Singlet–triplet oscillations and far-infrared spectrum of four-minima quantum-dot molecule

We study ground states and far-infrared spectra (FIR) of two electrons in four-minima quantum-dot molecule in magnetic field by exact diagonalization. Ground states consist of altering singlet and triplet states, whose frequency, as a function of magnetic field, increases with increasing dot–dot separation. When the Zeeman energy is included, only the two first singlet states remain as ground states. In the FIR spectra, we observe discontinuities due to crossing ground states. Non-circular symmetry induces anticrossings, and also an additional mode above ω₊ in the spin-triplet spectrum. In particular, we conclude that electron–electron interactions cause only minor changes to the FIR spectra and deviations from the Kohn modes result from the low-symmetry confinement potential.     

Composite fermion picture for multi-component plasmas in 2D electron–hole systems in a strong magnetic field

Low-lying states of a 2D electron–hole system contain electrons and one or more types of charged excitonic complexes. Binding energies and angular momenta of these excitonic ions, and the pseudopotentials describing their interactions with electrons and with one another are obtained from numerical studies of small systems. Incompressible fluid ground states of such multi-component plasmas are found in exact numerical diagonalizations. A generalized composite fermion (CF) picture involving Chern–Simons charges and fluxes of different types is proposed and shown to predict the low-lying states at any value of the magnetic field.     

Charged magneto-exciton states in semiconductor quantum dots

By embedding a layer of self-assembled quantum dots into a field-effect structure, we are able to control the exciton charge in a single dot. We present the results of photoluminescence experiments as a function of both charge and magnetic field. The results demonstrate a hierarchy of energy scales determined by quantization, the direct Coulomb interaction, the electron–electron exchange interaction, and the electron–hole exchange interaction. For excitons up to the triply charged exciton, the behavior can be understood from a model assuming discrete levels within the quantum dot. For the triply charged exciton, this is no longer the case. In a magnetic field, we discover a coherent interaction with the continuum states, the Landau levels associated with the wetting layer.     

Quantum Hall effect in back-gated InAs/GaSb heterostructures under a tilted magnetic field

We investigate the quantum Hall effect (QHE) in the InAs/GaSb hybridized electron–hole system grown on a conductive InAs substrate which act as a back-gate. In these samples, the electron density is constant and the hole density is controlled by the gate-voltage. Under a magnetic field perpendicular to the sample plane, the QHE appears along integer Landau-level (LL) filling factors of the net-carriers, where the net-carrier density is the difference between the electron and hole densities. In addition, longitudinal resistance maxima corresponding to the crossing of the extended states of the original electron and hole LLs make the QHE regions along integer-ν_net discontinuous. Under tilted magnetic fields, these R_xx maxima disappear in the high magnetic field region. The results show that the in-plane magnetic field component enhances the electron–hole hybridization and the formation of minigaps at LL crossings.     

Quantum rings in tilted magnetic fields

The electronic states of semiconductor quantum rings (QRs) under tilted magnetic fields are studied in the framework of the effective mass and envelope function approximations. For an axial field, the orbital Zeeman contribution prevails leading to the well-known Aharanov–Bohm spectrum, but it slowly decreases as the magnetic field direction declines. For an in-plane field, only the diamagnetic shift survives and it leads to the formation of double quantum well solutions, this result being relevant for experimental techniques which use in-plane magnetic fields to determine the spin of QR ground states. We also investigate the magnetic response of partially overlapped QRs, which are characteristic of high-density samples of self-assembled rings, and find that the spectrum is quite sensitive to ring coupling.     

Transport studies of localized and extended states of a two-dimensional electron gas in low magnetic fields

We have observed the quantum Hall effect in a high mobility two-dimensional electron gas to filling factors up to 80 at 0.3 K. This demonstrates the presence of both localized and extended states at low field, and explains the failure of the standard semi-classical analysis of Shubnikov–de Haas (SdH) oscillations in this regime. We go on to derive a general expression for the conductivity due to rectangular bands of extended states, and show that the observed temperature dependence of the SdH oscillations is consistent with this picture. An analysis of the oscillations using this expression reveals the predicted levitation of the extended states as the magnetic field is reduced.     

In-plane magnetic field-induced anisotropy and orientation energy of stripe phases at half-filled high Landau levels

We report on detailed Hartree–Fock calculations of the unidirectional charge density wave orientation energy induced by a tilted magnetic field. We find that for current experimental samples stripes are oriented perpendicular to the in-plane field, consistent with experiment. For wider two-dimensional electron systems we predict tilt-induced stripe states with variable anisotropy energy sign.     

Electronic states of quantum dots: beyond the 2D parabolic model

The quantum states of interacting electrons in a quantum dot in a magnetic field are calculated and the effects of corrections to the 2D parabolic model are examined. The quantum states are obtained by a new method which involves three steps: first the electrostatic potential of the device is obtained from a solution of the Poisson equation, next this potential is used together with a combination of variational and Hartree–Fock calculations to obtain an orthogonal basis whose low-lying states are localised in the region of the dot and finally this basis is used to perform an exact diagonalization. Special attention is paid to the effect of motion perpendicular to the ideal 2D plane and the effect of screening of the Coulomb interaction by metallic electrodes close to the dot. Both effects result in a weakened effective interaction and increase the magnetic fields at which ground-state transitions occur.     

Electron–hole states in the fractional quantum Hall regime probed by photoluminescence

The electron–hole states in the fractional quantum Hall regime is investigated with a back-gated undoped quantum well by photoluminesccence in magnetic fields. The evolution of the photoluminescence spectra is discussed depending on the electron density. We find anomalies of the photoluminescence at the integer as well as the fractional filling factors.     

Vertical magneto-tunneling through a quantum dot and the density of states of small electronic systems

One-electron tunneling through a quantum dot with a strong magnetic field in the direction of the current is studied. The linear magneto-conductance is computed for a model parabolic dot with seven electrons in the intermediate states and for different values of the magnetic field. It is shown that the dot density of states at low excitation energies can be extracted from a precise measurement of the conductance at the upper edge of the Coulomb blockade diamond. We parametrized the density of states with a single “temperature” parameter (in the so called “constant temperature approximation”), and found that this parameter depends very weakly on the magnetic field.     

Wave function mapping of self-assembled quantum dots by capacitance spectroscopy

We use frequency-dependent capacitance–voltage spectroscopy to study the dynamic charging of self-assembled InAs quantum dots. With increasing frequency, the AC charging becomes suppressed, beginning with the low-energy states. By applying an in-plane magnetic field, we generate an additional magnetic confinement that alters the tunneling barrier and hence the charging dynamics. In traveling through the potential barrier, the electrons acquire an additional momentum k₀, proportional to the magnetic field B. As the tunneling is enhanced, when k₀ matches the maximum of the electronic wave function Ψ (in momentum representation), we are able to map out the shape of Ψ by varying B.     

Trions in quantum wells

An overview is given of our investigation of the energy levels and of the correlation functions of the negatively and positively charged excitons (also called trions) in quantum wells in the presence of a perpendicular magnetic field. A detailed comparison is made with available experimental data in III–V and II–VI semiconductor quantum wells.     

Micropillar resonator in a magnetic field: Zero and finite temperature cases

In this work, we present a theoretical study of a quantum dot–microcavity system which includes a constant magnetic field in the growth direction of the micropillar. First, we study the zero temperature case by means of a self-consistent procedure with a trial function composed of a coherent photon field and a BCS function for the electron–hole pairs. The dependence of the ground state energy on the magnetic field and the number of polaritons is found. We show that the magnetic field can be used as a control parameter for the photon number, and we make explicit the scaling of the total energy with the number of polaritons. Next, we study this problem at finite temperatures and obtain the scaling of the critical temperature with the number of polaritons.     

Effect of the dielectric-constant mismatch and magnetic field on the binding energy of hydrogenic impurities in a spherical quantum dot

Within the effective mass approximation and variational method the effect of dielectric constant mismatch between the size-quantized semiconductor sphere, coating and surrounding environment on impurity binding energy in both the absence and presence of a magnetic field is considered. The dependences of the binding energy of a hydrogenic on-center impurity on the sphere and coating radii, alloy concentration, dielectric-constant mismatch, and magnetic field intensity are found for the GaAs–Ga_1−xAl_xAs–AlAs (or vacuum) system.     

Hybrid stable-chaotic states in coupled quantum well stadia

We use tunnel current spectroscopy to investigate the quantum states of two GaAs quantum wells coupled by a low (100 meV) (AlGa)As tunnel barrier. A high tilted magnetic field is used to generate strongly chaotic electron motion in the two wells which act as coupled chaotic ‘stadia'. The effect of the tunnel barrier on the dynamics of the system depends on the magnitude of the applied bias voltage V. For V375 mV, the central potential barrier acts as a perturbation which modifies the trajectories of selected periodic orbits in the quantum well. Scattering off the central barrier also generates new periodic orbits involving multiple collisions on all three barriers. These orbits ‘scar' distinct sets of eigenstates which generate periodic resonant peaks in the current–voltage characteristics of the device. When the device is biased such that the injected electrons just surmount the central barrier, our calculations reveal novel hybrid scarred states with both stable and chaotic characteristics.     

Simple theoretical analysis of the Einstein’s photoemission from quantum confined superlattices

In this paper, we study the Einstein’s photoemission from III–V, II–VI, IV–VI and HgTe/CdTe quantum well superlattices (QWSLs) with graded interfaces and quantum well effective mass superlattices in the presence of a quantizing magnetic field on the basis of newly formulated dispersion relations in the respective cases. Besides, the same has been studied from the afore-mentioned quantum dot superlattices and it appears that the photoemission oscillates with increasing carrier degeneracy and quantizing magnetic field in different manners. In addition, the photoemission oscillates with film thickness and increasing photon energy in quantum steps together with the fact that the solution of the Boltzmann transport equation will introduce new physical ideas and new experimental findings under different external conditions. The influence of band structure is apparent from all the figures and we have suggested three applications of the analyses of this paper in the fields of superlattices and microstructures.     

Tunneling singularities in the open Hubbard chain

We study singularities in the I–V characteristics for sequential tunneling from resonant localized levels (e.g. a quantum dot) into a one-dimensional electron system described by a Hubbard model. Boundary conformal field theory together with the exact solution of the Hubbard model subject to boundary fields allow to compute the exponents describing the singularity arising when the energy of the local level is tuned through the Fermi energy of the wire as a function of electron density and magnetic field. For boundary potentials with bound states a sequence of such singularities can be observed.     

AC-hopping conductance of self-organized Ge/Si quantum dot arrays

Dense (n=4×10¹¹ cm^-2) arrays of Ge quantum dots in a Si host were studied using attenuation of surface acoustic waves (SAWs) propagating along the surface of a piezoelectric crystal located near the sample. The SAW magneto-attenuation coefficient, ΔΓ=Γ(ω,H)-Γ(ω,0), and change of velocity of SAW, ΔV/V=(V(H)-V(0))/V(0), were measured in the temperature interval T=1.5–4.2 K as a function of magnetic field H up to 6 T for the waves in the frequency range f=30–300 MHz. Based on the dependences of ΔΓ on H, T and ω, as well as on its sign, we believe that the AC conduction mechanism is a combination of diffusion at the mobility edge with hopping between localized states at the Fermi level. The measured magnetic field dependence of the SAW attenuation is discussed based on existing theoretical concepts.     

Time evolution of initially localized states in two-dimensional quantum dot arrays in a magnetic field

The evolution of non-stationary localized states |Ψ(t=0) is investigated in two-dimensional tight binding systems of N potential wells with and without a homogeneous field perpendicular to the plane. Most results are presented in analytical form, what is almost imperative if the patterns are as complex as for rings in a magnetic field, where the qualitatively different features arise depending on rational or irrational numbers. The systems considered comprise finite linear chains (N=2,3), finite rings (N=3–6), infinite chains, finite rings (N=3–6) in a magnetic field, and rings with leads attached to each ring site. The position of the particle at time t is described by the projection of the wave function P_m(t)=|m|Ψ(t)|² onto the localized basis function at site m. For finite chains and rings with N=3,4,6 the time evolution is periodic, whereas it is non-periodic for N=5 and N greater then 6. Rings in a magnetic field show a rich spectrum of different features depending on N and the number of flux quanta through the ring, including periodic oscillation and rotation of the charge as well as non-periodic charge fluctuations.     

Spin effects in a quantum ring

Recent experiments that are reviewed explore the spin states of a ring-shaped many-electron quantum dot. Coulomb-blockade spectroscopy is used to access the spin degree of freedom. The Zeeman effect observed for states with successive electron number allows to select possible sequences of spin ground states of the ring. Spin-paired orbital levels can be identified by probing their response to magnetic fields normal to the plane of the ring and electric fields caused by suitable gate voltages. This narrows down the choice of ground-state spin sequences. A gate-controlled singlet–triplet transition is identified and the size of the exchange interaction matrix element is determined.