Model of tunnelling through periodic array of quantum dots in a magnetic field

Popov, I. Yu.; Osipov, S. A.

doi:10.1088/1674-1056/21/11/117306

Cited by 4 publications

(4 citation statements)

References 12 publications

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“…During the investigation of tunneling through single-layer lattices, wide zones in the resulting contour plot with very low value of T were discovered [18,19]. The widths of these zones are greater than the product of the Boltzmann constant and the temperature value and, thus, this phenomenon is physically measurable.…”

Section: Results and Comparison With Single-layer Arraysmentioning

confidence: 99%

“…We study the influence of the magnetic field and tunneling electron energy on the transmission coefficient and compare our results with the tunneling through the corresponding singlelayer periodic arrays studied earlier [18,19]. The main ideas of the present paper was described in an extended abstract [20].…”

Section: Introductionmentioning

confidence: 87%

“…Values α ± describe the quality of contacts C ± . This technique was used in [18] to construct a model of tunneling through single quantum electron layer.…”

Section: Fig 3 Model Of the Device With Connected Leadsmentioning

confidence: 99%

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Model of tunnelling through double quantum layer in a magnetic field

Meynster¹,

Popov²,

Popov³

2017

Nanosystems: Phys. Chem. Math.

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Several explicitly solvable models are constructed for electron tunneling in a system of double two-dimensional periodic arrays of quantum dots with two laterally coupled leads in a homogeneous magnetic field are constructed. The theory of self-adjoint extensions of symmetric operators is used for modelling of electron transport. Dependencies of the transmission coefficient on the magnetic field, the energy of electron and the distance between layers are investigated. The results are compared with those of tunnelling through the corresponding single-layer periodic arrays.

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Section: Results and Comparison With Single-layer Arraysmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 87%

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Model of tunnelling through double quantum layer in a magnetic field

Meynster¹,

Popov²,

Popov³

2017

Nanosystems: Phys. Chem. Math.

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“…Interesting results were obtained for tunneling through periodic arrays of quantum dots. [5,6] An explicitly solvable mathematical model for a description of tunnelling through a nanodevice was suggested in Refs. [7] and [8].…”

Section: Introductionmentioning

confidence: 99%

Dirac operator on the sphere with attached wires

et al. 2016

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An explicitly solvable model for tunnelling of relativistic spinless particles through a sphere is suggested. The model operator is constructed by an operator extensions theory method from the orthogonal sum of the Dirac operators on a semiaxis and on the sphere. The transmission coefficient is obtained. The dependence of the transmission coefficient on the particle energy has a resonant character. One observes pairs of the Breit-Wigner and the Fano resonances. It correlates with the corresponding results for a non-relativistic particle.

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Model of tunnelling through periodic array of quantum dots

2017

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Abstract. Several explicitly solvable models of electron tunnelling in a system of single and double twodimensional periodic arrays of quantum dots with two laterally coupled leads in a homogeneous magnetic field are constructed. First, a model of single layer formed by periodic array of zero-range potentials is described. The Landau operator (the Schrodinger operator with a magnetic field) with point-like interactions is the system Hamiltonian. We deal with two types of the layer lattices: square and honeycomb. The periodicity condition gives one an invariance property for the Hamiltonian in respect to magnetic translations group. The consideration of double quantum layer reduces to the replacement of the basic cell for the single layer by a cell including centers of different layers. Two variants of themodel for the double layer are suggested: with direct tunneling between the layers and with the connecting channels (segments in the model) between the layers. The theory of self-adjoint extensions of symmetric operators is a mathematical background of the model. The third stage of the construction is the description of leads connection. It is made by the operator extensions theory method too. Electron tunneling from input lead to the output lead through the double quantum layer is described. Energy ranges with extremely small (practically, zero) transmission were found. Dependencies of the transmission coefficient (particularly, "zero transmission bands" positions) on the magnetic field, the energy of electron and the distance between layers are investigated. The results are compared with the corresponding single-layer transmission.

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Model of tunnelling through periodic array of quantum dots in a magnetic field

Cited by 4 publications

References 12 publications

Model of tunnelling through double quantum layer in a magnetic field

Model of tunnelling through double quantum layer in a magnetic field

Dirac operator on the sphere with attached wires

Model of tunnelling through periodic array of quantum dots

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