The conductance of the asymmetric Aharonov–Bohm ring with a delta-potential barrier in the presence of Rashba spin–orbit interaction

Baltateanu, D.M.

doi:10.1016/j.physleta.2011.06.033

Cited by 3 publications

(8 citation statements)

References 29 publications

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“…The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15,16], δ-like singularities [17][18][19], supersymmetry [20,21], condensed matter [22,23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28][29][30], black hole [31,32] and noncommutative theories [33,34].…”

Section: Introductionmentioning

confidence: 99%

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

2013

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In this work the bound state and scattering problems for a spin-1/2 particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin-1/2 Aharonov-Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator.The Aharonov-Bohm (AB) effect [1] (first predicted by Ehrenberg and Siday [2]) is one of most weird results of quantum phenomena. The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15, 16], δ-like singularities [17-19], supersymmetry [20, 21], condensed matter [22, 23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28-30], black hole [31, 32] and noncommutative theories [33, 34].In the AB effect of spin-1/2 particles [7], besides the interaction with the magnetic potential, an additional two dimensional δ-function appears as the mathematical description of the Zeeman interaction between the spin and the magnetic flux tube [18,19]. This interaction is the basis of the spin-orbit coupling, which causes a splitting on the energy spectrum of atoms depending on the spin state. In Ref. [17] is argued that this δ-function contribution to the potential can not be neglected when the system has spin, having shown that changes in the amplitude and scattering cross section are implied in this case. The presence of a δ-function potential singularity, turns the problem more complicated to be solved. Such kind of point interaction potential can then be addressed by the self-adjoint extension approach [35]. The self-adjoint extension of symmetric operators [36] is a very powerful mathematical method and it can be applied to various systems in relativistic and nonrelativistic quantum mechanics, supersymmetric quantum mechanics and vortex-like models.This paper extends our previous report [37] on a general physical regularization method, both in details and depth. The method has the advantage of solving problems in relativistic and nonrelativistic quantum mechanics whose Hamiltonian is s...

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Section: Introductionmentioning

confidence: 99%

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

2013

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“…It is known that when we consider Eq. (25), that is, taking into account the δ -function, O 0 is not essentially self-adjoint. In this case, we must find the self-adjoint extensions of the operator O 0 corresponding to different types of boundary conditions.…”

Section: Aharonov-bohm Problem For the Spin-1 Sectormentioning

confidence: 99%

“…This radius may be understood as a kind of physical regularization for the δfunction in Eq. (25). Moreover, according to the BG method, the energy spectrum is given by…”

Section: Aharonov-bohm Problem For the Spin-1 Sectormentioning

confidence: 99%

“…This phenomenon is intimately related to a non-local boundary condition which relates the change in the phase of an electron wave function to the amount of flux in the solenoid. The interest in this issue appears in the different contexts, such as solid state physics [2], cosmic strings [3][4][5][6][7][8][9][10][11][12][13] κ-Poincaré-Hopf algebra [14,15], δ-like singularities [16], supersymmetry [17], condensed matter [18], Lorentz symmetry violation [19][20][21], quantum chromodynamics [22], general relativity [23], nanophysics [24], quantum ring [25][26][27][28], black hole [29] and noncommutative theories [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

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Relativistic quantum dynamics of vector bosons in an Aharonov–Bohm potential

Castro¹,

Silva²

2017

J. Phys. A: Math. Theor.

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The Aharonov-Bohm (AB) problem for vector bosons by the Duffin-Kemmer-Petiau (DKP) formalism is analyzed. Depending on the values of the spin projection, the relevant eigenvalue equation coming from the DKP formalism reveals an equivalence to the spin-1/2 AB problem. By using the self-adjoint extension approach, we examine the bound state scenario. The energy spectra are explicitly computed as well as their dependencies on the magnetic flux parameter and also the conditions for the occurrence of bound states.PACS 04.62.+v · 04.20.Jb · 03.65.Pm · 03.65.Ge

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“…Motivated by these works, we will study in this paper the case in which a one-dimensional and asymmetric ring (with unequal lengths of the arms) is subject to both magnetic flux and the Rashba SOI, considering different coupling parameters between the leads and the ring. Other details concerning the transport through asymmetric AB rings in the presence of the Rashba SOI have also been discussed [26], now with a special emphasis on the role of a delta-barrier.…”

Section: Introductionmentioning

confidence: 99%

On the Quantum Transport through an Asymmetric Aharonov-Bohm Ring with Rashba Spin-Orbit Interaction

Baltateanu

2011

Acta Phys. Pol. A

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The transmission amplitude through an asymmetric Aharonov-Bohm ring is derived analytically, in the presence of the Rashba spin-orbit interaction. For this purpose, one resorts to the transfer matrix method. The conductance is established in terms of the Landauer formalism and it is analyzed for different values of the asymmetry and ring-lead coupling parameters. A theoretical proposal to use the asymmetric ring like a spin filtering device is discussed, by an adequate tuning of the Aharonov-Bohm and Aharonov-Casher phases (via the magnetic field and the Rashba parameter).

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The conductance of the asymmetric Aharonov–Bohm ring with a delta-potential barrier in the presence of Rashba spin–orbit interaction

Cited by 3 publications

References 29 publications

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

Relativistic quantum dynamics of vector bosons in an Aharonov–Bohm potential

On the Quantum Transport through an Asymmetric Aharonov-Bohm Ring with Rashba Spin-Orbit Interaction

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