Electronic eigenstates in quantum rings: Asymptotics and numerics

Gridin, Dmitri; Adamou, Alexander

doi:10.1103/physrevb.69.155317

Cited by 42 publications

(38 citation statements)

References 21 publications

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“…3, it becomes clear that the in-plane wave functions in this system are quite similar to those in quantum rings, as expected. [39,40,13] The difference between the two systems concerns the wave functions in z-direction, which are spatially restricted in the latter, but free in the former. As in the rings case, in the presence of an axially applied magnetic field, the eigenenergies of individual carriers display oscillations due to the Aharonov-Bohm effect (not shown, see e.g.…”

Section: Single Shell Confinementmentioning

confidence: 99%

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Electric and magnetic field effects on the excitonic properties of elliptic core–multishell quantum wires

Macêdo

Silva

Chaves

et al. 2013

J. Phys.: Condens. Matter

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Abstract. The effect of eccentricity distortions of core-multishell quantum wires on their electron, hole and exciton states is theoretically investigated. Within the effective mass approximation, the Schrödinger equation is numerically solved for electrons and holes in systems with single and double radial heterostructures, and the exciton binding energy is calculated by means of a variational approach. We show that the energy spectrum of a core-multishell heterostructure with eccentricity distortions, as well as its magnetic field dependence, are very sensitive to the direction of an externally applied electric field, an effect that can be used to identify the eccentricity of the system. For a double heterostructure, the eccentricities of the inner and outer shells play an important role on the excitonic binding energy, specially in the presence of external magnetic fields, and lead to drastic modifications in the oscillator strength.PACS numbers: 78.67. Lt, Electric and magnetic field effects on excitons in core-multishell quantum wires 2

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Section: Single Shell Confinementmentioning

confidence: 99%

“…The main effect of the eccentricity is to create regions of higher curvature and, consequently, lower effective potential, [12,13] which work as traps to the otherwise circularly symmetric charge carriers wavefunctions. A similar effect is investigated e.g.…”

Section: Introductionmentioning

confidence: 99%

Electric and magnetic field effects on the excitonic properties of elliptic core–multishell quantum wires

Macêdo

Silva

Chaves

et al. 2013

J. Phys.: Condens. Matter

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“…We treat a gently thickening guide, the thickness variation repeating periodically along the guide. The methodology is similar to, say, Postnova & Craster (2006) and references therein, where trapping is sought in infinite structures or in finite structures such as rings (Gridin et al 2004). Let us take the thickness variation within a cell to be symmetric about the centreline and the upper boundary to be hðexÞ Z 1 C a e where e is a small parameter and the cell is KB=3!x !…”

Section: K1mentioning

confidence: 99%

Bloch waves in periodic multi-layered acoustic waveguides

Adams

Guenneau

2008

Proc. R. Soc. A.

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The band spectrum and associated Floquet-Bloch eigensolutions, arising in acoustic and electromagnetic waveguides, which have periodic structure along the guide while remaining of finite width, are found. Homogeneous Dirichlet or Neumann conditions along the guide walls, or an alternation of them, are taken. Importantly, in some cases, a total stop band at zero frequency is identified providing space for low-frequency localized modes; geometric defects in the structured waveguide also create these modes. Numerical and asymptotic techniques identify dispersion curves and trapped modes. Some cases demonstrate maxima and minima of the spectral edges within the Brillouin zone and also allow for ultraslow light or sound. Imaging applications using anomalous dispersion to generate subwavelength resolution are possible and are demonstrated.

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“…This differs from the WKBJ analysis in Shen et al (1968) for non-rotating free-surface waves and for rotating, stratified edge waves in Zhevandrov (1991), Smith (2004) and Adamou et al (2007) where the alongshore profile is fixed and the waves are short compared to the scale of offshore variations. Topography varying slowly in both horizontal directions is considered for non-rotating free-surface waves by Keller (1958), short topographic Rossby waves in Smith (1970), trapped modes in quantum rings by Gridin et al (2004) and Bruno-Alfonso & Latgé (2008), trapped modes in elastic plates by Gridin et al (2005) and trapped modes in slowly-varying acoustic waveguides by Biggs (2012). The quantum, elastic plate and acoustic problems are more straightforward than the shelf-wave problem in that the modal structure across the waveguide for corresponding forward-and backward-propagating modes is the same whereas in general the long forward-propagating shelf wave mode has cross-shelf structure different from the backward-propagating short shelf wave.…”

Section: Introductionmentioning

confidence: 99%

Localised continental shelf waves: geometric effects and resonant forcing

Rodney

Johnson

2015

J. Fluid Mech.

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Alongshore variations in coastline curvature or offshore depth profile can create localised regions of shelf wave propagation with modes decaying outside these regions. These modes, termed localised continental shelf waves ( CTWs) here, exist only at certain discrete frequencies lying below the maximum frequency for propagating shelf waves. The purpose of this paper is to obtain these frequencies and construct, both analytically and numerically, and discuss CTWs for shelves with arbitrary alongshore variations in offshore depth profile and coastline curvature. If the shelf curvature changes by a small fraction of its value over the shelf section of interest or a alongshore perturbation in offshore depth profile varies slowly over the same length scale then CTWs can be constructed using WKBJ theory. Two subcases are described: (i) if the propagating region is sufficiently long that the offshore structure of the CTW varies appreciably alongshore then the frequency and alongshore structure are found from a sequence of local problems; (ii) if the propagating region is sufficiently short that the alongshore change in offshore structure of the CTW is small then the alongshore modal structure is given in an explicit uniformly valid form. A separate asymptotic theory is required for curvature perturbations to shelves that are otherwise straight rather than curved. Comparison with highly accurately numerically determined CTWs shows that both theories are extremely accurate with the WKBJ theory having a significantly wider range of applicability and remaining accurate even when the underlying shelf curvature is small. An idealised model for the generation of CTWs is also suggested. A localised time-periodic wind stress generates an evanescent continental shelf wave in the far-field of a localised mode where the coast is almost straight and the response on the shelf is obtained numerically. If the forcing frequency is close to that of an CTW then the wind stress excites energetic motions in the region of maximum curvature, creating a significant localised response far from the forcing region.

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Electronic eigenstates in quantum rings: Asymptotics and numerics

Cited by 42 publications

References 21 publications

Electric and magnetic field effects on the excitonic properties of elliptic core–multishell quantum wires

Electric and magnetic field effects on the excitonic properties of elliptic core–multishell quantum wires

Bloch waves in periodic multi-layered acoustic waveguides

Localised continental shelf waves: geometric effects and resonant forcing

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