circular and linear-chain configurations of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behavior is mediated by exchange of transverse photons between the atoms. For a circular atomic configuration containing N atoms, the collective energy eigenstates can be determined by group-theoretical means making use of the fact that the configuration possesses a cyclic symmetry group Z _N . For these circular configurations, the carrier spaces of the various irreducible representations of the symmetry group are at most two-dimensional, so that the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. As a consequence, the radiationless energy eigenstates carry a Z _N quantum number p = 0, 1, …, N, which is analogous to the angular momentum quantum number l = 0, 1, … carried by particles propagating in a central potential, such as a hydrogen-like system. Just as the hydrogen s states are the only electronic wave functions that can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the circular atomic sample can occupy the central atom only for vanishing Z _N quantum number p. When a central atom is present, the p = 0 state splits into two, showing level crossing at certain radii; in the regions between these radii, damped oscillations between two “ extreme” p = 0 states occur, where the excitation occupies either the outer atoms or the central atom only. For large numbers of atoms in a maximally subradiant state, a critical interatomic distance of λ/2 emerges both in the linear-chain and in the circular configuration of atoms. The spontaneous decay rate of the linear configuration exhibits a jumplike “critical” behavior for next-neighbor distances close to a half-wavelength. Furthermore, both the linear-chain and the circular configurations exhibit exponential photon trapping once the next-neighbor distance becomes less than a half-wavelength, with the suppression of spontaneous decay being particularly pronounced in the circular system. In this way, circular configurations containing sufficiently many atoms may be natural candidates for single-photon traps.     

Zeeman effect for holes in a Ge/Si system with quantum dots

The tight binding approximation is employed to study the Zeeman effect for the hole ground state in a quantum dot. A method is proposed for calculating the g factor for localized states in a quantum dot. This method can be used both for hole states and for electron states. Calculations made for a Ge/Si system with quantum dots show that the g factor of a hole in the ground state is strongly anisotropic. The dependence of the g factor on the size of a germanium island is analyzed and it is shown that anisotropy of the g factor increases with the island size. It is shown that the value of the g factor is mainly determined by the contribution of the state with the angular momentum component J _z =±3/2 along the symmetry axis of the germanium island.     

Spurious states of the dirac equation in a finite basis set

The occurrence of spurious states for the Dirac equation in a finite basis set is considered. For a Coulomb central-field potential, the spectra of the radial Dirac operator in a finite basis set (without using the kinetic balance) are shown to coincide for two different values of the relativistic quantum number κ that differ in sign. For an attractive Coulomb potential, this means that, for any basis set, spurious states p _1/2, d _3/2, … (κ > 0) arise, whose energies exactly coincide with energies of the states 1s _1/2, 2p _3/2, … (κ < 0), respectively. In addition, the negative spectra of the Dirac operator in a finite basis set for κ > 0 and κ < 0 also coincide.     

Drag of ballistic electrons by an ion beam

Drag of electrons of a one-dimensional ballistic nanowire by a nearby one-dimensional beam of ions is considered. We assume that the ion beam is represented by an ensemble of heavy ions of the same velocity V. The ratio of the drag current to the primary current carried by the ion beam is calculated. The drag current turns out to be a nonmonotonic function of velocity V. It has a sharp maximum for V near v _nF/2, where n is the number of the uppermost electron miniband (channel) taking part in conduction and v _nF is the corresponding Fermi velocity. This means that the phenomenon of ion beam drag can be used for investigation of the electron spectra of ballistic nanostructures. We note that whereas observation of the Coulomb drag between two parallel quantum wires may in general be complicated by phenomena such as tunneling and phonon drag, the Coulomb drag of electrons of a one-dimensional ballistic nanowire by an ion beam is free of such spurious effects.     

Mechanisms of low-temperature high-frequency conductivity in systems with a dense array of Ge<Subscript>0.7</Subscript>Si<Subscript>0.3</Subscript> quantum dots in silicon

High-frequency (HF) conductivity in systems with a dense (with a density of n = 3 × 10¹¹ cm^?2) array of self-organized Ge_0.7Si_0.3 quantum dots in silicon with different boron concentrations n_B is determined by acoustic methods. The measurements of the absorption coefficient and the velocity of surface acoustic waves (SAWs) with frequencies of 30–300 MHz that interact with holes localized in quantum dots are carried out in magnetic fields of up to 18 T in the temperature interval from 1 to 20 K. Using one of the samples (n_B = 8.2 × 10¹¹ cm^?2), it is shown that, at temperatures T ≤ 4 K, the HF conductivity is realized by the hopping of holes between the states localized in different quantum dots and can be explained within a two-site model in the case of

Open image in new window

, where ω is the SAW frequency and τ₀ is the relaxation time of the populations of the sites (quantum dots). For T > 7 K, the HF conductivity has an activation character associated with the diffusion over the states at the mobility threshold. In the interval 4 K < T < 7 K, the HF conductivity is determined by a combination of the hopping and activation mechanisms. The contributions of these mechanisms are distinguished; it is found that the temperature dependence of the hopping HF conductivity approaches saturation at T* ≈ 4.5 K, which points to a τ₀ ≤ 1. A value of τ₀(T*) ≈ 5 × 10^?9 s is determined from the condition ωτ₀(T*) ≈ 1.

     

Influence of an external electric field on the probabilities of two-photon transitions between 2<Emphasis Type="Italic">s</Emphasis>, 2<Emphasis Type="Italic">p</Emphasis> and 1<Emphasis Type="Italic">s</Emphasis> levels for hydrogen and antihydrogen atoms

The probabilities of two-photon decay for hydrogen (H) and antihydrogen (\(\bar H\)) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and \(\bar H\) atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.     

Intertwining Symmetry Algebras of Quantum Superintegrable Systems on Constant Curvature Spaces

A class of quantum superintegrable Hamiltonians defined on a hypersurface in a n+1 dimensional ambient space with signature (p,q) is considered and a set of intertwining operators connecting them are determined. It is shown that the intertwining operators can be chosen such that they generate the su(p,q) and so(2p,2q) Lie algebras and lead to the Hamiltonians through Casimir operators. The physical states corresponding to the discrete spectrum of bound states as well as the degeneration are characterized in terms of some particular unitary representations.     

Electron interaction effects on the thermoelectric power of a quantum dot at T &gt; T<Subscript>K</Subscript>

In the absence of phonon thermal conductivity, we theoretically investigate the output power of an interacting quantum dot thermoelectric setup that is moderately coupled to two electronic reservoirs in the regime T ? T _K . In the noninteracting case, the output power is maximized when the energy level of the dot is around a critical value ε _c . We find that when the energy level of the dot is lower than ε _c , Coulomb interaction can enhance the maximum thermoelectric power that can be achieved by tuning the bias and a wider operating region is also observed. However, when the energy level of the dot is higher than ε _c , Coulomb interaction suppresses the maximum power. Finally when the dot level is around ε _c , Coulomb interaction has minimal effects on the maximum power.     

Asymmetry with respect to the magnetic field direction in the interaction between the quantum states of two coupled superconducting rings

The interaction between the quantum states of two circularly asymmetric superconducting aluminum rings forming figure eight, threaded by a magnetic flux and biased by an external sinusoidal ac current with zero dc component, has been investigated. Quantum oscillations in the dependence V _dc(B) of the rectified dc voltage on magnetic field for these structures have been measured at different external currents and temperatures close to critical. Fourier and wavelet analyses of the function V _dc(B) have revealed, along with the two fundamental ring frequencies, various combination frequencies; this fact is indicative of interaction in the structure. Deviation of the function V _dc(B) from oddness with respect to the magnetic field direction has been found for the first time.