Accurate modeling of electronic properties of nanostructures is a challenging theoretical problem. Methods making use of continuous media approximation, such as k.p, sometimes struggle to reproduce results obtained with more accurate atomistic approaches. On the contrary, atomistic schemes generally come with a substantially larger cost of computation. Here, we bridge between these two approaches by taking 8-band k.p method augmented with non-linear strain terms fit to reproduce sp3d5s* tight-binding results. We illustrate this method on the example of electron and hole states confined in quantum wells and quantum dots of photonics applications relevant InAs/GaAs material system, and demonstrate a good agreement of a non-linear k.p scheme with empirical tight-binding method. We discuss limits of our procedure as well as provide non-linear 8-band k.p parameter sets for InAs and GaAs. Finally, we propose a parameterization for effective term used to improve the accuracy of the standard effective mass method.
I present a systematic study of self-assembled InAs/InP and InAs/GaAs quantum dots single particle and many body properties as a function of quantum dot-surrounding matrix valence band offset. I use an atomistic, empirical tight-binding approach and perform numerically demanding calculations for half-million atom nanosystems. I demonstrate that the overall confinement in quantum dots is a nontrivial interplay of two key factors: strain effects and the valence band offset. I show that strain effects determine both the peculiar structure of confined hole states of lens type InAs/GaAs quantum dot…
The dynamics of an exciton-LO-phonon system after an ultrafast optical excitation in an InAs/GaAs quantum dot is studied theoretically. Influence of anharmonic phonon damping and its interplay with the phonon dispersion is analyzed. The signatures of the zone-edge decay process in the absorption spectrum and time evolution are highlighted, providing a possible way of experimental investigation on phonon anharmonicity effects.
Molecular beam epitaxy is employed to manufacture self-assembled InAs/GaAs quantum dot Schottky resonant tunneling diodes. By virtue of a thin AlAs insertion barrier, the thermal current is effectively reduced and electron resonant tunneling through quantum dots under both forward and reverse biased conditions is observed at relatively high temperature of 77K. The ground states of quantum dots are found to be at ~0.19eV below the conduction band of GaAs matrix. The theoretical computations are in conformity with experimental data.
We report on a new approach for positioning of self-assembled InAs quantum dots on (110) GaAs with nanometer precision. By combining self-assembly of quantum dots with molecular beam epitaxy on in-situ cleaved surfaces (cleaved-edge overgrowth) we have successfully fabricated arrays of long-range ordered InAs quantum dots. Both atomic force microscopy and micro-photoluminescence measurements demonstrate the ability to control size, position, and ordering of the quantum dots. Furthermore, single dot photoluminescence investigations confirm the high optical quality of the quantum dots fabricated…
Electron spin dynamics in InAs/GaAs heterostructures consisting of a single layer of InAs (1/3$\sim$1 monolayer) embeded in (001) and (311)A GaAs matrix was studied by means of time-resolved Kerr rotation spectroscopy. The spin relaxation time of the sub-monolayer InAs samples is significantly enhanced, compared with that of the monolayer InAs sample. We attributed the slowing of the spin relaxation to dimensionally constrained D\textquoteright{}yakonov-Perel\textquoteright{} mechanism in the motional narrowing regime. The electron spin relaxation time and the effective g-factor in sub-monolay…
Vertically stacked and coupled InAs/GaAs self-assembled quantum dots (SADs) are predicted to exhibit a strong non-parabolic dependence of the interband transition energy on the electric field, which is not encountered in single SAD structures nor in other types of quantum structures. Our study based on an eight-band strain-dependent ${\bf k}\cdot{\bf p}$ Hamiltonian indicates that this anomalous quantum confined Stark effect is caused by the three-dimensional strain field distribution which influences drastically the hole states in the stacked SAD structures.
Time-resolved microphotoluminescence study is presented for quantum dots which are formed in the InAs/GaAs wetting layer. These dots are due to fluctuations of In composition in the wetting layer. They show spectrally sharp luminescence lines with a low spatial density. We identify lines related to neutral exciton and biexciton as well as trions. Exciton emission antibunching (second order correlation value of g^2(0)=0.16) and biexciton-exciton emission cascade prove non-classical emission from the dots and confirm their potential as single photon sources.
We report on the magnetic field dispersion of the exciton spin-splitting and diamagnetic shift in single InAs/GaAs quantum dots (QDs) and dot molecules (QDMs) up to $B$ = 28 T. Only for systems with strong geometric confinement, the dispersions can be well described by simple field dependencies, while for dots with weaker confinement considerable deviations are observed: most importantly, in the high field limit the spin-splitting shows a non-linear dependence on $B$, clearly indicating light hole admixtures to the valence band ground state.
Surface energies play a dominant role in the self-assembly of three dimensional (3D) nanostructures. In this letter, we show that using surfactants to modify surface energies can provide a means to externally control nanostructure self-assembly, enabling the synthesis of novel hierarchical nanostructures. We explore Bi as a surfactant in the growth of InAs on the {1-10} sidewall facets of GaAs nanowires. The presence of surface Bi induces the formation of InAs 3D islands by a process resembling the Stranski-Krastanov mechanism, which does not occur in the absence of Bi on these surfaces. The I…
We have studied a near-surface two-dimensional electron gas based on an InAs quantum well on a GaAs substrate. In devices without a dielectric layer we estimated large electron mobilities on the order of $10^5$ cm$^2$/Vs. We have observed quantized conductance in a quantum point contact, and determined the g-factor. Using samples with an epitaxial Al layer, we defined multiple Josephson junctions and found the critical current to be gate tunable. Based on multiple Andreev reflections the semiconductor-superconductor interface is transparent, with an induced gap of 125 $μ$eV. Our results demons…
For InAs/GaAs(001) quantum dot (QD) system, the wetting layer (WL) evolution and its temperature dependence were studied using reflectance difference spectroscopy (RDS) and analyzed with a rate equation model. The WL thicknesses showed a monotonic increase at relatively low growth temperatures but a first increase and then decrease at higher temperatures, which were unexpected from the thermodynamic understanding. By adopting a rate equation model, the temperature dependence of QD growth was assigned as the origin of different WL evolutions. A brief discussion on the indium desorption was also…
Nanostructures in InAs quantum wells have so far remained outside of the scope of traditional microfabrication techniques based on etching. This is due to parasitic parallel conduction arising from charge carrier accumulation at the physical edges of samples. Here we present a technique which enables the realization of quantum point contacts and quantum dots in two-dimensional electron gases of InAs purely by electrostatic gating. Multiple layers of top gates separated by dielectric layers are employed. Full quantum point contact pinch-off and measurements of Coulomb-blockade diamonds of quant…
We report on the resonant optical pumping of the |\pm1> spin states of a single Mn dopant in an InAs/GaAs quantum dot embedded itself in a charge tuneable device. The experiment relies on a "W" scheme of transitions reached when a suitable longitudinal magnetic field is applied. The optical pumping is achieved via the resonant excitation of the central Λ system at the neutral exciton X0 energy. For a specific gate voltage, the red-shifted photoluminescence of the charged exciton X- is observed, which allows non-destructive readout of the spin polarization. An arbitrary spin preparation in the …
The preparation of a coherent heavy-hole spin via ionization of a spin-polarized electron-hole pair in an InAs/GaAs quantum dot in a Voigt geometry magnetic field is investigated. For a dot with a 17 ueV bright-exciton fine-structure splitting, the fidelity of the spin preparation is limited to 0.75, with optimum preparation occurring when the effective fine-structure of the bright-exciton matches the in-plane hole Zeeman energy. In principle, higher fidelities can be achieved by minimizing the bright-exciton fine-structure splitting.
A new generalised group-theoretical approach, based on master Maxwell-pseudospin equations, is proposed to explain recently observed enhanced circular dichroism in the excited state emission from p-doped quantum dot ensembles under resonant circularly polarised excitation into hot trion states, herein referred to as "spin-filtering effect". The theory agrees remarkably well with polarised time-resolved photoluminescence experiments, yielding largely unknown inter- and intra-shell spin relaxation time scales. This approach allows to predict optimum pulse parameters for control of spin dynamics,…
We investigate the optical properties of InAs quantum dots grown by molecular beam epitaxy on GaAs(110) using Bi as a surfactant. The quantum dots are synthesized on planar GaAs(110) substrates as well as on the {110} sidewall facets of GaAs nanowires. At 10 K, neutral excitons confined in these quantum dots give rise to photoluminescence lines between 1.1 and 1.4 eV. Magneto-photoluminescence spectroscopy reveals that for small quantum dots emitting between 1.3 and 1.4 eV, the electron-hole coherence length in and perpendicular to the (110) plane is on the order of 5 and 2 nm, respectively. T…
We report on coherent emission of the neutral exciton state in a single semiconductor self-assembled InAs/GaAs quantum dot embedded in a one-dimensional waveguide, under resonant picosecond pulsed excita- tion. Direct measurements of the radiative lifetime and coherence time are performed as a function of excitation power and temperature. The characteristic damping of Rabi oscillations which is observed, is attributed to an excitation-induced dephasing due to a resonant coupling between the emitter and the acoustic phonon bath of the matrix. Other sources responsible for the decrease of the co…
In this work, the effect of size and wetting layer on subband electronic envelop functions, eigenenergies, linear and nonlinear absorption coefficients and refractive indices of a dome-shaped InAs/GaAs quantum dot were investigated. In our model, a dome of InAs quantum dot with its wetting layer embedded in a GaAs matrix was considered. A finite height barrier potential at the InAs/GaAs interface was assumed. To calculate envelop functions and eigenenergies, the effective one electronic band Hamiltonian and electron effective mass approximation were used. The linear and nonlinear optical prope…
The exciton lifetimes $T_1$ in arrays of InAs/GaAs vertically coupled quantum dot pairs have been measured by time-resolved photoluminescence. A considerable reduction of $T_1$ by up to a factor of $\sim$ 2 has been observed as compared to a quantum dots reference, reflecting the inter-dot coherence. Increase of the molecular coupling strength leads to a systematic decrease of $T_1$ with decreasing barrier width, as for wide barriers a fraction of structures shows reduced coupling while for narrow barriers all molecules appear to be well coupled. The coherent excitons in the molecules gain the…
We report on linewidth analysis of optical transitions in InAs/GaAs coupled quantum dots as a function of bias voltage, temperature, and tunnel coupling strength. A significant line broadening up to 100 $μ$eV is observed at hole tunneling resonances where the coherent tunnel coupling between spatially direct and indirect exciton states is maximized, corresponding to a phonon-assisted transition rate of 150 ns${}^{-1}$ at 20 K. With increasing temperature, the linewidth shows broadening characteristic of single-phonon transitions. The linewidth as a function of tunnel coupling strength tracks t…
We have investigated the optical and transport properties of MBE grown short-period superlattices of InAs/GaAs with different numbers of periods (3 <= N <= 24) and a total thickness 14 nm. Bandstructure calculations show that these superlattices represent a quantum well with average composition In_0.16Ga_0.84As. The electron wave functions are only slightly modulated by the superlattice potential as compared to a single quantum well with the same composition, which was grown as a reference sample. The photoluminescence, the resistance, the Shubnikov-de Haas effect and the Hall effect have been…
Geometric phase analysis has been applied to high resolution aberration corrected (scanning) transmission electron microscopy images of InAs/GaAs quantum dot (QD) materials. We show quantitatively how the lattice mismatch induced strain varies on the atomic scale and tetragonally distorts the lattice in a wide region that extends several nanometers into the GaAs spacer layer below and above the QDs. Finally, we show how V-shaped dislocations originating at the QD/GaAs interface efficiently remove most of the lattice mismatch induced tetragonal distortions in and around the QD.
We derive analytically the change of exciton fine structure splitting (FSS) under the external stresses in the self-assembled InAs/GaAs quantum dots using the Bir-Pikus model. We find that the FSS change is mainly due to the strain induced valence bands mixing and valence-conduction band coupling. The exciton polarization angle under strain are determined by the argument of the electron-hole off-diagonal exchange integrals. The theory agrees well with the empirical pseudopotential calculations.
In this work the intersubband electronic properties of two laterally coupled dome-shaped InAs/GaAs quantum dots were investigated. The envelope functions and eigenenergies were calculated as function of distance between the dots. The coupling between the dots was studied using transition lifetime between the dots. The results showed that in close distances (smaller than 3 nm) the quantum dots are coupled and by increasing the distance transition lifetime fall down drastically and the dots become uncoupled.
The influences of Si sheet doping levels on the properties of InAs/GaAs quantum dots (QDs) are investigated by atomic force microscopy (AFM) and photoluminescence (PL). AFM measurements reveal that Si sheet doping doesn't change the morphology of InAs QDs. Conductive AFM exhibits a quick current decrease when the Si doping density reaches 5\times1011cm-2. PL measurements show that the Si doping can significantly enhance the PL intensity. The PL peak intensity of InAs QDs doped to 5\times1011cm-2 is increased about thirty-five times from that of the undoped ones at 300K. The results observed he…
We investigate the noise properties of a GaAs-AlAs-GaAs tunneling structure with embedded self-assembled InAs quantum dots in the single-electron tunneling regime. We analyze the dependence of the relative noise amplitude of the shot noise on bias voltage. We observe a non-monotonic behaviour of the Fano-factor $α$ with an average value of $α\approx 0.8$ consistent with the asymmetry of the tunneling barriers. Reproducible fluctuations observed in $α$ can be attributed to the successive participation of more and more InAs quantum dots in the tunneling current.
This work presents an analysis of the electronic and optical properties of InAs/GaAs columnar quantum dots (QDs) by performing multi-million-atom tight-binding simulations. The plots of the polarisation-dependent ground state optical transition strengths predict that a nearly zero degree of polarisation can be achieved at 1550 nm emission/absorption wavelength by engineering the number of QD layers in a columnar QD. These results are promising for the design of optical devices requiring polarisation insensitive optical response such as semiconductor optical amplifiers.
Electron spin polarization up to 100% has been observed in type-II narrow-gap heterostructures with ultrathin InSb insertions in an InAs matrix via investigation of circularly polarized photoluminescence in an external magnetic field applied in Faraday geometry. The polarization degree decreases drastically, changes its sign, and saturates finally at the value of 10% in the limit of either high temperature or strong excitation. The observed effect is explained in terms of strong Zeeman splitting of the electron conduction band in the InAs matrix and a heavy-hole state confined in the InSb inse…
We report a photoluminescence (PL) spectroscopy study of charge state control in single self-assembled InAs/GaAs quantum dots by applying electric and/or magnetic fields at 4.2 K. Neutral and charged exciton complexes were observed under applied bias voltages from -0.5 V to 0.5 V by controlling the carrier tunneling. The highly negatively charged exciton emission becomes stronger with increasing pumping power, arising from the fact that electrons have a smaller effective mass than holes and are more easily captured by the quantum dots. The integrated PL intensity of negatively charged excitons…
The InAs/InGaAs DWELL solar cell grown by MBE is a standard pin diode structure with six layers of InAs QDs embedded in InGaAs quantum wells placed within a 200-nm intrinsic GaAs region. The GaAs control wafer consists of the same pin configuration but without the DWELL structure. The typical DWELL solar cell exhibits higher short current density while maintaining nearly the same open-circuit voltage for different scales, and the advantage of higher short current density is more obvious in the smaller cells. In contrast, the smaller size cells, which have a higher perimeter to area ratio, make…
Using the mechano-optical stress sensor technique, we observe a counter-intuitive reduction of the compressive stress when InAs is deposited on GaAs (001) during growth of quantum posts. Through modelling of the strain fields, we find that such anomalous behaviour can be related to the strain-driven detachment of In atoms from the crystal and their surface diffusion towards the self-assembled nanostructures.
We study the effect of valence band spin-orbit interactions on the acoustic phonon assisted spin relaxation of holes confined in quantum dots. Heavy hole-light hole (hh-lh) mixing and all the spin-orbit terms arising from zinc-blende bulk inversion asymmetry (BIA) are considered on equal footing in a fully 3D Hamiltonian. We show that hh-lh mixing and BIA have comparable contributions to the hole spin relaxation in self-assembled QDs, but BIA becomes dominant in gated QDs. The dependence of the hole spin relaxation on the QD geometry and spin splitting energy is drastically different from that…
In semiconductor quantum dots, the electron hyperfine interaction with the nuclear spin bath is the leading source of spin decoherence at cryogenic temperature. Using high-resolution two-color differential transmission spectroscopy, we demonstrate that such electron-nuclear coupling also imposes a lower limit for the positively charged exciton dephasing rate, γ, in an ensemble of InAs/GaAs quantum dots. We find that the dephasing rate is sensitive to the strength of the hyperfine interaction, which can be controlled through the application of an external magnetic field in the Faraday configura…
The dynamic response of InAs/GaAs self-assembled quantum dots (QDs) to strain is studied experimentally by periodically modulating the QDs with a surface acoustic wave and measuring the QD fluorescence with photoluminescence and resonant spectroscopy. When the acoustic frequency is larger than the QD linewidth, we resolve phonon sidebands in the QD fluorescence spectrum. Using a resonant pump laser, we have demonstrated optical frequency conversion via the dynamically modulated QD, which is the physical mechanism underlying laser sideband cooling a nanomechanical resonator by means of an embed…
Current steps attributed to resonant tunneling through individual InAs quantum dots embedded in a GaAs-AlAs-GaAs tunneling device are investigated experimentally in magnetic fields up to 28 T. The steps evolve into strongly enhanced current peaks in high fields. This can be understood as a field-induced Fermi-edge singularity due to the Coulomb interaction between the tunneling electron on the quantum dot and the partly spin polarized Fermi sea in the Landau quantized three-dimensional emitter.
We report significant deviations from the usual quadratic dependence of the ground state interband transition energy on applied electric fields in InAs/GaAs self-assembled quantum dots. In particular, we show that conventional second-order perturbation theory fails to correctly describe the Stark shift for electric field below $F = 10$ kV/cm in high dots. Eight-band ${\bf k}\cdot{\bf p}$ calculations demonstrate this effect is predominantly due to the three-dimensional strain field distribution which for various dot shapes and stoichiometric compositions drastically affects the hole ground sta…
The electronic structure of pyramidal shaped InAs/GaAs quantum dots is calculated using an eight-band strain dependent $\bf k\cdot p$ Hamiltonian. The influence of strain on band energies and the conduction-band effective mass are examined. Single particle bound-state energies and exciton binding energies are computed as functions of island size. The eight-band results are compared with those for one, four and six bands, and with results from a one-band approximation in which m(r) is determined by the local value of the strain. The eight-band model predicts a lower ground state energy and a la…
We investigated the current-voltage characteristic of InAs/GaAs quantum dot intermediate band solar cells (QD IBSCs) with different n-type doping density in the QD layer. The n-type doping evidently increases the open circuit voltage, meanwhile decreases the short circuit current density, and leads to the conversion efficiency approaching that of the control solar cell, that is the major role of n-type doping is to suppress the effects of QDs on the current-voltage characteristic. Our model adopts practical parameters for simulation rather than those from detailed balanced method, so that the …
A transition from a cylindrical quantum dot to a highly elongated quantum dash is theoretically studied here with an atomistic approach combining empirical tight binding for single particle states and configuration interaction method for excitonic properties. Large nanostructure shape anisotropy leads to a peculiar trend of the bright exciton splitting, which at certain point is quenched with further shape elongation, contradicting predictions of simplified models. Moreover strong shape elongation promotes pronounced optical activity of the dark exciton, that can reach substantial $1\%$ fracti…
We report a valley photonic crystal (VPhC) waveguide in a GaAs slab with InAs quantum dots (QDs) as an internal light source exploited for experimental characterization of the waveguide. A topological interface state formed at the interface between two topologically-distinct VPhCs is used as the waveguide mode. We demonstrate robust propagation for near-infrared light emitted from the QDs even under the presence of sharp bends as a consequence of the topological protection of the guided mode. Our work will be of importance for developing robust photonic integrated circuits with small footprint…
Superlattices are promising low-dimensional nanomaterials for thermoelectric technology that is capable of directly converting low-grade heat energy to useful electrical power. In this work, the thermal conductivities of GaAs/Ge superlattice nanostructures were investigated systematically in relation to their morphologies and interfaces. Thermal conductivities were measured using ultrafast time-domain thermoreflectance and were found to decrease with increasing interface densities, consistent with our understanding of microscopic phonon transport in the particle regime. Lower thermal conductiv…
A nano-fabrication technique is presented which enables the fabrication of highly tunable devices on p-type, C-doped GaAs/AlGaAs heterostructures containing shallow two-dimensional hole systems. The high tunability of these structures is provided by the complementary electrostatic effects of intrinsic in-plane gates and evaporated metallic top-gates. Quantum point contacts fabricated with this technique were tested by electrical conductance spectroscopy.
Coupled hybrid nanostructures are demonstrated using the combination of lithographically patterned graphene on top of a two-dimensional electron gas (2DEG) buried in a GaAs/AlGaAs heterostructure. The graphene forms Schottky barriers at the surface of the heterostructure and therefore allows tuning the electronic density of the 2DEG. Conversely, the 2DEG potential can tune the graphene Fermi energy. Graphene-defined quantum point contacts in the 2DEG show half-plateaus of quantized conductance in finite bias spectroscopy and display the 0.7 anomaly for a large range of densities in the constri…
We present a simulation to characterize the dependence on hydrostatic pressure for the photoluminescence spectra in self-assembled quantum dots with lens shape geometry. We have tested the physical effects of the band offset and electron-hole effective masses on the optical emission in dot lens. The model could be implemented to get qualitative information of the parameters involved in the quantum dot or the measured optical properties as function of pressure.
A detailed theoretical study of the optical absorption in self-assembled quantum dots is presented in this paper. A rigorous atomistic strain model as well as a sophisticated electronic band structure model are used to ensure accurate prediction of the optical transitions in these devices . The optimized models presented in this paper are able to reproduce the experimental results with an error less than 1$\%$. The effects of incident light polarization, alloy mole fraction, quantum dot dimensions, and doping have been investigated. The in-plane polarized light absorption is more significant t…
The electronic properties and nanostructure of InAs nanowires are correlated by creating multiple field effect transistors (FETs) on nanowires grown to have low and high defect density segments. 4.2 K carrier mobilities are ~4X larger in the nominally defect-free segments of the wire. We also find that dark field optical intensity is correlated with the mobility, suggesting a simple route for selecting wires with a low defect density. At low temperatures, FETs fabricated on high defect density segments of InAs nanowires showed transport properties consistent with single electron charging, even…
The hot carrier dynamics and its effect on the device performance of GaAs solar cell and InAs/GaAs quantum dot solar cell (QDSC) was investigated. At first, the fundamental operation feature of conventional hot carrier solar cell was simulated based on the detailed balance thermodynamic model. Then we investigated the hot carrier dynamics in the normal junction based solar cell using hydrodynamic/energy Boltzmann transportation model (HETM) where the two temperature (carrier temperature and lattice temperature are treated separately. For the first time, we report an inherent quasi-equivalence …
We present a detailed study of the use of Fabry-Perot (FP) cavities for the spectroscopy of single InAs quantum dots (QDs). We derive optimal cavity characteristics and resolution limits, and measure photoluminescence linewidths as low as 0.9 GHz. By embedding the QDs in a planar cavity, we obtain a sufficiently large signal to actively feed back on the length of the FP to lock to the emission of a single QD with a stability below 2% of the QD linewidth. An integration time of approximately two seconds is found to yield an optimum compromise between shot noise and cavity length fluctuations.
We study the electronic properties of GaAs nanowires composed of both the zincblende and wurtzite modifications using a ten-band k.p model. In the wurtzite phase, two energetically close conduction bands are of importance for the confinement and the energy levels of the electron ground state. These bands form two intersecting potential landscapes for electrons in zincblende/wurtzite nanostructures. The energy difference between the two bands depends sensitively on strain, such that even small strains can reverse the energy ordering of the two bands. This reversal may already be induced by the …
The purpose of this research is to study laser dynamics of InAs/GaAs Quantum Dot Lasers (QDLs) by changing QD energy levels. To date, most of the investigations have focused on only one of these circumstances, and hardly the result of change in the energy levels can be seen in lasing. In this work, in the first step, energy levels of lens-shape QDs are investigated by the eight-band k.p method, their variation for different QD sizes are surveyed, and recombination energies of the discrete levels are determined. Then, by representing a three-level InAs/GaAs QD laser, dynamics of such a laser de…
Interplay between Aharonov-Bohm and Altshuler-Aronov-Spivak oscillations in phase-pure GaAs/InAs core/shell nanowires of different lengths
Forschungszentrum Jülich（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；Reykjavik University（雷克雅未克大学）；The University of Birmingham（伯明翰大学）；University of Warwick（华威大学）
Two dimensional InAs/GaAs quantum ring (QR) is considered using the effective potential approach. The symmetry of QR shape is violated as it is in the well-known Bohigas annular billiard. We calculate energy spectrum and studied the spatial localization of a single electron in such QR. For weak violation of the QR shape symmetry, the spectrum is presented as a set of quasi-doublets. Tunneling between quasi-doublet states is studied by the dependence on energy of the states. The dependence is changed with variation of the QR geometry that is related to the eccentricity of the QR. An interpretat…
