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Chains and arrays of phosphorus donors in silicon have recently been used to demonstrate dopant-based quantum simulators. The dopant disorder present in fabricated devices must be accounted for. Here, we theoretically study transport through disordered donor-based $3\times 3$ arrays that model recent experimental results. We employ a theory that combines the exact diagonalization of an extended Hubbard model of the array with a non-equilibrium Green's function formalism to model transport in interacting systems. We show that current flow through the array and features of measured stability diagrams are highly resilient to disorder. We interpret this as an emergence of uncomplicated behavior in the multi-electron system dominated by strong correlations, regardless of array filling, where the current follows the shortest paths between source and drain sites that avoid possible obstacles. The reference $3\times 3$ array has transport properties very similar to three parallel 3-site chains coupled only by interchain Coulomb interaction, which indicates a challenge in characterizing such devices., Comment: 8 pages, 6 figures

We characterize the single-electron energies and the wavefunction structure of arrays with two, three, and four phosphorus atoms in silicon by implementing atomistic tight-binding calculations and analyzing wavefunction overlaps to identify the single-dopant states that hybridize to make the array states. The energy spectrum and wavefunction overlap variation as a function of dopant separation for these arrays shows that hybridization mostly occurs between single-dopant states of the same type, with some cross-hybridization between $A_1$ and $E$ states occurring at short separations. We also observe energy crossings between hybrid states of different types as a function of impurity separation. We then extract tunneling rates for electrons in different dopants by mapping the state energies into hopping Hamiltonians in the site representation. Significantly, we find that diagonal and nearest neighbor tunneling rates are similar in magnitude in a square array. Our analysis also accounts for the shift of the on-site energy at each phosphorus atom resulting from the nuclear potential of the other dopants. This approach constitutes a solid protocol to map the electron energies and wavefunction structure into Fermi-Hubbard Hamiltonians needed to implement and validate analog quantum simulations in these devices.

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 figures

Cryo-electron microscopy (cryo-EM) has revolutionized experimental protein structure determination. Despite advances in high resolution reconstruction, a majority of cryo-EM experiments provide either a single state of the studied macromolecule, or a relatively small number of its conformations. This reduces the effectiveness of the technique for proteins with flexible regions, which are known to play a key role in protein function. Recent methods for capturing conformational heterogeneity in cryo-EM data model it in volume space, making recovery of continuous atomic structures challenging. Here we present a fully deep-learning-based approach using variational auto-encoders (VAEs) to recover a continuous distribution of atomic protein structures and poses directly from picked particle images and demonstrate its efficacy on realistic simulated data. We hope that methods built on this work will allow incorporation of stronger prior information about protein structure and enable better understanding of non-rigid protein structures.

Quantum dots are arguably one of the best platforms for optically accessible spin based qubits. The paramount demand of extended qubit storage time can be met by using quantum-dot-confined dark exciton: a longlived electron-hole pair with parallel spins. Despite its name the dark exciton reveals weak luminescence that can be directly measured. The origins of this optical activity remain largely unexplored. In this work, using the atomistic tight-binding method combined with configuration-interaction approach, we demonstrate that atomic-scale randomness strongly affects oscillator strength of dark excitons confined in self-assembled cylindrical InGaAs quantum dots with no need for faceting or shape-elongation. We show that this process is mediated by two mechanisms: mixing dark and bright configurations by exchange interaction, and equally important appearance of non-vanishing optical transition matrix elements that otherwise correspond to nominally forbidden transitions in a non-alloyed case. The alloy randomness has essential impact on both bright and dark exciton states, including their energy, emission intensity, and polarization angle. We conclude that, due to the atomic-scale alloy randomness, finding dots with desired dark exciton properties may require exploration of a large ensemble, similarly to how dots with low bright exciton splitting are selected for entanglement generation.

We report studies of $k$-dependent Land\'e $g$-factor, performed by both continuous media approximation k.p method, and atomistic tight-binding sp$^3$d$^5$s$^*$ approach. We propose an effective, mesoscopic model for InAs that we are able to successfully compare with atomistic calculations, for both very small and very large nanostructures, with a number of atoms reaching over 60 million. Finally, for nanostructure dimensions corresponding to near-zero $g$-factor we report electron spin states anti-crossing as a function of system size, despite no shape-anisotropy nor strain effects included, and merely due to breaking of atomistic symmetry of cation/anion planes constituting the system.

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.

Excitons in alloyed nanowire quantum dots have unique spectra as shown here using atomistic calculations. The bright exciton splitting is triggered solely by alloying and despite cylindrical quantum dot shape reaches over $15~\mu$eV, contrary to previous theoretical predictions, however, in line with experimental data. This splitting can however be tuned by electric field to go below $1$~$\mu$eV threshold. The dark exciton optical activity is also strongly affected by alloying reaching notable $1/3500$ fraction of the bright exciton and having large out-of-plane polarized component., Comment: 5 figures, 4 pages (plus bibliography)

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 $1\%$ fraction of the bright exciton intensity without application of any external fields. An atomistic calculation is augmented with a elementary phenomenological model expressed in terms of light-hole exciton add-mixture increasing with the shape deformation. Finally, exctionic complexes $X^-$, $X^+$, and $XX$ are studied as well and the correlations due to presence of higher excited states are identified as a key-factor affecting excitonic binding energies and the fine structure., Comment: 16 pages, 17 figures

Numerical calculations of excitonic properties of novel nanostructures, such as nanowire and crystal phase quantum dots, must combine atomistic accuracy with an approachable computational complexity. The key difficulty comes from the fact that excitonic spectra details arise from atomicscale contributions that must be integrated over a large spatial domain containing a million and more of atoms. In this work we present a step-by-step solution to this problem: combined empirical tight-binding and configuration interaction scheme that unites linearly scaling computational time with the essentials of the atomistic modeling. We benchmark our method on the example of wellstudied self-assembled InAs/GaAs quantum dot. Next, we apply our atomistic approach to crystal phase quantum dots containing more than 10 million atoms.

Last mile link is often a bottleneck for end user. However, users typically have multiple ways of accessing the Internet (cellular, ADSL, public Wifi). This observation led to creation of protocols like mTCP or R-MTP. Current bandwidth aggregation protocols are packet based. However, this is not always practical - for example, non-TCP protocols are often blocked on firewalls. Moreover, a lot of effort was devoted over the years into making single-path TCP work well over various types of links. In this paper we introduce protocol which uses multiple TCP streams to establish single reliable connection attempting to maximize bandwidth and minimize latency.