arXiv subjects

B. Szafran

Publications and source records attributed to B. Szafran.

At least 37 records · Page 2Linked to original sources

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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arXiv2016

Spin transitions driven by electric dipole spin resonance in fluorinated single- and bilayer-graphene quantum dots

Spin transitions driven by a periodically varying electric potential in dilute fluorinated graphene quantum dots are investigated. Flakes of monolayer graphene are considered as well as electrostatic electron traps induced in bilayer graphene. The stationary states are obtained within the tight-binding approach and are used to the basis of eigenstates to describe the system dynamics. The dilute fluorination of the top layer lifts the valley degeneracy of the confined states and attenuates the orbital magnetic dipole moments due to current circulation within the flake. Moreover, the spin-orbit coupling introduced by the surface deformation of the top layer induced by the adatoms allows spin flips to be driven by the AC electric field. For the bilayer quantum dots the spin flip times is substantially shorter than the experimental spin relaxation. Dynamical effects including many-photon and multilevel transitions are also discussed.

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arXiv2016

Spin-valley dynamics of electrically driven ambipolar carbon-nanotube quantum dots

An ambipolar $n$-$p$ double quantum dot defined by potential variation along a semiconducting carbon-nanotube is considered. We focus on the (1e,1h) charge configuration with a single excess electron in the conduction band state confined in the $n$-type dot and a single missing electron in the valence band state of the $p$-dot for which lifting of the Pauli blockade of the current was observed in the electric-dipole spin resonance [E. A. Laird et al. Nat. Nanotech. 8 , 565 (2013)]. The dynamics of the system driven by periodic electric field is studied with the Floquet theory and the time-dependent configuration interaction method with the single-electron spin-valley-orbitals determined for atomistic tight-binding Hamiltonian. We find that the transitions lifting the Pauli blockade are strongly influenced by coupling to a vacuum state with an empty $n$ dot and a fully filled $p$ dot. The coupling shifts the transition energies and strongly modifies the effective $g$ factors for axial magnetic field. The coupling is modulated by the bias between the dots but it appears effective for surprisingly large energy splitting between the (1e,1h) ground state and the vacuum (0e,0h) state. Multiphoton transitions and high harmonic generation effects are also discussed.

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arXiv2016

Imaging snake orbits at graphene n-p junctions

We consider conductance mapping of the snake-orbits confined along the n-p junction defined in graphene by the electrostatic doping in the quantum Hall regime. We explain the periodicity of conductance oscillations at the magnetic field and the Fermi energy scales by the properties of the n-p junction as a conducting channel. We evaluate the conductance maps for a floating gate scanning the surface of the device. In the quantum Hall conditions the currents flow near the edges of the sample and along the n-p junction. The conductance mapping resolves only the n-p junction and not the edges. The conductance oscillations along the junction are found in the maps with periodicity related to the cyclotron orbits of the scattering current. Stronger probe potentials provide support to localized resonances at one of the sides of the junction with current loops that interfere with the n-p junction currents. The interference results in a series of narrow lines parallel to the junction with positions that strongly depend on the magnetic field through the Aharonov-Bohm effect. The consequences of a limited transparency of finite width n-p junctions are also discussed.

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arXiv2016

Conductance measurement of spin-orbit coupling in the two-dimensional electron systems with in-plane magnetic field

We consider determination of spin-orbit (SO) coupling constants for the two-dimensional electron gas from measurements of electric properties in rotated in-plane magnetic field. %Due to the interplay Due to the SO coupling the electron backscattering is accompanied by spin precession and spin mixing of the incident and reflected electron waves. The competition of the external and SO-related magnetic fields produces a characteristic conductance dependence on the in-plane magnetic field value and orientation which, in turn, allows for determination of the absolute value of the effective spin-orbit coupling constant as well as the ratio of the Rashba and Dresselhaus SO contributions.

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arXiv2016

Theory of ballistic quantum transport in presence of localized defects

We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function matching approach, Lippmann-Schwinger equation (LEQ) and the scattering matrix formalism. We show that the number of matrix elements of the Green's function to be evaluated for the unperturbed system can be essentially reduced by projection of the time reversed scattering wave functions on LEQ which radically improves the speed and lowers the memory consumption of the calculations. Our approach can be applied to quantum devices of an arbitrary geometry and any number of degrees of freedom or leads attached. We provide a couple of examples of possible applications of the theory, including current equilibration at the p-n junction in graphene and scanning gate microscopy mapping of electron trajectories in the magnetic focusing experiment on a graphene ribbon. Additionally, we provide a simple toy example of electron transport through 1D wire with added onsite perturbation and obtain a simple formula for conductance showing that Green's function of the device can be obtained from the conductance versus impurity strength characteristics.

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arXiv2016

Electronic structure of (1e,1h) states of carbon nanotube quantum dots

We provide an atomistic tight-binding description of a few carriers confined in ambipolar (n-p) double quantum dots defined in a semiconducting carbon nanotube. We focus our attention on the charge state of the system in which Pauli blockade of the current flow is observed [F. Pei et al., Nat. Nanotechnol. 7, 630 (2012); E. A. Laird et al., ibid 8, 565 (2013)] with a single excess electron in the n-dot and a single hole in the p-dot. We use the configuration interaction approach to determine the spin-valley structure of the states near the neutrality point and discuss its consequences for the interdot exchange interaction, the degeneracy of the energy spectrum and the symmetry of the confined states. We calculate the transition energies lifting the Pauli blockade and analyze their dependence on the magnetic field vector. Furthermore, we introduce bending of the nanotube and demonstrate its influence on the transition energy spectra. The best qualitative agreement with the experimental data is observed for nanotubes deflected in the gated areas in which the carrier confinement is induced.

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arXiv2016

Interference features in scanning gate conductance maps of quantum point contacts with disorder

We consider quantum point contacts (QPCs) defined within disordered two-dimensional electron gases as studied by scanning gate microscopy. We evaluate the conductance maps in the Landauer approach and wave function picture of electron transport for samples with both low and high electron mobility at finite temperatures. We discuss the spatial distribution of the impurities in the context of the branched electron flow. We reproduce the surprising temperature stability of the experimental interference fringes far from the QPC. Next, we discuss -- previously undescribed -- funnel-shaped features that accompany splitting of the branches visible in previous experiments. Finally, we study elliptical interference fringes formed by an interplay of scattering by the point-like impurities and by the scanning probe. We discuss the details of the elliptical features as functions of the tip voltage and the temperature, showing that the first interference fringe is very robust against the thermal widening of the Fermi level. We present a simple analytical model that allows for extraction of the impurity positions and the electron gas depletion radius induced by the negatively charged tip of the atomic force microscope, and apply this model on experimental scanning gate images showing such elliptical fringes.

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arXiv2016

Spin-orbit coupling measurement by the scanning gate microscopy

We propose a procedure for extraction of the Fermi surface for a two-dimensional electron gas with a strong Rashba spin-orbit coupling from conductance microscopy. Due to the interplay between the effective spin-orbit magnetic field and the external one within the plane of confinement, the backscattering induced by a charged tip of an atomic force microscope located above the sample, leads to the spin precession, and thus to the spin mixing of the incident and reflected modes. This mixing leads to a characteristic angle-dependent beating pattern visible in the conductance maps. We show that the structure of the Fermi level, bearing signatures of the spin-orbit coupling, can be extracted from the Fourier transform of the interference fringes in the conductance maps as a function of the magnetic field direction. We propose a simple analytical model which can be used to fit the experimental data in order to obtain the spin-orbit coupling constant.

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arXiv2015

Spin-orbit interaction in bent carbon nanotubes: resonant spin transitions

We develop an effective tight-binding Hamiltonian for spin-orbit (SO) interaction in bent carbon nanotubes (CNT) for the electrons forming the $π$ bonds between the nearest neighbor atoms. We account for the bend of the CNT and the intrinsic spin-orbit interaction which introduce mixing of $π$ and $σ$ bonds between the $p_z$ orbitals along the CNT. The effect contributes to the main origin of the SO coupling--the folding of the graphene plane into the nanotube. We discuss the bend-related contribution of the SO coupling for resonant single-electron spin and charge transitions in a double quantum dot. We report that although the effect of the bend-related SO coupling is weak for the energy spectra, it produces a pronounced increase of the spin transition rates driven by an external electric field. We find that spin-flipping transitions driven by alternate electric fields have usually larger rates when accompanied by charge shift from one dot to the other. Spin-flipping transition rates are non-monotonic functions of the driving amplitude since they are masked by stronger spin-conserving charge transitions. We demonstrate that the fractional resonances--counterparts of multiphoton transitions for atoms in strong laser fields--occurring in electrically controlled nanodevices already at moderate ac amplitudes--can be used to maintain the spin-flip transitions.

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arXiv2015

Charging graphene nanoribbon quantum dots

We describe charging a quantum dot induced electrostatically within a semiconducting graphene nanoribbon by electrons or holes. The applied model is based on a tight-binding approach with the electron-electron interaction introduced by a mean field local spin density approximation. The numerical approach accounts for the charge of all the $p_z$ electrons and screening of external potentials by states near the charge neutrality point. Both a homogenous ribbon and a graphene flake embedded within the ribbon are discussed. The formation of transport gaps as functions of the external confinement potential (top gate potential) and the Fermi energy (back gate potential) are described in good qualitative agreement with the experimental data. For a fixed number of excess electrons we find that the excess charge added to the system is, - depending on the voltages defining the work point of the device: $(i)$ delocalized outside the quantum dot, - in the transport gap due to the top gate potential $(ii)$ localized inside the quantum dot, - in the transport gap due to the back gate potential or $(iii)$ extended over both the quantum dot area and the ribbon connections, - outside the transport gaps. The applicability of the frozen valence band approximation to describe charging the quantum dot by excess electrons is also discussed.

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arXiv2015

Transconductance and effective Landé factors for quantum point contacts: spin-orbit coupling and interaction effects

We analyze the effective $g^*$ factors and their dependence on the orientation of the external magnetic field for a quantum point contact defined in the two-dimensional electron gas. The paper simulates the experimental procedure for evaluation of the effective Landé factors from the transconductance of a biased device in external magnetic field. The contributions of the orbital effects of the magnetic field, the electron-electron interaction and spin-orbit (SO) coupling are studied. The anisotropy of the $g^*$ factors for the in-plane magnetic field orientation, which seems counterintuitive from the perspective of the effective SO magnetic field, is explained in an analytical model of the constriction as due to the SO-induced subband mixing. The asymmetry of the transconductance as a function of the gate voltage is obtained in agreement with the experimental data and the results are explained as due to the depletion of the electron gas within the quantum point contact constriction and the related reduction of the screening as described within the DFT approach. The results for transconductance and the $g^*$ factors are in a good agreement with the experimental data [Phys. Rev. B {\bf 81}, 041303, 2010].

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arXiv2015

Electron paths and double-slit interference in the scanning gate microscopy

We analyze electron paths in a solid-state double-slit interferometer based on the two-dimensional electron gas and their mapping by the scanning gate microscopy (SGM). A device with a quantum point source contact of a split exit and a drain contact used for electron detection is considered. We study the SGM maps of source-drain conductance ($G$) as functions of the probe position and find that for a narrow drain the classical electron paths are clearly resolved but without any trace of the double-slit interference. The latter is present in the SGM maps of backscattering ($R$) probability only. The double-slit interference is found in the $G$ maps for a wider drain contact but at the expense of the loss of information on the electron trajectories. Stability of $G$ and $R$ maps versus the geometry parameters of the scattering device is also discussed. We discuss the interplay of the Young interference and interference effects between various electron paths introduced by the tip and the electron detector.

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arXiv2015

Multitip scanning gate microscopy for ballistic transport studies in systems with two-dimensional electron gas

We consider conductance mapping of systems based on the two-dimensional electron gas with scanning gate microscopy using two and more tips of the atomic force microscope. The paper contains results of numerical simulations for a model tip potential with a proposal of a few procedures for extraction and manipulation the ballistic transport properties. In particular, we demonstrate that the multi-tip techniques can be used for readout of the Fermi wavelength, detection of potential defects, filtering specific transverse modes, tuning the system into resonant conditions under which a stable map of a local density of states can be extracted from conductance maps using a third tip.

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arXiv2015

Two-electron n-p double quantum dots in carbon nanotubes

We consider electron states in n-p double quantum dots defined in a semiconducting carbon nanotube (CNT) by an external potential. We describe formation of extended single-electron orbitals originating from the conduction and valence bands confined in a minimum and a maximum of the external potential, respectively. We solve the problem of a confined electron pair using an exact diagonalization method within the tight-binding approach, which allows for a straightforward treatment of the conduction and valence band states, keeping an exact account for the intervalley scattering mediated by the atomic defects and the electron-electron interaction. The exchange interaction - which in the unipolar double dots is nearly independent of the axial magnetic field (B) and forms singlet-like and triplet-like states - in the n-p system appears only for selected states and narrow intervals of B. In particular the ground-state energy level of a n-p double dot is not split by the exchange interaction and remains four-fold degenerate at zero magnetic field also for a strong tunnel coupling between the dots.

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arXiv2015

Single-electron shell occupation and effective $g$-factor in few-electron nanowire quantum dots

Nanowire double quantum dots occupied by an even number of electrons are investigated in the context of energy level structure revealed by electric dipole spin resonance measurements. We use numerically exact configuration interaction approach up to 6 electrons for systems tuned to Pauli spin blockade regime. We point out the differences between the spectra of systems with two and a greater number of electrons. For two-electrons the unequal length of the dots results in a different effective $g$-factors in the dots as observed by the recent experiments. For an increased number of electrons the $g$-factor difference between the dots appears already for symmetric systems and it is greatly amplified when the dots are of unequal length. We find that in the lowest energy states all except of two electrons form a frozen core of singlet shells that can be separated away for description of the properties of the system.

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arXiv2014

Tight-binding simulations of electrically driven spin-valley transitions in carbon nanotube quantum dots

We describe dynamics of spin and valley transitions driven by alternating electric fields in quantum dots defined electrostatically within semiconducting carbon nanotubes (CNT). We use the tight-binding approach to describe the states localized within a quantum dot taking into account the circumferential spin-orbit interaction due to the s-p hybridization and external fields. The basis of eigenstates localized in the quantum dot is used in the solution of the time-dependent Schroedinger equation for description of spin flips and inter-valley transitions that are driven by periodic perturbation in the presence of coupling between the spin, valley and orbital degrees of freedom. Besides the first order transitions we find also fractional resonances. We discuss the transition rates with selection rules that are lifted by atomic disorder and the bend of the tube. We demonstrate that the electric field component perpendicular to the axis of the CNT activates spin transitions which are otherwise absent and that the resonant spin-flip time scales with the inverse of the electric field.

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arXiv2014

Imaging transition to fractional quantum Hall regime by Coulomb blockade microscopy

We consider electron systems in quantum dots and imaging of the confined charge density by the Coulomb blockade microscopy (CBM) with the scanning probe technique. We apply an exact diagonalization method to study the reaction of the electron system to the potential induced by the model potential of the probe and calculate the energy maps as functions of the position of the probe. The charge densities derived from the energy maps are confronted to the exact charge densities. We focus on the transition of the electron system to the fractional quantum Hall conditions in external magnetic field. For magnetic fields corresponding to the integer fillings of the lowest Landau level the electron system exhibits a liquid-like reaction to the potential of the probe and the confined charge density can be quite accurately mapped by the CBM. For fractional fillings of the lowest Landau level the single-electron charge density islands nucleate in presence of the tip. In circular quantum dots the single-electron islands evade imaging by CBM. We demonstrate that mapping the molecular charge densities is possible for confinement potentials of symmetry that is lower and consistent with the geometry of the lowest-energy charge distribution of the single-electron islands.

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