Quantum rings of arbitrary shape and non-uniform width in a threading magnetic field

Bruno-Alfonso, Alexys; Latgé, A.

doi:10.1103/physrevb.77.205303

Cited by 58 publications

(29 citation statements)

References 33 publications

(62 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Self-organized semiconductor quantum nanostructures have attracted extensive interest and intensive research owing to their great potential applications in basic physics and advanced solid state devices-for example, quantum rings for Aharonov-Bohm interferometers and entangled quantum dots for quantum information processes [1][2][3][4][5][6][7]. Among the different self-organized epitaxial growth methods, droplet epitaxy has considerable potential for the fabrication of such peculiar nanostructures and advanced semiconductor devices [8,9].…”

Section: Introductionmentioning

confidence: 99%

Holed nanostructures formed by aluminum droplets on a GaAs substrate

Wang

et al. 2010

Nano Res.

View full text Add to dashboard Cite

We have studied the morphology evolution of holed nanostructures formed by aluminum droplet epitaxy on a GaAs surface. Unique outer rings with concentric inner holed rings were observed. Further, an empirical equation to describe the size distribution of the outer rings in the holed nanostructures has been established. The contour line generated by the equation provides physical insights into quantum ring formation by droplets of group Ⅲ materials on Ⅲ-Ⅴ substrates.

show abstract

Section: Introductionmentioning

confidence: 99%

Holed nanostructures formed by aluminum droplets on a GaAs substrate

Wang

et al. 2010

Nano Res.

View full text Add to dashboard Cite

show abstract

“…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.

View full text Add to dashboard Cite

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.

show abstract

“…12-17) have stimulated theoretical and experimental studies of the AB oscillations in the persistent currents carried by single-and few-particle states (see, e.g., Refs. [18][19][20][21][22][23][24]. Using an ultrasensitive torsion magnetometer, AB oscillations in the magnetic moment of In x Ga 1−x As self-assembled quantum rings have been observed 18 with a magnitude of oscillation as large as 60% to 70% of the corresponding magnitude in an ideal ring.…”

Section: Introductionmentioning

confidence: 98%