Bardeen's tunneling theory applied to intraorbital and interorbital hopping integrals between dopants in silicon

We utilize Bardeen's tunneling theory to calculate intra- and interorbital hopping integrals between phosphorus donors in silicon using known orbital wave functions. While the two-donor problem can be solved directly, the knowledge of hoppings for various pairs of orbitals is essential for constructing multi-orbital Hubbard models for chains and arrays of donors. To assure applicability to long-range potentials, we rederive Bardeen's formula for the matrix element without assuming non-overlapping potentials. Moreover, we find a correction to the original expression allowing us to use it at short distances. We also show that accurate calculation of the lowest donor-pair eigenstates is possible based on these tunnel couplings, and we characterize the obtained states. The results are in satisfactory quantitative agreement with those obtained with the standard H\"uckel tight-binding method. The calculation relies solely on the wave functions in the barrier region and does not explicitly involve donor or lattice potentials, which has practical advantages. We find that neglecting the central correction potential in the standard method may lead to qualitatively incorrect results, while its explicit inclusion raises severe numerical problems, as it is contained in a tiny volume. In contrast, using wave functions obtained with this correction in the proposed method does not raise such issues. Nominally, the computational cost of the method is to calculate a double integral along the plane that separates donors. For donor separation in directions where valley interference leads to oscillatory behavior, additional averaging over the position of the integration plane is needed. Despite this, the presented approach offers a competitive computational cost as compared to the standard one. This work may be regarded as a benchmark of a promising method for calculating hopping integrals in lattice models.Comment: 12 pages, 11 figure

Quantum dots as optimized chiral emitters for photonic integrated circuits

Chiral coupling, which allows directional interactions between quantum dots (QDs) and photonic crystal waveguide modes, holds promise for enhancing the functionality of quantum photonic integrated circuits. Elliptical polarizations of QD transitions offer a considerable enhancement in directionality. However, in epitaxial QD fabrication, the lack of precise control over lateral QD positions still poses a challenge in achieving efficient chiral interfaces. Here, we present a theoretical analysis in which we propose to optimize the polarization of a QD emitter against the spatially averaged directionality and demonstrate that the resulting emitter offers a considerable technological advantage in terms of the size and location of high-directionality areas of the waveguide as well as their overlap with the regions of large Purcell enhancement, thereby improving the scalability of the device. Moreover, using $\mathbf{\mathit{k}}\cdot\mathbf{\mathit{p}}$ modeling, we demonstrate that the optimal elliptical polarization can be achieved for neutral exciton transitions in a realistic QD structure. Our results present a viable path for efficient chiral coupling in QD-based photonic integrated circuits, to a large extent overcoming the challenges and limitations of the present manufacturing technology.Comment: Some text modifications in the Introduction, references added, typos corrected, Fig. 7 updated, and the title change

Impact of MBE-grown (In,Ga)As/GaAs metamorphic buffers on excitonic and optical properties of single quantum dots with single-photon emission tuned to the telecom range

Tuning GaAs-based quantum emitters to telecom wavelengths makes it possible to use the existing mature technology for applications in, e.g., long-haul ultra-secure communication in the fiber networks. A promising method re-developed recently is to use a metamorphic InGaAs buffer that redshifts the emission by reducing strain. However, the impact of such a buffer causes also a simultaneous modification of other quantum dot properties. Knowledge of these effects is crucial for actual implementations of QD-based non-classical light sources for quantum communication schemes. Here, we thoroughly study single GaAs-based quantum dots grown by molecular-beam epitaxy on specially designed, digital-alloy InGaAs metamorphic buffers. With a set of structures varying in the buffer indium content and providing quantum dot emission through the telecom spectral range up to 1.6 $\mu$m, we analyze the impact of the buffer and its composition on QD structural and optical properties. We identify the mechanisms of quantum dot emission shift with varying buffer composition. We also look into the charge trapping processes and compare excitonic properties for different growth conditions with single-dot emission successfully shifted to both, the second and the third telecom windows.Comment: 20 pages, 9 figure

Lateral interdot coupling among dense ensemble of InAs quantum dots grown on InP substrate observed at cryogenic temperatures

The lateral interdot coupling is investigated in high density (~10 cm−2 ) self-assembled InAs quantum dots (QDs) grown on an InP substrate. Two types of structures are selected for this study, in which QDs are embedded into an InAlAs matrix, forming nearly twice stronger confinement for an electron and a hole than expected for an InAlGaAs counterpart. Resonantly injected low carrier population in these families of QDs gives very different spectral and temporal response in the temperature range of 5-30 K. While InAs/InAlGaAs QDs show monotonic temperature quench of photoluminescence (PL), the process seems to be ineffective in the family of InAs/InAlAs dots. Moreover, the PL decay traces for InAs/InAlGaAs QDs reveal a two-exponential decay as compared to a mono-exponential one observed for InAs/InAlAs dots. While a short decay component of ≤1.9 ns has been attributed to recombination of an electron-hole pair confined in the dot, the long one of >2.4 ns, observed exclusively for InAs/InGaAlAs QDs, is attributed to recombination of spatially separated electron-hole pairs formed due to carrier exchange between adjacent dots.ISSN:1742-6588ISSN:1742-659