Parallel in-plane-gated wires coupled by a ballistic window

Hirayama, Y.; Wieck, A. D.; Bever, T.; Klitzing, K. von

doi:10.1103/physrevb.46.4035

Cited by 33 publications

(20 citation statements)

References 32 publications

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“…In two dimensions the guides we will consider consist of two straight parallel waveguides connected through a window in the common boundary. Experimental observations of a waveguide with a similar configuration can be found in Hirayama et al (1992) and Hirayama et al (1993). A numerical model, based on classical rebound effects in a straight wire for the experimental specification described in Hirayama et al (1992), was provided in Takagaki and Ploog (1994).…”

Section: Introductionmentioning

confidence: 99%

Bound states in coupled guides. I. Two dimensions

Linton

Ratcliffe

2004

Journal of Mathematical Physics

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Bound states in coupled guides. I. Two dimensions.C. M. Linton and K. RatcliffeBound states that can occur in coupled quantum wires are investigated. We consider a two-dimensional configuration in which two parallel waveguides (of different widths) are coupled laterally through a finite length window and construct modes which exist local to the window connecting the two guides. We study both modes above and below the first cut-off for energy propagation down the coupled guide. The main tool used in the analysis is the so-called residue calculus technique in which complex variable theory is used to solve a system of equations which is derived from a mode-matching approach. For bound states below the first cut-off a single existence condition is derived, but for modes above this cut-off (but below the second cut-off), two conditions must be satisfied simultaneously. A number of results have been presented which show how the bound-state energies vary with the other parameters in the problem.

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Section: Introductionmentioning

confidence: 99%

Bound states in coupled guides. I. Two dimensions

Linton

Ratcliffe

2004

Journal of Mathematical Physics

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“…In contrast to the electric current in household wiring, charge flow in small chips with multiple leads may exhibit complex spatial distribution patterns depending on the external bias, electrostatic environment, chip geometry, and magnetic field. Traditionally, such patterns were detected using nonlocal transport measurements [1][2][3][4][5][6][7], i.e. by measuring voltage drops between various leads other than the source and drain.…”

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confidence: 99%

Giant nonlocality in nearly compensated 2D semimetals

Danz,

Titov,

Narozhny

2019

Preprint

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“…Also, for the 2D straight Dirichlet wave guide the existence of the bound state below the essential spectrum was predicted when the Neumann window is placed on its confining surface [16,18]. From practical point of view, such configuration can be realized in the form of the two window-coupled semiconductor channels of equal widths [16,19] whose experimental creation and study has been made possible [45] due to the advances of the modern growth nanotechnologies. The number of the bound states increases with the window length L and their energies are monotonically decreasing functions of L [24].…”

Section: Introductionmentioning

confidence: 99%

Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

Najar¹,

Olendski²

2011

J. Phys. A: Math. Theor.

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Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii a and b located on the opposite walls and the Dirichlet boundary condition on the remaining part of the boundary of the strip. We prove that such a system exhibits discrete eigenvalues below the essential spectrum for any a, b > 0. When a and b tend to the infinity, the asymptotic of the eigenvalue is derived. A comparative analysis with the one-window case reveals that due to the additional possibility of the regulating energy spectrum the anticrossing structure builds up as a function of the inner radius with its sharpness increasing for the larger outer radius. Mathematical and physical interpretation of the obtained results is presented; namely, it is derived that the anticrossings are accompanied by the drastic changes of the wave function localization. Parallels are drawn to the other structures exhibiting similar phenomena; in particular, it is proved that, contrary to the two-dimensional geometry, at the critical Neumann radii true bound states exist.

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Parallel in-plane-gated wires coupled by a ballistic window

Cited by 33 publications

References 32 publications

Bound states in coupled guides. I. Two dimensions

Bound states in coupled guides. I. Two dimensions

Giant nonlocality in nearly compensated 2D semimetals

Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs

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