Electron dynamics in graphene with gate-defined quantum dots

Pieper, Andreas; Heinisch, R. L.; Fehske, Holger

doi:10.1209/0295-5075/104/47010

Cited by 26 publications

(23 citation statements)

References 20 publications

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“…For the density of states the presence of well-quantized states in the quantum dot leads to an additional peak structure 14 . These results, obtained within Dirac theory, were confirmed for a tightbinding graphene lattice model utilizing exact numerical techniques 15 . From an application-oriented point of view, graphene quantum dots with 'confined' electrons may serve as hosts for spin qbits [16][17][18] .…”

Section: Introductionsupporting

confidence: 54%

Scattering of two-dimensional Dirac fermions on gate-defined oscillating quantum dots

2015

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Within an effective Dirac-Weyl theory we solve the scattering problem for massless chiral fermions impinging on a cylindrical time-dependent potential barrier. The set-up we consider can be used to model the electron propagation in a monolayer of graphene with harmonically driven quantum dots. For static small-sized quantum dots scattering resonances enable particle confinement and interference effects may switch forward scattering on and off. An oscillating dot may cause inelastic scattering by excitation of states with energies shifted by integer multiples of the oscillation frequency, which significantly modifies the scattering characteristics of static dots. Exemplarily the scattering efficiency of a potential barrier with zero bias remains finite in the limit of low particle energies and small potential amplitudes. For an oscillating quantum dot with finite bias, the partial wave resonances at higher energies are smeared out for small frequencies or large oscillation amplitudes, thereby dissolving the quasi-bound states at the quantum dot.

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Section: Introductionsupporting

confidence: 54%

Scattering of two-dimensional Dirac fermions on gate-defined oscillating quantum dots

2015

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“…Again the relatively large conductance at

V = - 0.080 t

(compared to G for

V = - 0.065 t

) originates from an effective (coherent) inter‐dot transfer of the electron. This hopping process is expected to take place on a reduced time scale (). As can be seen from the lowermost panel, at

V = - 0.065 t

, the LDOS notably shrinks if we move to the centre of the GNR; this depletion of the local particle density reduces the inter‐dot hopping and consequently the conductance.…”

Section: Resultsmentioning

confidence: 99%

“…Forward scattering and Klein tunnelling will also be suppressed if a Fano resonance arises between the background partition and the resonant contribution to electron scattering [9]. These results, obtained within continuum Dirac theory, were numerically confirmed for a lattice model [10,11]. The role of resonances have been analysed in various graphene scattering experiments [12,13].…”

mentioning

confidence: 87%

Electron confinement in graphene with gate-defined quantum dots

Fehske

Hager

Pieper

2015

Phys. Status Solidi B

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We theoretically analyse the possibility to electrostatically confine electrons in circular quantum dot arrays, impressed on contacted graphene nanoribbons by top gates. Utilising exact numerical techniques, we compute the scattering efficiency of a single dot and demonstrate that for small-sized scatterers the cross-sections are dominated by quantum effects, where resonant scattering leads to a series of quasi-bound dot states. Calculating the conductance and the local density of states for quantum dot superlattices we show that the resonant carrier transport through such graphene-based nanostructures can be easily tuned by varying the gate voltage.Schematic representation of a Dirac electron wave packet impinging on a circular, electrostatically defined quantum dot.Copyright line will be provided by the publisher 1 Introduction High-quality graphene nanostructures are the most likely building blocks in future electronics, plasmonics and photonics assemblies. Most of their striking features arise from the strictly two-dimensional, honeycomb lattice structure of the basic material, which causes the nontrivial topology of the electronic wave function and an almost linear low-energy spectrum of the chiral quasiparticles (charge carriers) near the so-called Dirac nodal points [1]. From an application-technological point of view, the tunability of the transport properties of graphene by external electric and magnetic fields is of particular importance [2]. This allows a controlled modification of selected areas of the sample by gating. For instance, applying nanoscale top gates on graphene nanoribbons (GNRs) or bilayer graphene, single or double quantum dots with particular shape have been produced in recent experiments [3,4,5].

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“…an equilibrium situation (without incident wave) the normal modes can be interpreted as decaying states, where, for small values of ω, the lifetime of these quasi-bound dot states (appearing for R dot V dot = j n,m , where j n,m denotes the m-th zero of the n-th Bessel function of the first kind) can be extraordinarily long. This has been confirmed for a discrete (graphene) lattice by exact diagonalization 28,37 . As can be seen from the middle and bottom panels of Fig.…”

Section: Ti With a Gate-defined Quantum Dotmentioning

confidence: 57%

Topological insulators in random potentials

Pieper

Fehske

2016

Phys. Rev. B

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We investigate the effects of magnetic and nonmagnetic impurities on the two-dimensional surface states of three-dimensional topological insulators (TIs). Modeling weak and strong TIs using a generic four-band Hamiltonian, which allows for a breaking of inversion and time-reversal symmetries and takes into account random local potentials as well as the Zeeman and orbital effects of external magnetic fields, we compute the local density of states, the single-particle spectral function, and the conductance for a (contacted) slab geometry by numerically exact techniques based on kernel polynomial expansion and Green's function approaches. We show that bulk disorder refills the suface-state Dirac gap induced by a homogeneous magnetic field with states, whereas orbital (Peierlsphase) disorder perserves the gap feature. The former effect is more pronounced in weak TIs than in strong TIs. At moderate randomness, disorder-induced conducting channels appear in the surface layer, promoting diffusive metallicity. Random Zeeman fields rapidly destroy any conducting surface states. Imprinting quantum dots on a TI's surface, we demonstrate that carrier transport can be easily tuned by varying the gate voltage, even to the point where quasi-bound dot states may appear.

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Electron dynamics in graphene with gate-defined quantum dots

Cited by 26 publications

References 20 publications

Scattering of two-dimensional Dirac fermions on gate-defined oscillating quantum dots

Scattering of two-dimensional Dirac fermions on gate-defined oscillating quantum dots

Electron confinement in graphene with gate-defined quantum dots

Topological insulators in random potentials

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