arXiv subjects

B. Szafran

Publications and source records attributed to B. Szafran.

At least 19 recordsLinked to original sources

arXiv2026

Spin SWAP operation in double quantum dots at the LaAlO3/SrTiO3 interface

Progress in the fabrication of nanoscale transition-metal-oxide heterostructures makes these platforms promising candidates for the realization of spin qubits, mainly due to the $d$-character of their electronic structures, which could potentially result in a reduction of hyperfine interactions and spin decoherence. Here, we present a systematic study of spin control within the SWAP operation in double quantum dots embedded in a two-dimensional electron gas at the LaAlO$_3$/SrTiO$_3$ interface. Our analysis starts with a study of single-electron spin dynamics, focusing on the influence of spin-orbit and interorbital coupling on the spin evolution. In this case, our findings are supported by semiclassical calculations based on the Bloch equations, which show good agreement with full quantum mechanical simulations. We then simulate the SWAP operation by analyzing the crossover between two regimes: (i) large quantum dots, where the electronic structure is dominated by the $d_{xy}$ orbitals and the spin dynamics is affected primarily by Rashba-type spin-orbit interaction; and (ii) small quantum dots, where higher-energy orbitals $d_{xz/yz}$ contribute to the electronic structure, leading to a significant reduction in the SWAP fidelity. In the first regime, particularly relevant from the application point of view, we analyze in detail the anisotropy of the SWAP operation induced by the spin-orbit coupling.

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arXiv2025

Snakelike trajectories of electrons released from quantum dots driven by the spin Hall effect

Using time dependent simulations, we analyze the trajectories of electrons released from a quantum dot in a waveguide made of a spin-orbit-coupled material (InSb). An electron released from the quantum dot, when driven by an electric field follows a trajectory that is deflected by spin-orbit interaction and undergoes spin precession that results in a spin-dependent, snake-like trajectory. The trajectory strongly depends on the initial state of the electron, enabling detection of the electron quantum state in the dot when connected to the T-junction. Notably, we show that the snake-like trajectory persists even under a small external magnetic field with low, incomplete initial electron spin polarization. Our findings are supported by semiclassical calculations of the electron trajectory, which show good agreement with full quantum mechanical simulations

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arXiv2025

Scanning gate microscopy probing of anisotropic electron flow in a two dimensional electron gas at the (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interface: A theoretical investigation

We theoretically investigate the anisotropic dispersion features of a two dimensional electron gas at the (110) oriented $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interfaces, as revealed by scanning gate microscopy of electronic flow from a quantum point contact. The dispersion relation of the (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ interface is characterized by a highly non-circular Fermi surface. Here, we develop an efficient tight-binding model for the electron gas at the interface. We show that the anisotropy of the Fermi surface causes both the direction of the electron flux from the quantum point contact and the periodicity of the self-interference conductance fringes to depend strongly on the orientation of the constriction relative to the crystal lattice. We show that the radially non-uniform distribution of the Fermi velocity on the Fermi surface results in skewing of electron trajectories when the quantum point contact gates are not aligned with the in-plane primitive vectors. We show that this effect results in the separation of electrons belonging to different orbitals for wide (110) $\mathrm{LaAlO}_3/\mathrm{SrTiO}_3$ quantum wells.

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arXiv2024

Scaled tight binding model for a two dimensional electron gas at the (001) LaAlO$_3$/SrTiO$_3$ interface

The progress in the fabrication of nanoscale systems based on the two-dimensional electron gas at the interface between LaAlO$_3$ and SrTiO$_3$ (LAO/STO) has created an increased demand for simulations of these nanostructures, which typically range in size from tens to hundreds of nanometers. Due to the low lattice constant of LAO/STO, approximately 0.394 nm, these calculations become extremely time-consuming. Here, we present a scaled tight-binding approximation defined on a mesh with size that can be several times larger than in the ordinary approach. The scaled model is analyzed within the context of quantum transport simulations and electronic structure calculations. Our findings demonstrate that the scaled model closely aligns with the ordinary one up to a scaling factor of 8. These results pave the way for more efficient simulations of LAO/STO nanostructures with realistic sizes relevant to experimental applications.

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arXiv2024

Electrical spin manipulation in double SrTiO$_3$/LaAlO$_3$ quantum dots

The spin dynamics in two electron double quantum dots embedded in two dimensional electron gas at the interface between SrTiO$_3$ and LaAlO$_3$ is studied by an exact numerical solution of the time-dependent Schrödinger equation, in the context of the electric dipole spin resonance experiment. Based on the three band model of $3d$-electrons localized at Ti ions on the square lattice we analyze in details the singlet-triplet transition induced by the AC electric field, in the magnetic field range close to the avoided crossing which appears as a result of the spin-orbit coupling. Our calculations show that for symmetric double quantum dots the single photon spin-flip transitions is prohibited due to the parity symmetry and the transition can occur only by the higher order two-photon processes. For a weakly asymmetric system, when the first order singlet-triplet transitions are released due to the parity symmetry breaking, the spin-flip transition has a character of the Rabi oscillations for a low electric field amplitude. As the amplitude is increased the frequency of the transition is blueshifted (redshifted) for the magnetic field below (above) the single-triplet avoided crossing. Interestingly, for a sufficiently high magnetic field and high AC field amplitude the electric field drives the system across the avoided crossing inducing the spin-flip by the Landau-Zener-Stueckelberg-Majorana transitions with 100\% spin flip probability for a slow sweep. Finally, the optimization of the geometrical parameters of the system with respect to the time of spin-flip of its fidelity is also presented.

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arXiv2024

Electric dipole spin resonance in single and two electron quantum dot defined in two-dimensional electron gas at the SrTiO$_3$/LaAlO$_3$ interface

We investigate the energy spectrum of a single and two electron quantum dot (QD) embedded in two dimensional electron gas at the interface between SrTiO$_3$ and LaAlO$_3$, in the presence of the external magnetic field. For this purpose the three band model of $3d$-electrons defined on the square lattice of Ti ions was utilized. We demonstrate that, for the weak parabolic confinement potential, the low energy spectrum is sufficiently well described by the effective Hamiltonian reduced to the one $d_{xy}$ orbital with the spin-orbit interaction originating from the coupling to the $d_{xz}$, $d_{yz}$ bands. This is not the case for stronger confinement where contribution of the states related to the $d_{xz/yz}$ orbital is relevant. Based on the time depended calculations we discuss in details the manipulation of the electron spin in QD by external AC voltages, in the context of the electric dipole spin resonance. The allowed and forbidden transitions are discussed in details with respect to the parity selection rule. Our calculations show that for a single electron QD the spin-flip in the ground-state has a character of a Rabi resonance while for two electrons the singlet-triplet transition is forbidden by the parity symmetry. For the two electrons QD, we demonstrate that the spin-flip transition can still be accomplished via a second-order, two-photon process that has a two-state Rabi character for low AC field amplitude. The violation of the parity symmetry on the spin-flip transitions is also analyzed.

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arXiv2022

Exciton localization on p-i-n junctions in two-dimensional crystals

We consider a neutral exciton localized on a model p-i-n junction defined in a two-dimensional crystal: MoSe$_2$ and phosphorene, using a variational approach to the effective mass Hamiltonian. The non-homogeneous electric field at the junction prevents the separation of the center of mass. The variational solution provides the exciton density in the real space and accounts for the kinetic energy due to the exciton localization. For low values of the potential step across the junction, the exciton occupies an area which is much larger than the nominal range of the junction and the energy remains essentially insensitive to the value of the step. Localization of the exciton within the junction area is accompanied by the appearance of the dipole moment induced by the local electric field. The dipole moment becomes a linear function of the potential step only when the step is sufficiently large. In consequence, the energy dependence on the step value is non-parabolic. We demonstrate that the exciton gets localized not exactly at the center of the junction but on the side which is more energetically favourable for the heavier carrier: electron or hole.

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arXiv2021

Annular confinement for electrons on liquid helium

We discuss annular confinement for electrons on liquid helium surface induced by a tubular electrode submerged beneath the surface. For shallow liquid layer above the tube the resulting potential has a minimum off the axis of the tube. The symmetry transitions in the ground-state driven by external magnetic field can be resolved by the microwave spectroscopy provided that the confinement radii in the first and second Rydberg subbands of the vertical quantization are different. This condition can be fulfilled for submersion depth of the tube comparable to its radius. Then, discontinuities in the main absorption line appear with the period that corresponds to the subsequent magnetic flux quanta passing across the area within the ground-state confinement radius.

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arXiv2020

Electrostatic quantum dot confinement in phosphorene

We consider states localized by electrostatic potentials in phosphorene using an atomistic tight binding approach. From the results of the tight-binding calculations of the confined states we extract effective masses for the conduction band electrons in the armchair and zigzag directions. The masses derived in this way are used for a simple single-band effective mass model which, as we find, reproduces very well the tight-binding energy spectrum in external magnetic field, the probability densities and the interaction effects. Both methods produce Wigner crystallization for the ground-state of the electron pair with the single-electron islands separated in the armchair direction already for small quantum dots.

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arXiv2020

Paired electron motion in interacting chains of quantum dots

We study the motion of a pair of electrons along two separate parallel chains of quantum dots. The electrons that are released from the central dot of each chain tend to accompany and not avoid each other. The correlated electron motion involves entanglement of the wave functions which is generated in time upon release of the initial confinement. Observation of the simultaneous presence of electrons at the same side of the chain can provide fingerprint of the paired electron motion.

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arXiv2019

Topologically protected wave packets and quantum rings in silicene

We study chiral wave packets moving along the zero-line of a symmetry breaking potential of vertical electric field in buckled silicene using an atomistic tight-binding approach with initial conditions set by an analytical solution of the Dirac equation. We demonstrate that the wave packet moves with a constant untrembling velocity and with a presevered shape along the zero line. Backscattering by the edge of the crystal is observed that appears with the transition of the packet from $K$ to $K'$ valley or vice versa. We propose a potential profile with branching of the flip line that splits the wave packet and produces interference of the split parts that acts as a quantum ring. The transition time exhibits Aharonov-Bohm oscillations in the external magnetic field that are translated to conductance oscillations when the intervalley scattering is present within the ring.

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arXiv2019

Finite difference method for Dirac electrons in circular quantum dots

A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function components at the external edge of the system and then sweeps the radial mesh in search for the energies for which the boundary conditions are met inside the flake. The sweep that is performed from the edge of the system towards the origin allows for application of a two-point finite difference quotient of the first derivative, which prevents the fermion doubling problem and the appearance of the spurious solutions with rapid oscillations of the wave functions in space.

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arXiv2018

Spin and valley manipulation in single and double electrostatic silicene quantum dots

We study single and double quantum dots defined electrostatically within silicene. The spin-valley structure of the confined single- and two-electron system is determined and the effects of the intervalley scattering induced by the crystal edge and the Coulomb interaction are quantified. The states in a double quantum system are discussed in the context of the spatial symmetry of the single- and two-electron extended orbitals. We determine the charge, spin and valley transitions times induced by alternate electric fields of the microwave frequency. The valley transition times can be controlled by several orders of magnitude by the confinement potential. Also, the spin transition rates can be enhanced by orders of magnitude by the coupling of the bonding and antibonding orbitals mediated by the Rashba interaction.

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arXiv2018

Electrostatic quantum dots in silicene

We study electrostatic quantum dot confinement for charge carriers in silicene. The confinement is formed by vertical electric field surrounding the quantum dot area. The resulting energy gap in the outside of the quantum dot traps the carriers within, and the difference of electrostatic potentials on the buckled silicene sublattices produces nonzero carrier masses outside the quantum dot. We study the electrostatic confinement defined inside a silicene flake with both the atomistic tight-binding approach as well as with the continuum approximation for a circularly symmetric electrostatic potential. We find localization of the states within the quantum dot and their decoupling from the edge that makes the spectrum of the localized states independent of the crystal termination. For an armchair edge of the flake removal of the intervalley scattering by the electrostatic confinement is found

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arXiv2017

Pauli blockade microscopy of quantum dots

We propose a spin-sensitive scanning probe microscopy experiment on double quantum dots in Pauli blockade conditions. Electric spin resonance is induced by an AC voltage applied to the scanning gate which induces lifting of the Pauli blockade of the current. The stationary Hamiltonian eigenstates are used as a basis for description of the spin dynamics with the AC potential of the probe. For the two-electron system we evaluate the transitions rates from triplet $\mathrm{T}_+$ state to singlet $\mathrm{S}$ or triplet $\mathrm{T}_0$ states, i.e. to conditions in which the Pauli blockade of the current is lifted. The rates of the spin-flip transitions are consistent with the transition matrix elements and strongly dependent on the tip position. Probing the spin densities and identification of the final transition state are discussed.

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arXiv2017

Double quantum dots defined in bilayer graphene

Artificial molecular states of double quantum dots defined in bilayer graphene are studied with the atomistic tight-binding and its low-energy continuum approximation. We indicate that the extended electron wave functions have opposite parities on each of the sublattices at both graphene layers and that the ground-state wave function components change from bonding to antibonding with the interdot distance. In the weak coupling limit -- the most relevant for the quantum dots defined electrostatically -- the signatures of the interdot coupling include -- for the two-electron ground state -- formation of states with symmetric or antisymmetric spatial wave functions split by the exchange energy. In the high energy part of the spectrum the states with both electrons in the same dot are found with the splitting of energy levels corresponding to simultaneous tunneling of the electron pair from one dot to the other.

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arXiv2017

Spin-valley resolved photon-assisted tunneling in carbon nanotube double quantum dots

We consider the photon-assisted tunneling (PAT) and the Landau-Zener-Stueckelberg (LZS) interference for double quantum dots induced electrostatically along a semiconducting carbon nanotube. An atomistic tight-binding approach and the time-dependent configuration interaction method are employed for description of the systems of a few confined electrons and holes. We reproduce the patterns of the LZS interference recently observed for the quantum double dots describing transport across hole-localized states. Moreover, we indicate that for charge configurations for which the ground-state is Pauli blocked PAT can be used for resolution of the transitions that involve spin-flip or intervalley transitions without the spin-valley conserving background signal.

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arXiv2017

Spin separation and exchange for quantum dots in the Overhauser field

We describe the spin and charge dynamics of the system of two electrons confined within a double quantum dot defined in a quantum wire. The spin dynamics is driven by the electron motion in presence of the spin-orbit interaction and the randomly varying local Overhauser field due to the nuclear spins. The Schroedinger equation is solved with the time-dependent configuration interaction method that allows for an exact description of the system dynamics. The procedures of the spin separation, exchange and read-out by the spin to charge conversion all induced by the detuning variation are simulated. The rates of the potential variation that are necessary for the spin separation and spin to charge conversion in the context of the Landau-Zener transitions are determined. The average over random configurations of the hyperfine field produce spin exchange results which qualitatively agree with the experimental data.

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