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Michal Zielinski - Welcome to my webpage.
Welcome and thank you for visiting my webpage.
I am head of
Department of Quantum Physics at
Institute of Physics,
Nicolaus Copernicus University,
Torun,
Poland.
Office address:
Instytut Fizyki UMK, Grudziadzka 5, 87-100; Torun, Poland
Phone: ++48 56 611 2405 (office)
e-mail:
mzielin@fizyka.umk.pl
ResearcherID:C-2587-2013
Google Scholar:s2BJ5XEAAAAJ
ORCID:0000-0002-7239-2504
atomistic many-body calculation for varius nanosystems include quantum dots, nanowires and nanowire quantum dots,
strain effects in semiconductor quantum dots and nanocrystals, 3D interactive computer graphics applications in nanostructure 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 massively-parallel 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 post-growth 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.
- Light-hole excitons in nanowire quantum dots
In the project it has also been shown that high aspect ratio (tall) nanowire quantum dots can exhibit light-hole 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 light-hole
excitons confined in nanowire quantum dots. Nanostructures of such properties could find novel applications in information technology and telecommunication.
- Dark excitons in low-shape symmetry quantum dots
Another important result was obtained for InAs/GaAs self-assembled 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 long-lived, 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 large-scale calculations of spectral properties
of silicon nanodevices doped with single impurity atoms. We built theory and performed high-performance 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 tight-binding 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 atom-based
nanoscale devices for future quantum computing applications. Recently, several papers showed that a metrology of scanning
tunnelling microscopy (STM) imaging combined with atomistic tight-binding 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 multi-dopant clusters to provide reliable position information. In
contrast to previous work, we demonstrate that a metrology combining STM imaging with tight-binding simulations may lead to
pronounced uncertainty due to tip orbital model, effects of dangling bonds and choice of local atomic basis for the tight-binding
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/s41524-022-00857-w
- Exploiting underlying crystal lattice for efficient computation of Coulomb matrix elements in multi-million 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 multi-million
atom nanostructures, Comput. Phys. Commun. (2019) 254.), we presented a practical solution to this problem, where quasi-linear efficiency,
both in time and memory, was obtained by utilizing the fast Fourier transform. Here, we present an updated version of our highly-parallelized
computer program, named Coulombo-Lattice,
that eliminates the necessity of introducing an auxiliary basis set for the wave-function transfer to the computational grid.
Here, we instead exploit the properties the underlying crystal lattice and run calculations on a regular three-dimensional grid superimposed
on the original, lower-symmetry 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(N2) 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 zinc-blend/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
- Single-electron states of phosphorus-atom arrays in silicon
We characterize the single-electron energies and the wave-function structure of arrays with two, three, and four phosphorus atoms in silicon by implementing atomistic
tight-binding calculations and analyzing wave-function overlaps to identify the single-dopant states that hybridize to make the array states.
The energy spectrum and wave-function 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 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 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 wave-function structure into Fermi-Hubbard Hamiltonians needed to implement and validate
analog quantum simulations in these devices.
For more, see Phys. Rev. B 109, 205412, https://doi.org/10.1038/s41524-022-00857-w
- Double P dopants in Si: Wave functions and spatial metrology from STM images
The design and implementation of dopant-based 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 tight-binding simulations to reverse-engineer dopant coordinates. This work shows that such an approach may not be
straightforwardly extended to double-dopant systems. We find that the ground (quasi-molecular) state of a pair of coupled
phosphorous dopants often cannot be fully explained by the linear combination of single-dopant ground states. Although the
contributions from excited single-dopant states are relatively small, they can lead to ambiguity in determining individual dopant
positions from a multi-dopant STM image. To overcome that, we exploit knowledge about dopant-pair wave functions and
propose a simple yet effective scheme for finding double-dopant positions based on STM images.
For more, see paper draft
- Disorder-resilient transport through dopant arrays in silicon
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 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
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 observe the emergence of current flow uncomplicated by strong correlation in the
multi-electron 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 3-site chains coupled only by interchain Coulomb interaction.
For more, see https://arxiv.org/abs/2405.05217
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