
Michal Zielinski  Welcome to my webpage.
Welcome and thank you for visiting my webpage.
I am a full professor at the
Department of Quantum Physics at
Institute of Physics,
Nicolaus Copernicus University,
Torun,
Poland.
Office address:
Instytut Fizyki UMK, Grudziadzka 5, 87100; Torun, Poland
Phone: ++48 56 611 2405 (office)
email:
mzielin@fizyka.umk.pl
ResearcherID:C25872013
Google Scholar:s2BJ5XEAAAAJ
ORCID:0000000272392504
Atomistic manybody calculations for single and double quantum dots, nanocrystals, nanowires, quantum dashes, crystal phase quantum dots... you name it ;)
Efficient parallel algorithms (and codes!) for various nanostructures
Single and multiple dopants (chains, grids, clusters) in silicon
3D interactive graphics applications in nanostructure physics
Machine learning in physics
The project (financed by National Science Centre) focused on theory and computational tools development aiming for atomistic calculations of
nanostructure properties under external strain. The improved and newly created software allows for massivelyparallel computations for
nanosystems with numbers of atoms exceeding 100 million.
Results of large scale atomistic calculations have shown a significant effect of external strain on spectral properties of nanowires and nanowire quantum dots.
A fundamental role of quantum dot shape symmetry and lattice composition fluctuations [Phys. Rev. B 91, 085303 (2015)].
on excitonic spectra has also been found.
 Externally strained nanowire quantum dots
It has been shown that the lattice mismatched shells allow for a wide range control of excitonic emission energy of InAs/InP nanowire quantum dots
[Nano Letters 12, 6202 (2012)] and ZnTe nanowires [Applied Physics Letters 104, 163111 (2014)].
The key factor responsible for the modification of the emission energy is tensile strain due to the nanowire shell.
Atomistic theory was successfully applied to estimate the character of combined internal/external strain and the magnitude of excitonic spectra shifts.
Atomistic calculations give a clue on how the postgrowth process can lead to a nanosystem design of desired specifications. Results of theoretical
calculations were in qualitative and quantitative agreement with the experiment, whereas the cited papers were the first in the field.
The large degree of control due to strain could be useful for quantum dots and nanowires applications in telecommunication or quantum cryptography.
 Lighthole excitons in nanowire quantum dots
In the project it has also been shown that high aspect ratio (tall) nanowire quantum dots can exhibit lighthole excitonic ground state with a pronounced
effect on details of excitonic spectra (excitonic fine structure). Paper Phys. Rev. B 88, 115424 (2013) was the first to discuss properties of lighthole
excitons confined in nanowire quantum dots. Nanostructures of such properties could find novel applications in information technology and telecommunication.
 Dark excitons in lowshape symmetry quantum dots
Another important result was obtained for InAs/GaAs selfassembled quantum dots.
It has been shown that the low shape symmetry can have a fundamental effect on excitonic spectra and lead to bright and dark excitons mixing [Phys. Rev. B 99, 085403 (2015)].
These results has been recently confirmed by an experiment and could be considered as a stepping stone towards dark excitons manipulation by purely optical means.
Dark excitons can effectively form a longlived, charge neutral qubits with potential applications in quantum information.
The project (financed by the National Science Centre) was focused on the formulation of theoretical description and performing largescale calculations of spectral properties
of silicon nanodevices doped with single impurity atoms. We built theory and performed highperformance atomistic calculations for single, double, and multiple phosphorus dopant
systems embedded in a silicon matrix.
A single dopant embedded in a host environment of millions of silicon atoms forms a complicated nanosystem where every atom must be accounted for individually.
In other words, every atom matters. Our approach, therefore, utilizes the atomistic tightbinding method that naturally incorporates effects of quantum confinement,
external fields, and atomistic effects such as interface steps and composition disorder. We applied our methodology to solve the currently untraceable problems where
the impurity wave function extends over many million atomic sites. The project was conducted in close collaboration with the National Institute of Standards and Technology (NIST).
Main project results include:
 Scanning tunneling microscopy of buried dopants in silicon: images and their uncertainties
The ability to determine the locations of phosphorous dopants in silicon is crucial for the design, modelling, and analysis of atombased
nanoscale devices for future quantum computing applications. Recently, several papers showed that a metrology of scanning
tunnelling microscopy (STM) imaging combined with atomistic tightbinding simulations could be used to determine coordinates
of a dopant buried close to a Si surface. We identify effects which play a crucial role in the simulation of STM images and have to be
precisely modelled for STM imaging of buried dopants and multidopant clusters to provide reliable position information. In
contrast to previous work, we demonstrate that a metrology combining STM imaging with tightbinding simulations may lead to
pronounced uncertainty due to tip orbital model, effects of dangling bonds and choice of local atomic basis for the tightbinding
representation. Additional work is still needed to obtain a reliable STM metrology of buried dopant position.
For more, see npj Computational Materials (2022) 8:182, https://doi.org/10.1038/s4152402200857w
 Exploiting underlying crystal lattice for efficient computation of Coulomb matrix elements in multimillion atoms nanostructures
Atomistic modeling of nanostructures often leads to computationally challenging problems involving millions of atoms and tens of
thousands of Coulomb matrix elements. In our previous work (P.T. Różanski, M. Zieliński, Efficient computation of Coulomb and exchange integrals for multimillion
atom nanostructures, Comput. Phys. Commun. (2019) 254.), we presented a practical solution to this problem, where quasilinear efficiency,
both in time and memory, was obtained by utilizing the fast Fourier transform. Here, we present an updated version of our highlyparallelized
computer program, named CoulomboLattice,
that eliminates the necessity of introducing an auxiliary basis set for the wavefunction transfer to the computational grid.
Here, we instead exploit the properties the underlying crystal lattice and run calculations on a regular threedimensional grid superimposed
on the original, lowersymmetry lattice. Due to removal of spurious interactions from other supercells,
the resulting Coulomb matrix elements are, up to numerical precision, identical to those obtained by the
direct summation O(N^{2}) method, yet our code maintains O(N log N) scaling. We illustrate our approach
by calculations involving up to 1.7 million integrals, and number of atoms reaching up to 2.8 million,
for the problem of dopant charging energy for a single phosphorus dopant embedded in a silicon lattice.
Next, to emphasize the broad applicability of our code, we show the results for mixed zincblend/wurtzite
lattice systems, also known as crystal phase quantum dots.
For more, see Computer Physics Communications 287 (2023) 108693, https://doi.org/10.1016/j.cpc.2023.108693
 Singleelectron states of phosphorusatom arrays in silicon
We characterize the singleelectron energies and the wavefunction structure of arrays with two, three, and four phosphorus atoms in silicon by implementing atomistic
tightbinding calculations and analyzing wavefunction overlaps to identify the singledopant 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 singledopant states of the same type,
with some cross hybridization between A1 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 nearestneighbor tunneling rates are similar in magnitude in a square array.
Our analysis also accounts for the shift of the onsite 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 FermiHubbard Hamiltonians needed to implement and validate
analog quantum simulations in these devices.
For more, see Phys. Rev. B 109, 205412 (2024) https://doi.org/10.1103/PhysRevB.109.205412
 Challenges to extracting spatial information about double P dopants in Si from STM images
The design and implementation of dopantbased silicon nanoscale devices rely heavily on knowing precisely the locations of
phosphorous dopants in their host crystal. One potential solution combines scanning tunneling microscopy (STM) imaging with
atomistic tightbinding simulations to reverseengineer dopant coordinates. This work shows that such an approach may not be
straightforwardly extended to doubledopant systems. We find that the ground (quasimolecular) state of a pair of coupled
phosphorous dopants often cannot be fully explained by the linear combination of singledopant ground states. Although the
contributions from excited singledopant states are relatively small, they can lead to ambiguity in determining individual dopant
positions from a multidopant STM image. To overcome that, we exploit knowledge about dopantpair wave functions and
propose a simple yet effective scheme for finding doubledopant positions based on STM images.
For more, see Sci. Rep. 14, 18062 (2024) https://doi.org/10.1038/s4159802467903z
 Disorderresilient transport through dopant arrays in silicon
Chains and arrays of phosphorus donors in silicon have recently been used to demonstrate dopantbased quantum simulators.
The dopant disorder present in fabricated devices must be accounted for. Here, we theoretically study transport through disordered donorbased 3x3 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
nonequilibrium 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 observe the emergence of current flow uncomplicated by strong correlation in the
multielectron system, regardless of array filling. Instead, the current follows the shortest paths between source and drain sites that avoid possible obstacles.
The reference 3x3 array has transport properties very similar to transport through three parallel 3site chains coupled only by interchain Coulomb interaction.
For more, see https://arxiv.org/abs/2405.05217
The project (financed by the National Science Centre) was focused on formulating theoretical descriptions and performing challenging
atomistic calculations of single and multiexcitons confined in artificial molecular systems formed by two and three quantum dots embedded in semiconductor nanowires.
The project aimed to develop the theory and run highly demanding atomistic calculations for a family of nanowireembedded artificial molecules, including alloyed
InAsxP1x quantum dots in InP nanowires of realistic dimensions. We aimed to understand how quantum dot dimensions, chemical composition and distance,
and therefore coupling, between individual quantum dots, as well as nanowire growth orientation, alloy randomness and composition inhomogeneity,
affect optical and energy spectra of excitons and multiexcitons confined in these nanowire artificial molecules.
In this project, through theoretical research, we demonstrated that a system consisting of two quantum dots can offer significant advantages over individual quantum dots,
particularly given potential future applications in optics, cryptography, and quantum computing. We showed that these systems allow for practical control of their spectra
via an external electric field, which theoretically enables using quasimolecules in nanowires to generate entangled photon pairs. Additionally, we demonstrated that
the random arrangements of atoms constituting the quantum dots can lead to a scenario where optically inactive states, known as dark excitons, become optically active. We also showed that one of the newly studied types of quantum dots behaves as if it were, in fact, a quasimolecule rather than a single quantum dot.
Main project results include:
 Electric field tuning of excitonic finestructure splitting in asymmetric InAs/InP nanowire quantum dot molecules
We use an atomistic model to show that coupling between two nanowire quantum dots, forming an artificial
molecule, can be used to control bright exciton splitting in these systems with external electric field and even
reduce it to zero or reverse it. Importantly, strong interdot coupling allows this reduction to occur without a
simultaneous detrimental reduction of excitonic optical activity, which is inherently present in weakly coupled
systems. Our results indicate that nanowire quantum dot molecules could form a promising platform for quantum
dot–based entanglement generation.
For more, see Phys. Rev. B 100, 235417 (2019), https://doi.org/10.1103/PhysRevB.100.235417
 Electricfield control of exciton fine structure in alloyed nanowire quantum dot molecules
Alloyed InAs0.2P0.8/InP nanowire quantum dot molecules reveal nontrivial electricfield evolution of the
brightexciton spectra; this was studied here using the atomistic theory. For a quantum dot molecule composed of
two nanowire quantum dots of dissimilar sizes, the overall field dependence resembles the typical selfassembled
quantum dot molecule spectra with an avoided crossing of direct and indirect excitons. However, for coupled
nanowire quantum dots of identical dimensions and chemical compositions—where the brightexciton splitting
is triggered by alloy randomness—the notion of direct/indirect excitons is mostly lost, with the brightexciton
splitting field evolution varying strongly between various random realizations of nominally identical systems.
Nonetheless, for several random samples, lowerhigher excitonic branch mixing leads to the reduction of bright
exciton splitting below the 1 µeV threshold but with the restoration of pronounced optical activity away from
the crossing. Thus, a simultaneous reduction of the brightexciton splitting, without the detrimental reduction in
the lower excitonic branch optical activity, makes alloyed nanowire quantum dot molecules a possible platform
for applications in quantum optics and information.
For more, see Phys. Rev. B 104, 195411 (2021), https://doi.org/10.1103/PhysRevB.104.195411
 Antibonding ground states in crystal phase quantum dots
Crystal phase quantum dots are formed during the nanowire growth by vertically stacking distinct crystal
phases of the same chemical compound. In this Letter we show, using an atomistic manybody approach, that
InP crystal phase quantum dots may exhibit a peculiar and rare antibonding hole ground state. Interestingly, even
small strains due to a wurtzite–zincblende lattice mismatch—which is often neglected—can strongly affect the
properties of the lowest hole states, resulting in unusual doublepeak features in the excitonic optical spectra.
For more, see Phys. Rev. B 106, L041405 (2022) https://doi.org/10.1103/PhysRevB.106.L041405
 Crystal feld splitting and spontaneous polarization in InP crystal phase quantum dots
Crystal phase quantum dots are formed by vertically stacking zincblende and wurtzite phases
during nanowire growth. In this work, we show, using an atomistic manybody approach, that
crystal feld splitting in the wurtzite phase, as well as spontaneous polarization originating from
the phase interfaces, will strongly afect the properties of lowest hole states in InP crystal phase
quantum dots, and in turn the excitonic optical spectra. We also show that the artifactfree modeling
of crystal phase quantum dots should incorporate any additional potentials on equal footing with
the electronhole interaction. In this paper, we discuss a reliable theoretical framework that can be
applied to investigate the electronic and optical properties of InPbased crystal phase quantum dots.
The importance of accurate excitonic calculations for such systems is highlighted in view of their
potential applications in nanowire photonics, yet further research is necessary for bringing theory and
experiment in agreement.
For more, see Sci. Rep. 12, 15561 (2022), https://doi.org/10.1038/s4159802219076w
 Vanishing fine structure splitting in highly asymmetric InAs/InP quantum dots without wetting layer
Contrary to simplifed theoretical models, atomistic calculations presented here reveal that
sufciently large inplane shape elongation of quantum dots can not only decrease, but even reverse
the splitting of the two lowest optically active excitonic states. Such a surprising cancellation of
brightexciton splitting occurs for shapeanisotropic nanostructures with realistic elongation ratios,
yet without a wetting layer, which plays here a vital role. However, this nontrivial efect due to shape elongation
is strongly diminished by alloy randomness resulting from intermixing of InAs quantum dot material with the surrounding InP matrix.
Alloying randomizes, and to some degree fattens the shape dependence of fnestructure splitting giving a practical justifcation for the application
of simplifed theories. Finally, we fnd that the darkexciton spectra are rather weakly afected by
alloying and are dominated by the efects of lateral elongation.
For more, see Sci. Rep. 10, 13542 (2020), https://doi.org/10.1038/s41598020701561
 Darkbright excitons mixing in alloyed InGaAs selfassembled quantum dots
Quantum dots are arguably one of the best platforms for optically accessible spinbased qubits. The paramount
demand of extended qubit storage time can be met by using a quantumdotconfined dark exciton: a longlived
electronhole 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 tightbinding method combined with the configurationinteraction approach, we demonstrate that
atomicscale randomness strongly affects the oscillator strength of dark excitons confined in selfassembled
cylindrical InGaAs quantum dots with no need for faceting or shapeelongation. We show that this process is
mediated by two mechanisms: mixing dark and bright configurations by exchange interaction, and the equally
important appearance of nonvanishing optical transition matrix elements that otherwise correspond to nominally
forbidden transitions in a nonalloyed case. The alloy randomness has an essential impact on both bright and dark
exciton states, including their energy, emission intensity, and polarization angle. We conclude that, due to the
atomicscale alloy randomness, finding dots with the 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.
For more, see Phys. Rev. B 103, 155418, 2021 https://doi.org/10.1103/PhysRevB.103.155418
