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Bound states in the continuum in open Aharonov-Bohm rings

Evgeny N. Bulgakov·Konstantin N. Pichugin·Almas F. Sadreev·Ingrid Rotter
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Abstract

Using formalism of effective Hamiltonian we consider bound states in continuum (BIC). They are those eigen states of non-hermitian effective Hamiltonian which have real eigen values. It is shown that BICs are orthogonal to open channels of the leads, i.e. disconnected from the continuum. As a result BICs can be superposed to transport solution with arbitrary coefficient and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are opened by attaching single-channel leads to them allow exact consideration of BICs. BICs occur at discrete values of energy and magnetic flux however it's realization strongly depend on a way to the BIC's point.

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Evgeny N. Bulgakov, Konstantin N. Pichugin, Almas F. Sadreev, Ingrid Rotter. 2006-10-07. Bound states in the continuum in open Aharonov-Bohm rings. https://doi.org/10.1134/s0021364006200057

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