Electrical spin switch in a two-electron triangular graphene quantum dot

On electron propagation in triangular graphene quantum dots

“…Considering only the nearest neighbour coupling, the two-component armchair wave functions [53, equation (48)] become the current (renormalized) armchair determinant sign homomorphism wave functions (113) that are discretized separately on the sublattices A + M and A − M . Even though properties of the triangular zigzag graphene quantum dots that are identical with the currently analysed shape have been recently studied [43,44], the majority of theoretical and experimental research has been conducted on the triangular zigzag dots which do not include the three corner positions [2,15,16,24,55,56,61] and which admit the nearest-neighbour coupling zero-energy states [51]. Precise relations between the electron wave functions and energy spectra inherent in these two slightly different types of the triangular zigzag graphene quantum dots deserve further study.…”

“…. Let A M be the armchair honeycomb lattice (16) and let L σ,± A,M be the armchair weight sets (39) which correspond to any magnifying factor M ∈ N and sign homomorphism σ ∈ Σ. Then the following products of the E-functions (48) and armchair honeycomb Weyl orbit functions (77) decompose for any point a ∈ A M and weight λ ∈ L σ,± A,M into sums over the armchair neighbourhood sets ( 22) and (23) as…”

“…The purpose of this article is to formulate and analytically solve classes of tight-binding models [8,21] that describe an electron propagating in single-layer triangular graphene quantum dots with armchair and zigzag edges [2,16,24,61]. Extending the results for the armchair dots [53] via the honeycomb Weyl orbit functions and the corresponding discrete Fourier-Weyl transforms [26,28], explicit exact forms of the electron wave functions and energy spectra are constructed.…”

“…Single and multilayer graphene quantum dots [23,41,45,59], nanoribbons [9,63] and nanotubes [10,12] represent significant classes of mesoscopic graphenebased structures [54]. Single and multiparticle propagation characteristics [16,52], behaviours in electric and magnetic fields [17,18,39] together with optical properties [6,35,50] of these graphene structures have been researched. As fundaments for further theoretical and experimental analysis, single-electron properties of single-layer circular [22,57], hexagonal [14,52,61] and triangular [2,18,21,24,53,61] quantum dots have been extensively numerically and analytically investigated.…”

Two-electron conduction band of a graphene quantum dot and coherent spin manipulation

“…To suppress hyperfine-induced dephasing, it is desirable to develop qubits in carbon-based materials, where hyperfine interaction is absent [4]. GQDs exhibit very long spin-decoherence times and thus are expected to become an ideal platform for fabricating spin qubits [5][6][7][8][9]. For extending spin decoherence times, it is helpful to use two-electron spins with a different degree of freedom from nuclear spins [10][11][12].…”