Magnetic field control of the intraband optical absorption in two-dimensional quantum rings

Olendski, O.; Barakat, T.

doi:10.1063/1.4866873

Cited by 17 publications

(21 citation statements)

References 56 publications

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“…From Eqs. (46) and (47a) it is seen that the product r 2 k 2 is a B-independent quantity again. Let us also note that the lowest band of the AB-free QD does saturate the uncetainty relation, Eq.…”

Section: Discussionmentioning

confidence: 80%

“…4 depicts a variation of the field-indepdendent quantity S ρ 00 + S γ 00 with the strength of the antidot a for the zero AB flux, φ AB = 0. At the small a, corresponding to the "thick" ring [46], the sum increases quite rapidly from its threshold QD value 2(1 + ln π) = 4.2894 . .…”

Section: Measures In Uniform Magnetic Field Bmentioning

confidence: 95%

“…Moreover, the limit ω 0 → ∞ with the requirement of the constant radius r min reduces the problem to the 1D ring whereas a suitable form for the 2D straight wire is given by the condition of the constant ω 0 and unrestrictedly enlarging r min . It is known that the QR with the small antidot strength describes a "thick" ring whereas the structure with the large a is deemed as a "thin" annulus [46]. A huge advantage of the theoretical consideration of Eq.…”

Section: Position and Momentum Waveformsmentioning

confidence: 99%

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Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Olendski

2019

Physics Letters A

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Shannon quantum information entropies S ρ,γ , Fisher informations I ρ,γ , Onicescu energies O ρ,γ and complexities e S O are calculated both in the position (subscript ρ) and momentum (γ) spaces for the azimuthally symmetric twodimensional nanoring that is placed into the combination of the transverse uniform magnetic field B and the Aharonov-Bohm (AB) flux φ AB and whose potential profile is modeled by the superposition of the quadratic and inverse quadratic dependencies on the radius r. The increasing intensity B flattens momentum waveforms Φ nm (k) and in the limit of the infinitely large fields they turn to zero: Φ nm (k) → 0 at B → ∞, what means that the position wave functions Ψ nm (r), which are their Fourier counterparts, tend in this limit to the δ-functions. Position (momentum) Shannon entropy depends on the field B as a negative (positive) logarithm of ω ef f ≡ ω 2 0 + ω 2 c /4 1/2 , where ω 0 determines the quadratic steepness of the confining potential and ω c is a cyclotron frequency. This makes the sum S ρ nm + S γ nm a field-independent quantity that increases with the principal n and azimuthal m quantum numbers and does satisfy entropic uncertainty relation. Position Fisher information does not depend on m, linearly increases with n and varies as ω ef f whereas its n and m dependent Onicescu counterpart O ρ nm changes as ω −1 ef f . The products I ρ nm I γ nm and O ρ nm O γ nm are B-independent quantities. A dependence of the measures on the ring geometry is discussed. It is argued that a variation of the position Shannon entropy or Onicescu energy with the AB field uniquely determines an associated persistent current as a function of φ AB at B = 0. An inverse statement is correct too.

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Section: Discussionmentioning

confidence: 80%

Section: Measures In Uniform Magnetic Field Bmentioning

confidence: 95%

Section: Position and Momentum Waveformsmentioning

confidence: 99%

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Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Olendski

2019

Physics Letters A

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“…In an attempt to expand quantum-information theory to the study of the quantum rings (QRs) [1], a recent analysis [2] addressed an influence of the combination of the transverse uniform magnetic field B and the AB flux φ AB [3] on the position and momentum components of, among others, Shannon entropy [4] of the one-particle orbitals of the flat 2D annulus whose rotationally symmetric potential profile U(r) is modeled in the position of polar coordinates (r, ϕ r ) by the superposition of the quadratic and inverse quadratic dependencies on the radius r [5][6][7][8][9][10][11][12][13][14][15]:…”

Section: Introductionmentioning

confidence: 99%

“…where a non-negative coefficient 0 ≤ α < ∞ controls the reaction of the system to its deviation from the equilibrium; namely, the l'Hôpital's rule deduces that at α → 1, both Rényi and Tsallis entropies degenerate to their Shannon counterpart, Equations (2), whereas at vanishingly small magnitudes, this parameter allows equal contributions from the random events of any frequency of actual occurrence, which in the case of the infinite or semi-infinite region of integration in Equations. (13) and 14leads to the divergence of the corresponding measure (provided it exists) at α → 0. On the other hand, extremely strong Rényi or Tsallis parameters pick up in the corresponding probability distributions the global maxima only with a full discard of all other happenings.…”

Section: Introductionmentioning

confidence: 99%

Rényi and Tsallis Entropies of the Aharonov–Bohm Ring in Uniform Magnetic Fields

Olendski

2019

Entropy

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One-parameter functionals of the Rényi R ρ,γ (α) and Tsallis T ρ,γ (α) types are calculated both 1 in the position (subscript ρ) and momentum (γ) spaces for the azimuthally symmetric 2D nanoring that 2 is placed into the combination of the transverse uniform magnetic field B and the Aharonov-Bohm (AB) 3 flux φ AB and whose potential profile is modelled by the superposition of the quadratic and inverse 4 quadratic dependencies on the radius r. Position (momentum) Rényi entropy depends on the field B as 5 a negative (positive) logarithm of ω e f f ≡ ω 2 0 + ω 2 c /4 1/2 , where ω 0 determines the quadratic steepness 6 of the confining potential and ω c is a cyclotron frequency. This makes the sum R ρ nm (α)field-independent quantity that increases with the principal n and azimuthal m quantum numbers and 8 does satisfy corresponding uncertainty relation. In the limit α → 1 both entropies in either space tend to 9 their Shannon counterparts along, however, different paths. Analytic expression for the lower boundary 10 of the semi-infinite range of the dimensionless coefficient α where the momentum entropies exist reveals 11 that it depends on the ring geometry, AB intensity and quantum number m. It is proved that there is the 12 only orbital for which both Rényi and Tsallis uncertainty relations turn into the identity at α = 1/2 and 13 which is not necessarily the lowest-energy level. At any coefficient α, the dependence of the position 14 Rényi entropy on the AB flux mimics the energy variation with φ AB what, under appropriate scaling, can 15 be used for the unique determination of the associated persistent current. Similarities and differences 16 between the two entropies and their uncertainty relations are discussed too. 17 Note that, as it follows from Eqs. (49a) and (49c), the sum of the entropies of the generalized Gaussian 111 approaches its edge values (which are equal to each other due to the fact that each item in it has the 112 same dependence on the Rényi parameter and, as a result, due to the condition from Eq. (18), at the rims 113 α and β simply interchange their places) from above and since the expression in the square brackets in 114 Eq. (49b) is always positive, left-hand side of Eq. (21) reaches its maximum at the Shannon entropy. Also, 115 the leading terms in all three cases are increasing functions of the magnetic index what means that at 116 the greater |m| the corresponding curve lies higher satisfying, of course, the uncertainty relation. As our 117 numerical results show, the same statement holds true at the fixed quantum number m and the increasing 118 principal index n. 119For the QR, a > 0, a comparison of Eqs. (25), (39) and (48) proves that the n = m = 0 orbital does 120 convert at α = 1/2 the Rényi uncertainty into the identity, as it did for the Tsallis inequality too. This is 121 also exemplified in Fig. 2(a), which shows that its sum R ρ (α) + R γ (β) at any parameter α is the smallest 122 one as compared to other levels. Dependence of the left-hand side of Eq. (21) on n and |m| is...

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Dispersive Spectra of Phonon Modes and Fröhlich Electron–Phonon Coupling Properties in AlGaN Quantum Rings: Wurzite versus Zinc‐Blende Structure

Zhang

Shao

Pang³

2022

Physica Status Solidi (b)

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The influence of crystal structure on the phonon modes and electron–phonon coupling properties in nitride quantum ring (QR) structures is investigated based on the macroscopic dielectric continuum model. It is found that three types of phonon modes including the surface optical (SO) phonon modes, the exact confined (EC) modes, and quasiconfined (QC) modes can coexist in the wurtzite nitride QR. However, only the SO modes and EC modes may appear in zinc‐blende nitride QR, and the QC modes cannot exist in zinc‐blende QRs in general. Numerical calculation on AlN QR shows that the SO modes of zinc‐blende QR are more dispersive than those of wurtzite QR. Furthermore, the degenerative behavior of QC modes to SO modes in wurtzite QRs is clearly observed. Moreover, the electron–phonon coupling functions in zinc‐blende QRs are larger than those in wurtzite QRs. These results reveal that the crystal structures greatly affect not only the type of phonon mode, but also the coupling strength of electron–phonon interaction. The present theoretical scheme and the numerical results are quite useful and important for further understanding and investigating the polaronic effect and related physical properties in wurtzite and zinc‐blende nitride QRs.

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Magnetic field control of the intraband optical absorption in two-dimensional quantum rings

Cited by 17 publications

References 56 publications

Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Quantum information measures of the Aharonov–Bohm ring in uniform magnetic fields

Rényi and Tsallis Entropies of the Aharonov–Bohm Ring in Uniform Magnetic Fields

Dispersive Spectra of Phonon Modes and Fröhlich Electron–Phonon Coupling Properties in AlGaN Quantum Rings: Wurzite versus Zinc‐Blende Structure

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