We report electronic transport on silicon double and triple dots created with the optimized number of two gates. Using silicon nitride spacers two dots in series are created below two top gates overlapping a silicon nanowire. Coupling between dots is controlled by gate voltages. A third dot is created either by combined action of gate voltages or local doping depending on the spacers length. The main characteristics of the triple dot stability diagram are quantitatively fitted.
Spins of donor electrons and nuclei in silicon are promising quantum bit (qubit) candidates which combine long coherence times with the fabrication finesse of the silicon nanotechnology industry. We outline a potentially scalable spin qubit architecture where donor nuclear and electron spins are coupled to spins of electrons in quantum dots and discuss requirements for donor placement aligned to quantum dots by single ion implantation.
We electrically measure intrinsic silicon quantum dots with electrostatically defined tunnel barriers. The presence of both p-type and n-type ohmic contacts enables the accumulation of either electrons or holes. Thus we are able to study both transport regimes within the same device. We investigate the effect of the tunnel barriers and the electrostatically defined quantum dots. There is greater localisation of charge states under the tunnel barriers in the case of hole conduction leading to higher charge noise in the p-regime.
We report on ambipolar gate-defined quantum dots in silicon on insulator (SOI) nanowires fabricated using a customised complementary metal-oxide-semiconductor (CMOS) process. The ambipolarity was achieved by extending a gate over an intrinsic silicon channel to both highly doped n-type and p-type terminals. We utilise the ability to supply ambipolar carrier reservoirs to the silicon channel to demonstrate an ability to reconfigurably define, with the same electrodes, double quantum dots with either holes or electrons. We use gate-based reflectometry to sense the inter-dot charge transition(IDT…
We report charge sensing measurements on a silicon quantum dot (QD) with a nearby silicon single electron transistor (SET) acting as an electrometer. The devices are electrostatically formed in bulk silicon using surface gates. We show that as an additional electron is added onto the quantum dot, a charge is induced on the SET of approximately 0.2e. These measurements are performed in the many electron regime, where we can count in excess of 20 charge additions onto the quantum dot.
We integrate ambipolar quantum dots in silicon fin field-effect transistors using exclusively standard complementary metal-oxide-semiconductor fabrication techniques. We realize ambipolarity by replacing conventional highly-doped source and drain electrodes by a metallic nickel silicide with Fermi level close to the silicon mid-gap position. Such devices operate in a dual mode, either as classical field-effect or single-electron transistor. We implement a classical logic NOT gate at low temperature by tuning two interconnected transistors into opposite polarities. In the quantum regime, we dem…
We present a novel reconfigurable metal-oxide-semiconductor multi-gate transistor that can host a quadruple quantum dot in silicon. The device consist of an industrial quadruple-gate silicon nanowire field-effect transistor. Exploiting the corner effect, we study the versatility of the structure in the single quantum dot and the serial double quantum dot regimes and extract the relevant capacitance parameters. We address the fabrication variability of the quadruple-gate approach which, paired with improved silicon fabrication techniques, makes the corner state quantum dot approach a promising …
We study the optical properties of hydrogen passivated silicon, germanium and mixed Ge/Si core/shell quantum dots (QDs) using high accuracy Density Functional Theory (DFT) and time-dependent DFT (TDFT). We employ the hybrid DFT functional of Becke, Lee, Yang and Parr (B3LYP) in combination with good quality basis sets. As we have shown in our previous work, this combination is an accurate and computationally efficient way for such calculations. The mixed quantum dots, as would be expected, are more versatile and offer more possibilities for band gap engineering, with gap values (electronic and…
We present data on the electrical transport properties of highly-doped silicon-on-insulator quantum dots under the effect of pulsed magnetic fields up to 48 T. At low field intensities, B<7 T, we observe a strong modification of the conductance due to the destruction of weak localization whereas at higher fields, where the magnetic field length becomes comparable to the effective Bohr radius of phosphorous in silicon, a strong decrease in conductance is demonstrated. Data in the high and low electric field bias regimes are then compared to show that close to the Coulomb blockade edge magnetica…
We report charge detection in degenerately phosphorus-doped silicon double quantum dots (DQD) electrically connected to an electron reservoir. The sensing device is a single electron transistor (SET) patterned in close proximity to the DQD. Measurements performed at 4.2K show step-like behaviour and shifts of the Coulomb Blockade oscillations in the detector's current as the reservoir's potential is swept. By means of a classical capacitance model, we demonstrate that the observed features can be used to detect single-electron tunnelling from, to and within the DQD, as well as to reveal the DQ…
Reliable detection of single electron tunneling in quantum dots (QD) is paramount to use this category of device for quantum information processing. Here, we report charge sensing in a degenerately phosphorus-doped silicon QD by means of a capacitively coupled single-electron tunneling device made of the same material. Besides accurate counting of tunneling events in the QD, we demonstrate that this architecture can be operated to reveal asymmetries in the transport characteristic of the QD. Indeed, the observation of gate voltage shifts in the detector's response as the QD bias is changed is …
We have observed a negative differential conductance with singular gate and source-drain bias dependences in a phosphorus-doped silicon quantum dot. Its origin is discussed within the framework of weak localization. By measuring the current-voltage characteristics at different temperatures as well as simulating the tunneling rates dependences on energy, we demonstrate that the presence of shallow energy defects together with an enhancement of localization satisfactory explain our observations. Effects observed in magnetic fields are also discussed.
Deterministic control over the location and number of donors is crucial to donor spin quantum bits (qubits) in semiconductor based quantum computing. In this work, a focused ion beam is used to implant antimony donors close to quantum dots. Ion detectors are integrated next to the quantum dots to sense the implants. The numbers of donors implanted can be counted to a precision of a single ion. In low-temperature transport measurements, regular coulomb blockade is observed from the quantum dots. Charge offsets indicative of donor ionization are also observed in devices with counted donor implan…
Many electrical applications of quantum dots rely on capacitively coupled gates; therefore, to make reliable devices we need those gate capacitances to be predictable and reproducible. We demonstrate in silicon nanowire quantum dots that gate capacitances are reproducible to within 10% for nominally identical devices. We demonstrate the experimentally that gate capacitances scale with device dimensions. We also demonstrate that a capacitance simulator can be used to predict measured gate capacitances to within 20%. A simple parallel plate capacitor model can be used to predict how the capacita…
The bandstructure of bulk silicon has a six-fold valley degeneracy. Strain in the Si/SiGe quantum well system partially lifts the valley degeneracy, but the materials factors that set the splitting of the two lowest lying valleys are still under intense investigation. We propose a method for accurately determining the valley splitting in Si/SiGe double quantum dots embedded into a superconducting microwave resonator. We show that low lying valley states in the double quantum dot energy level spectrum lead to readily observable features in the cavity transmission. These features generate a "fin…
We replace the established aluminium gates for the formation of quantum dots in silicon with gates made from palladium. We study the morphology of both aluminium and palladium gates with transmission electron microscopy. The native aluminium oxide is found to be formed all around the aluminium gates, which could lead to the formation of unintentional dots. Therefore, we report on a novel fabrication route that replaces aluminium and its native oxide by palladium with atomic-layer-deposition-grown aluminium oxide. Using this approach, we show the formation of low-disorder gate-defined quantum d…
We study double quantum dots in a Ge/SiGe heterostructure and test their maturity towards singlet-triplet ($S-T_0$) qubits. We demonstrate a large range of tunability, from two single quantum dots to a double quantum dot. We measure Pauli spin blockade and study the anisotropy of the $g$-factor. We use an adjacent quantum dot for sensing charge transitions in the double quantum dot at interest. In conclusion, Ge/SiGe possesses all ingredients necessary for building a singlet-triplet qubit.
The presence of degenerate conduction band valleys and how they are mixed by interfaces play critical roles in determining electron interaction and spectrum in a silicon nanostructure. Here we investigate how the valley phases affect the exchange interaction in a symmetric two-electron silicon double quantum dot. Through a configuration interaction calculation, we find that exchange splitting is suppressed at a finite value of valley phase difference between the two dots, and reaches its minimum value ({\sim} 0) when the phase difference is π. Such a suppression can be explained using the Hubb…
In this Report we show the role of charge defects in the context of the formation of electrostatically defined quantum dots. We introduce a barrier array structure to probe defects at multiple locations in a single device. We measure samples both before and after an annealing process which uses an Al$_2$O$_3$ overlayer, grown by atomic layer deposition. After passivation of the majority of charge defects with annealing we can electrostatically define hole quantum dots up to 180 nm in length. Our ambipolar structures reveal amphoteric charge defects that remain after annealing with charging ene…
We describe important considerations to create top-down fabricated planar quantum dots in silicon, often not discussed in detail in literature. The subtle interplay between intrinsic material properties, interfaces and fabrication processes plays a crucial role in the formation of electrostatically defined quantum dots. Processes such as oxidation, physical vapor deposition and atomic-layer deposition must be tailored in order to prevent unwanted side effects such as defects, disorder and dewetting. In two directly related manuscripts written in parallel we use techniques described in this wor…
We present a systematic study of various ways (top gates, local doping, substrate bias) to fabricate and tune multi-dot structures in silicon nanowire multigate MOSFETs (metal-oxide-semiconductor field-effect transistors). The carrier concentration profile of the silicon nanowire is a key parameter to control the formation of tunnel barriers and single-electron islands. It is determined both by the doping profile of the nanowire and by the voltages applied to the top gates and to the substrate. Local doping is achieved with the realisation of up to two arsenic implantation steps in combination…
We report the fabrication and electrical characterization of depletion-mode quantum dots in a two-dimensional hole gas (2DHG) in intrinsic silicon. We use fixed charge in a SiO$_2$/Al$_2$O$_3$ dielectric stack to induce a 2DHG at the Si/SiO$_2$ interface. Fabrication of the gate structures is accomplished with a single layer metallization process. Transport spectroscopy reveals regular Coulomb oscillations with charging energies of 10-15 meV and 3-5 meV for the few- and many-hole regimes, respectively. This depletion-mode design avoids complex multilayer architectures requiring precision align…
The heteroepitaxy of III-V semiconductors on silicon is a promising approach for making silicon a photonic platform for on-chip optical interconnects and quantum optical applications. Monolithic integration of both material systems is a long-time challenge, since different material properties lead to high defect densities in the epitaxial layers. In recent years, nanostructures however have shown to be suitable for successfully realising light emitters on silicon, taking advantage of their geometry. Facet edges and sidewalls can minimise or eliminate the formation of dislocations, and due to t…
Weakly coupled quantum dots in the Pauli spin blockade regime are considered with respect to spin-dependent transport. By attaching one half-metallic and one non-magnetic lead, the Pauli spin blockade if formed by a pure triplet state with spin moment $S_z=1$ or -1. Furthermore, additional spin blockade regimes emerge because of full occupation in states with opposite spin to that of the half-metallic lead.
We apply an elementary measurement scheme to calculate the electronic triplet-singlet transition mediated by hyperfine interaction in a double quantum dot. We show how the local character of the hyperfine interaction and the nuclear back-action process (flip-flop) are crucial to cancel destructive interferences of the triplet-singlet transition probability. It is precisely this cancellation which differentiates the hyperfine interaction from an anisotropic magnetic field which mixes the triplet and the singlet eigenstates.
Electronic states in silicon quantum dots are examined theoretically, taking into account a multivalley structure of the conduction band. We find that (i) exchange interaction hardly works between electrons in different valleys. In consequence electrons occupy the lowest level in different valleys in the absence of Hund's coupling when the dot size is less than 10 nm. High-spin states are easily realized by applying a small magnetic field. (ii) When the dot size is much larger, the electron-electron interaction becomes relevant in determining the electronic states. Electrons are accommodated i…
A fundamental question in quantum transport is how quantum coherence influences charge transfer through nanostructures. We address this issue for linear triple quantum dots by comparison of a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics for coherent and sequential charge tunneling, respectively. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of lar…
A scaled quantum computer with donor spins in silicon would benefit from a viable semiconductor framework and a strong inherent decoupling of the qubits from the noisy environment. Coupling neighbouring spins via the natural exchange interaction according to current designs requires gate control structures with extremely small length scales. We present a silicon architecture where bismuth donors with long coherence times are coupled to electrons that can shuttle between adjacent quantum dots, thus relaxing the pitch requirements and allowing space between donors for classical control devices. …
Electronic transport through a triple quantum dot system, with only a single dot coupled directly to external leads, is considered theoretically. The model includes Coulomb correlations in the central dot, while such correlations in the two side-coupled dots are omitted. The infinite-U mean-field slave-boson approach is used to obtain basic transport characteristics in the Kondo regime. When tuning position of the side-coupled dots' levels, transition from subradiant to superradiant like mode (and vice versa) has been found in the spectral function, in analogy to the Dicke effect in atomic phy…
The controlled depletion of electrons in semiconductors is the basis for numerous devices. Reactive-ion etching provides an effective technique for fabricating both classical and quantum devices. However, Fermi level pinning can occur, and must be carefully considered in the development of small devices, such as quantum dots. Because of depletion, the electrical size of the device is reduced in comparison with its physical dimension. To investigate this issue, we fabricate several types of devices in silicon-germanium heterostructures using two different etches, CF$_4$ and SF$_6$. We estimate …
Extremely long coherence times, excellent single-qubit gate fidelities and two-qubit logic have been demonstrated with silicon metal-oxide-semiconductor spin qubits, making it one of the leading platforms for quantum information processing. Despite this, a long-standing challenge in this system has been the demonstration of tunable tunnel coupling between single electrons. Here we overcome this hurdle with gate-defined quantum dots and show couplings that can be tuned on and off for quantum operations. We use charge sensing to discriminate between the (2,0) and (1,1) charge states of a double …
We analyze transport through both a double quantum dot and a triple quantum dot with inhomogeneous Zeeman splittings in the presence of crossed dc and ac magnetic fields. We find that strongly spin-polarized current can be achieved by tuning the relative energies of the Zeeman-split levels of the dots, by means of electric gate voltages: depending on the energy level detuning, the double quantum dot works either as spin-up or spin-down filter. We show that a triple quantum dot in series under crossed dc and ac magnetic fields can act not only as spin-filter but also as spin-inverter.
We analyze coherent spin phenomena in triple quantum dots in triangular configuration under crossed DC and AC magnetic fields. In particular, we discuss the interplay between Aharonov-Bohm current oscillations, coherent electron trapping and spin blockade under electron spin resonance conditions. We demonstrate that, for certain field frequencies, AC magnetic fields induce an antiresonant behavior in the current, allowing for both removal and restoration of entangled spin blockaded states by tuning the AC field frequency. Our theoretical predictions indicate how to manipulate spin qubits in a …
We study exchange coupling in Si double quantum dots, which have been proposed as suitable candidates for spin qubits due to their long spin coherence times. We discuss in detail two alternative schemes which have been proposed for implementing spin qubits in quantum dots. One scheme uses spin states in a single dot and the interdot exchange coupling controls interactions between unbiased dots. The other scheme employs the singlet and triplet states of a biased double dot as the two-level system making up the qubit and exchange controls the energy splitting of the levels. Exchange in these two…
We perform an excited state spectroscopy analysis of a silicon corner dot in a nanowire field-effect transistor to assess the electric field tunability of the valley splitting. First, we demonstrate a back-gate-controlled transition between a single quantum dot and a double quantum dot in parallel that allows tuning the device in to corner dot formation. We find a linear dependence of the valley splitting on back-gate voltage, from $880~μ\text{eV}$ to $610~μ\text{eV}$ with a slope of $-45\pm 3~μ\text{eV/V}$ (or equivalently a slope of $-48\pm 3~μ\text{eV/(MV/m)}$ with respect to the effective …
Quantum shot noise probes the dynamics of charge transfers through a quantum conductor, reflecting whether quasiparticles flow across the conductor in a steady stream, or in syncopated bursts. We have performed high-sensitivity shot noise measurements in a quantum dot obtained in a silicon metal-oxide-semiconductor field-effect transistor. The quality of our device allows us to precisely associate the different transport regimes and their statistics with the internal state of the quantum dot. In particular, we report on large current fluctuations in the inelastic cotunneling regime, correspond…
We propose a novel concept of achieving silicon quantum dots with radiative rates enhanced by more than two orders of magnitude up to the values characteristic for direct band gap semiconductors. Our tight-binding simulations show how the surface engineering can dramatically change the density of confined electrons in real- and $k$-space and give rise to the new conduction band levels in $Γ$-valley, thus promoting the direct radiative transitions. The effect may be realized by covering the silicon dots with covalently bonded electronegative ligands, such as alkyl or teflon chains and/or by emb…
Holes in silicon quantum dots are receiving significant attention due to their potential as fast, tunable, and scalable qubits in semiconductor quantum circuits. Despite this, challenges remain in this material system including difficulties using charge sensing to determine the number of holes in a quantum dot, and in controlling the coupling between adjacent quantum dots. In this work, we address these problems by fabricating an ambipolar complementary metal-oxide-semiconductor (CMOS) device using multilayer palladium gates. The device consists of an electron charge sensor adjacent to a hole …
We present a comprehensive and integrated model-independent ab initio study of the structural, cohesive, electronic, and optical properties of silicon quantum dots of various morphologies and sizes in the framework of all-electron static and time-dependent density functional theory (DFT, TDFT), using the well-tested B3LYP and other properly chosen functional(s). Our raw ab initio results for all these properties for hydrogen passivated nanocrystals of various growth models and sizes from 1 to 32 Angstroms, are subsequently fitted, using power-law dependence with judicially selected exponents, …
Preparation and transfer of quantum states is a fundamental task in quantum information. We propose a protocol to prepare a state in the left and center quantum dots of a triple dot array and transfer it directly to the center and right dots. Initially the state in the left and center dots is prepared combining the exchange interaction and magnetic field gradients. Once in the desired state, ac gate voltages in the outer dots are switched on, allowing to select a given photoassisted long-range path and to transfer the prepared state directly from one edge to the other with high fidelity. We in…
Tunneling in a quantum coherent structure is not restricted to only nearest neighbours. Hopping between distant sites is possible via the virtual occupation of otherwise avoided intermediate states. Here we report the observation of long range transitions in the transport through three quantum dots coupled in series. A single electron is delocalized between the left and right quantum dots while the centre one remains always empty. Superpositions are formed and both charge and spin are exchanged between the outermost dots. Detection of the process is achieved via the observation of narrow reson…
We report highly tunable control of holes in Ge/Si core/shell nanowires (NWs). We demonstrate the ability to create single quantum dots (QDs) of various sizes, with low hole occupation numbers and clearly observable excited states. For the smallest dot size we observe indications of single-hole occupation. Moreover, we create double and triple tunnel-coupled quantum dot arrays. In the double quantum dot configuration we observe Pauli spin blockade (PSB). These results open the way to perform hole spin qubit experiments in these devices.
We show that spin-orbit coupling in a quantum dot molecule allows for coherent manipulation of two electron spin states using Raman transitions. Such two-electron spin states defined by the singlet and triplet states of two exchange coupled quantum dots can have favorable coherence properties. In addition, two of the four metastable ground states in this system can be used as auxiliary states that could facilitate implementation of tasks such as mapping of spin states to that of a single propagating photon. We find that even weak spin-orbit effects -- manifesting themselves as slightly differe…
Silicon quantum dots are considered an excellent platform for spin qubits, partly due to their weak spin-orbit interaction. However, the sharp interfaces in the heterostructures induce a small but significant spin-orbit interaction which degrade the performance of the qubits or, when understood and controlled, could be used as a powerful resource. To understand how to control this interaction we build a detailed profile of the spin-orbit interaction of a silicon metal-oxide-semiconductor double quantum dot system. We probe the derivative of the Stark shift, $g$-factor and $g$-factor difference…
We investigate by low-temperature transport experiments the sub-threshold behavior of triple-gate silicon field-effect transistors. These three-dimensional nano-scale devices consist of a lithographically defined silicon nanowire surrounded by a gate with an active region as small as a few tens of nanometers, down to 50x60x35 nm^3. Conductance versus gate voltage show Coulomb-blockade oscillations with a large charging energy due to the formation of a small potential well below the gate. According to dependencies on device geometry and thermionic current analysis, we conclude that sub-threshol…
We investigate spin-flip processes of Si quantum dots due to spin-orbit coupling. We utilize the spin-orbit coupling constants related to bulk and structure inversion asymmetry obtained numerically for two dimensional heterostructures. We find that the spin-flip rate is very sensitive to these coupling constants. We investigate the nuclei-mediated spin-flip process and find the level of the isotope $^{29}$Si concentration for which this mechanism become dominant.
We consider the transport through a system of three coupled quantum dots in a perpendicular magnetic field. At zero field, destructive interference can trap an electron in a dark state -- a coherent superposition of dot states that completely blocks current flow. The magnetic field can disrupt this interference giving rise to oscillations in the current and its higher-order statistics as the field is increased. These oscillations have a period of either the flux-quantum or half the flux-quantum, depending on the dot geometry. We give results for the stationary current and for the shotnoise and…
We investigate the Josephson effect in one triple-terminal junction with embedded parallel-coupled double quantum dots. It is found that the inter-superconductor supercurrent has opportunities to oscillate in $4π$ period, with the adjustment of the phase differences among the superconductors. What is notable is that such a result is robust and independent of fermion parities, intradot Coulomb strength, and the dot-superconductor coupling manner. By introducing the concept of spinful many-particle Majorana modes, we present the analytical definition of the Majorana operator via superposing elec…
We investigate small artificial quantum dots obtained by geometrically controlled resistive confinement in low mobility silicon-on-insulator nanowires. Addition spectra were recorded at low temperature for various dot areas fixed by lithography. We compare the standard deviation of the addition spectra with theory in the high electron concentration regime. We find that the standard deviation scales as the inverse area of the dot and its absolute value is comparable to the energy spacing of the one particle spectrum.
We calculate, via spin density functional theory (SDFT) and exact diagonalization, the eigenstates for electrons in a variety of external potentials, including double and triple dots. The SDFT calculations employ realistic wafer profiles and gate geometries and also serve as the basis for the exact diagonalization calculations. The exchange interaction J between electrons is the difference between singlet and triplet ground state energies and reflects competition between tunneling and the exchange matrix element, both of which result from overlap in the barrier. For double dots, a characterist…
We expand on previous work that treats relaxation physics of low-lying excited states in ideal, single electron, silicon quantum dots in the context of quantum computing. These states are of three types: orbital, valley, and spin. The relaxation times depend sensitively on system parameters such as the dot size and the external magnetic field. Generally, however, orbital relaxation times are short in strained silicon (from a tenth of a microsecond to picoseconds), spin relaxation times are long (microseconds to greater than seconds), while valley relaxation times are expected to lie in between…
In the semi-conductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle in the way towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose singlet-triplet qubits based on two quantum dots of different sizes. Such asymmetric double dot systems allow the implementation of exchange gates with controllable exchange splitting $J$ operated in the do…
The effect of long distance coherent tunneling (LDCT) on the charge and heat currents in serially coupled triple quantum dots (TQDs) connected to electrodes is illustrated by using a combination of the extended Hurbbard model and Anderson model. The charge and heat currents are calculated with a closed-form Landauer expression for the transmission coefficient suitable for the Coulomb blockade regime. The physical parameters including bias-dependent quantum dot energy levels, electron Coulomb interactions, and electron hopping strengths are calculated in the framework of effective mass theory f…
We review our recent efforts in building atom-scale quantum-dot cellular automata circuits on a silicon surface. Our building block consists of silicon dangling bond on a H-Si(001) surface, which has been shown to act as a quantum dot. First the fabrication, experimental imaging, and charging character of the dangling bond are discussed. We then show how precise assemblies of such dots can be created to form artificial molecules. Such complex structures can be used as systems with custom optical properties, circuit elements for quantum-dot cellular automata, and quantum computing. Consideratio…
Few-electron quantum dots are investigated in the regime of strong tunneling to the leads. Inelastic cotunneling is used to measure the two-electron singlet-triplet splitting above and below a magnetic field driven singlet-triplet transition. Evidence for a non-equilibrium two-electron singlet-triplet Kondo effect is presented. Cotunneling allows orbital correlations and parameters characterizing entanglement of the two-electron singlet ground state to be extracted from dc transport.
The magnetic character of the ground-state of two electrons on a double quantum dot, connected in series to left and right single-channel leads, is considered. By solving exactly for the spectrum of the two interacting electrons, it is found that the coupling to the continuum of propagating states on the leads, in conjunction with the electron-electron interactions, may result in a delocalization of the bound state of the two electrons. This, in turn, reduces significantly the range of the Coulomb interaction parameters over which singlet-triplet transitions can be realized. It is also found t…
