arXiv subjects

B. Szafran

Publications and source records attributed to B. Szafran.

At least 55 records · Page 3Linked to original sources

arXiv2014

Signatures of spin-orbit coupling in scanning gate conductance images of electron flow from quantum point contacts

Electron flow through a quantum point contact in presence of spin-orbit coupling is investigated theoretically in the context of the scanning gate microscopy (SGM) conductance mapping. Although in the absence of the floating gate the spin-orbit coupling does not significantly alter the conductance, we find that the angular dependence of the SGM images of the electron flow at the conductance plateaux is substantially altered as the spin-orbit interaction mixes the orbital modes that enter the quantum point contact. The radial interference fringes that are obtained in the SGM maps at conductance steps are essentially preserved by the spin-orbit interaction as backscattering by the tip preserves the electron spin although the effects of the mode mixing are visible.

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arXiv2014

Imaging of double slit interference by scanning gate microscopy

We consider scanning gate microscopy imaging of the double slit interference for a pair of quantum point contacts (QPCs) defined within the two-dimensional electron gas. The interference is clearly present in the scattered electron wave functions for each of the incident subbands. Nevertheless, we find that the interference is generally missing in the experimentally accessible conductance maps for many incident subbands. We explain this finding on the basis of the Landauer approach. A setup geometry allowing for observation of the double slit interference by the scanning gate microscopy is proposed.

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arXiv2014

Conductance microscopy of quantum dots weakly or strongly coupled to the conducting channel

We consider scanning gate conductance microscopy of an open quantum dot that is connected to the conducting channel using the wave function description of the quantum transport and a finite difference approach. We discuss the information contained in conductance ($G$) maps. We demonstrate that the maps for a delta-like potential perturbation exactly reproduce the local density of states for the quantum dot that is weakly coupled to the channel, i.e. when the connection of the channel to the dot transmits a single transport mode only. We explain this finding in terms of the Lippmann-Schwinger perturbation theory. We demonstrate that the signature of the weak coupling conditions is the conductance which for $P$ subbands at the Fermi level varies between $P-1$ and $P$ in units of ${2e^2}/{h}$. For stronger coupling of the quantum dot to the channel the $G$ maps resolve the local density of states only for very specific work points with the Fermi energy coinciding with quasi-bound energy levels.

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arXiv2014

Spontaneous and resonant lifting of the spin blockade in nanowire quantum dots

A complete numerical description of the charge and spin dynamics of a two-electron system confined in narrow nanowire quantum dots under oscillating electric field is presented in the context of recent electric dipole spin resonance experiments. We find that the spin-orbit coupling results in lifting the spin blockade by phonon mediated relaxation provided that the initially occupied state is close in energy to the ground state. This leads to suppression of the blockade from the triplet state with spins polarized parallel to the external magnetic field B. At higher B, after singlet-triplet ground-state transition a new channel for lifting the Pauli blockade opens which results in an appearance of additional resonance lines. The calculated signatures of this transition are consistent with recent experimental results [S. M. Frolov et al., Phys. Rev. Lett. 109, 236805 (2012)].

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arXiv2014

Wave function description of conductance mapping for quantum Hall electron interferometer

Scanning gate microscopy of quantum point contacts (QPC) in the integer quantum Hall regime is considered in terms of the scattering wave functions with a finite-difference implementation of the quantum transmitting boundary approach. Conductance ($G$) maps for a clean QPC as well as for a system including an antidot within the constriction are evaluated. The step-like locally flat $G$ maps for clean QPCs turn into circular resonances that are reentrant in external magnetic field when the antidot is introduced to the constriction. The current circulation around the antidot and the spacing of the resonances at the magnetic field scale react to the probe approaching the QPC. The calculated $G$ maps with a rigid but soft antidot potential reproduce the features detected recently in the electron interferometer [F. Martins et al. Nature Sci. Rep. 3, 1416 (2013)].

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arXiv2013

Spin current source based on a quantum point contact with local spin-orbit interaction

Proposal for construction of a source of spin-polarized current based on quantum point contact with local spin-orbit interaction is presented. We show that spin-orbit interaction present within the narrowing acts like a spin filter. The spin polarization of the current is discussed as a function of the Fermi energy and the width of the quantum point contact.

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arXiv2013

Simulations of imaging of the local density of states by charged probe technique for resonant cavities

We simulate scanning probe imaging of the local density of states related to scattering Fermi level wave functions inside a resonant cavity. We calculate potential landscape within the cavity taking into account the Coulomb charge of the probe and its screening by deformation of the two-dimensional electron gas using the local density approximation. Approximation of the tip potential by a Lorentz function is discussed. The electron transfer problem is solved with a finite difference approach. We look for stable work points for the extraction of the local density of states from conductance maps. We find that conductance maps are highly correlated with the local density of states when the Fermi energy level enters into Fano resonance with states localized within the cavity. Generally outside resonances the correlation between the local density of states and conductance maps is low.

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arXiv2013

Confined states in quantum dots defined within finite flakes of bilayer graphene: Coupling to the edge, ionization threshold, and valley degeneracy

We study quantum dots defined by external potentials within finite flakes of bilayer graphene using the tight-binding approach. We find that in the limit of large flakes containing zigzag edges the dot-localized energy levels appear within the energy continuum formed by extended states. As a consequence no ionization threshold for the carriers contained within the dot exists. For smaller flakes with zigzag boundaries the dot-localized energy levels appear interlaced with the energy levels outside the flake, so in a charging experiment the electrons will be added alternately to the dot area and to its neighborhood. We demonstrate that for flakes with armchair boundaries only, an energy window accessible uniquely to the dot-localized states is opened. Then a number of electrons can be added to the dot before the external states start to be occupied. We also discuss coupling of the dot-localized states to the edge states in the context of the valley degeneracy lifting. Moreover, we extract smooth envelope wave functions from the tight-binding solution and discuss their spatial symmetries. The coupling of the dot localized energy levels with reconstructed zigzag edges and atomic vacancies present within the layers is also considered.

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arXiv2013

Simulations of electric-dipole spin resonance for spin-orbit-coupled quantum dots in Overhauser field: fractional resonances and selection rules

We consider spin rotations in single- and two-electron quantum dots that are driven by external AC electric field with two mechanisms that couple the electron spatial motion and the spin degree of freedom: the spin-orbit interaction and a random fluctuation of the Overhauser field due to nuclear spin bath. We perform a systematic numerical simulation of the driven system using a finite difference approach with an exact account taken for the electron-electron correlation. The simulation demonstrates that the electron oscillation in fluctuating nuclear field is translated into an effective magnetic field during the electron wave packet motion. The effective magnetic field drives the spin transitions according to the electric-dipole spin resonance mechanism. We find distinct signatures of selection rules for direct and higher-order transitions in terms of the spin-orbital symmetries of the wave functions. The selection rules are violated by the random fluctuation of the Overhauser field.

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arXiv2013

Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by scanning probe technique

We perform a numerical simulation of mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps in function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are confronted with the original ones. The present study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limit case. We concentrate on large quantum dots for which strong electron-electron correlations appear. For circular dots the correlations lead to formation of Wigner molecules that in the presence of the tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for repulsive tip potential and overestimated for the attractive tip. In lower-symmetry quantum dots the Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of the tip. These charge densities are well resolved by the mapping. The single-electron islands appear in the laboratory frame provided that classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.

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arXiv2013

Spin polarization anisotropy in a narrow spin-orbit-coupled nanowire quantum dot

One and two-electron systems confined in a single and coupled quantum dots defined within a nanowire with a finite radius are studied in the context of spin-orbit coupling effects. Anisotropy of the spin-orbit interaction is discussed in terms of the system geometry and orientation of the external magnetic field vector. We find that there are easy and hard spin polarization axes and in the quantum dot with strong lateral confinement electron spin becomes well defined in spite of the presence of spin-orbit coupling. We present an analytical solution for the one-dimensional limit and study its validity for nanowires of finite radii by comparing the results with a full three-dimensional calculation. The results are also confronted with the recent measurements of the effective Lande factor and avoided crossing width anisotropy in InSb nanowire quantum dots [S. Nadj-Perge et al., Phys. Rev. Lett. 108, 166801 (2012)].

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arXiv2012

Resonant harmonic generation and collective spin rotations in electrically driven quantum dots

Spin rotations induced by an AC electric field in a two-electron double quantum dot are studied by an exact numerical solution of the time dependent Schroedinger equation in the context of recent electric dipole spin resonance experiments based on the Pauli blockade. We demonstrate that the splitting of the main resonance line by the spin exchange coupling is accompanied by the appearance of fractional resonances and that both these effects are triggered by interdot tunnel coupling. We find that the AC driven system generates residual but distinct harmonics of the driving frequency which are amplified when tuned to the main transition frequency. The mechanism is universal for electron systems in electrically driven potentials and works also in the absence of electron-electron interaction or spin-orbit coupling.

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arXiv2011

Carrier-carrier inelastic scattering events for spatially separated electrons: magnetic asymmetry and turnstile electron transfer

We consider a single electron traveling along a strictly one-dimensional quantum wire interacting with another electron in a quantum ring capacitively coupled to the wire. We develop an exact numerical method for treating the scattering problem within the stationary two-electron wave function picture. The considered process conserves the total energy but the electron within the wire passes a part of its energy to the ring. We demonstrate that the inelastic scattering results in both magnetic asymmetry of the transfer probability and a turnstile action of the ring on the electrons traveling separately along the ring. We demonstrate that the inelastic backscattering and / or inelastic electron transfer can be selectively eliminated from the process by inclusion of an energy filter into the wire in form of a double barrier system with the resonant energy level tuned to the energy of the incident electron. We demonstrate that the magnetic symmetry is restored when the inelastic backscattering is switched o?, and the turnstile character of the ring is removed when the energy transfer to the ring is excluded for both transferred and backscattered electron waves. We discuss the relation of the present results to the conductance systems based on the electron gas.

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arXiv2011

Fano resonances and electron spin transport through a two-dimensional spin-orbit-coupled quantum ring

Electron transport through a spin-orbit-coupled quantum ring is investigated within linear response theory. We show that the finite width of the ring results in the appearance of Fano resonances in the conductance. This turns out to be a consequence of the spin-orbit interaction that leads to a breaking of the parity of the states localized in the ring. The resonances appear when the system is close to maxima of Aharonov-Casher conductance oscillations where spin transfer is heavily modified. When the spin-orbit coupling strength is detuned from the Aharonov-Casher maxima the resonances are broadened resulting in a dependence of the spin transport on the electron Fermi energy in contrast to predictions from one-dimensional models

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arXiv2011

Multisubband transport and magnetic deflection of Fermi electron trajectories in three terminal junctions and rings

We study the electron transport in three terminal junctions and quantum rings looking for the classical deflection of electron trajectories in presence of intersubband scattering. We indicate that although the Aharonov-Bohm oscillations and the Lorentz force effects co-exist in the low subband transport, for higher Fermi energies a simultaneous observation of the both effects is difficult and calls for carefully formed structures. In particular, in quantum rings with channels wider than the input lead the Lorentz force is well resolved but the Aharonov-Bohm periodicity is lost in chaotic scattering events. In quantum rings with equal length of the channels and $T$-shaped junctions the Aharonov-Bohm oscillations are distinctly periodic but the Lorentz force effects are not well pronounced. We find that systems with the wedge shaped junctions allow for observation of both the periodic Aharonov-Bohm oscillations and the magnetic deflection.

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arXiv2011

Tuning of the spin-orbit interaction in a quantum dot by an in-plane magnetic field

Using an exact diagonalization approach we show that one- and two-electron InAs quantum dots exhibit avoided crossing in the energy spectra that are induced by the spin-orbit coupling in the presence of an in-plane external magnetic field. The width of the avoided crossings depends strongly on the orientation of the magnetic field which reveals the intrinsic anisotropy of the spin-orbit coupling interactions. We find that for specific orientations of the magnetic field avoided crossings vanish. Value of this orientation can be used to extract the ratio of the strength of Rashba and Dresselhaus interactions. The spin-orbit anisotropy effects for various geometries and orientations of the confinement potential are discussed. Our analysis explains the physics behind the recent measurements performed on a gated self-assembled quantum dot [S. Takahashi et al. Phys. Rev. Lett. 104, 246801 (2010)].

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arXiv2010

Magnetic forces and localized resonances in electron transfer through quantum rings

We study the current flow through semiconductor quantum rings. In high magnetic field the current is usually injected to the arm of the ring preferred by classical magnetic forces. However, for narrow magnetic field intervals that appear periodically on the magnetic field scale the current is injected to the other arm of the ring. We indicate that the appearance of the anomalous -- non-classical -- current circulation results from Fano interference involving localized resonant states. The identification of the Fano interference is based on the comparison of the solution of the scattering problem with the results of the stabilization method. The latter employs the bound-state type calculations and allows to extract both the energy of metastable states localized within the ring and the width of resonances by analysis of the energy spectrum of a finite size system in function of its length. The Fano resonances involving states of anomalous current circulation become extremely narrow on both magnetic field and energy scales. This is consistent with the orientation of the Lorentz force that tends to keep the electron within the ring and thus increases the lifetime of the electron localization within the ring. Absence of periodic Fano resonances in electron transfer probability through a quantum ring containing an elastic scatterer is also explained.

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arXiv2010

Tuning Fano resonances by magnetic forces for electron transport through a quantum wire side-coupled to a quantum ring

We consider electron transport in a quantum wire with a side-coupled quantum ring in a two-dimensional model that accounts for a finite width of the channels. We use the finite difference technique to solve the scattering problem as well as to determine the ring-localized states of the energy continuum. The backscattering probability exhibits Fano peaks for magnetic fields for which a ring-localized states appear at the Fermi level. We find that the width of the Fano resonances changes at high magnetic field. The width is increased (decreased) for resonant states with current circulation that produce the magnetic dipole moment that is parallel (antiparallel) to the external magnetic field. We indicate that the opposite behavior of Fano resonances due to localized states with clockwise and counterclockwise currents results from the magnetic forces which change the strength of their coupling to the channel and modify the lifetime of localized states.

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