Two-channel quantum wire with an adatom impurity: Role of the van Hove singularity in the quasibound state in continuum, decay rate amplification, and the Fano effect

Journal Article · Tue Sep 15 00:00:00 EDT 2009 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.80.115318· OSTI ID:21294341

Garmon, S ^[1]; Nakamura, H ^[2]; Hatano, N ^[3]; Petrosky, T ^[4]

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1. Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen O (Denmark)
2. National Institute for Fusion Science, Oroshi-cho 322-6, Toki, Gifu 509-5292 (Japan)
3. Institute of Industrial Science, University of Tokyo, Komaba 4-6-1, Meguro, Tokyo 153-8505 (Japan)
4. Center for Complex Quantum Systems, University of Texas at Austin, 1 University Station, C1609, Austin, Texas 78712 (United States)

We provide detailed analysis of the complex eigenenergy spectrum for a two-channel quantum wire with an attached adatom impurity. The study is based on our previous work [Phys. Rev. Lett. 99, 210404 (2007)], in which we presented the quasibound states in continuum (or QBIC states). These are resonant states with very long lifetime that form as a result of two overlapping continuous energy bands, one of which, at least, has a divergent van Hove singularity at the band edge. We provide analysis of the full energy spectrum for all solutions, including the QBIC states, and obtain an expansion for the complex eigenvalue of the QBIC state. We show that it has a small decay rate of the order g{sup 6}, where g is the coupling constant of the adatom impurity. As a result of this expansion, we find that this state is a nonanalytic effect resulting from the van Hove singularity; it cannot be predicted from the ordinary perturbation analysis that relies on Fermi's golden rule. We also show that the QBIC state emerges as a direct result of the destabilization of the stable state that often exists on the outside edge of a band due to the divergence. As another result of the van Hove singularity, it has been previously reported that the decay rate of an unstable state is amplified in the vicinity of the band edge such that it is proportional to g{sup 4/3}. This again results from a breakdown of the Fermi rule. Here we explicitly show how the system behaves in the crossover region between the g{sup 4/3} region and the Fermi region. Finally, we calculate the local density of states near the adatom. We are able to demonstrate that the interference between two unstable states with a very large decay rate and one unstable state with a small decay rate results in a characteristic asymmetric Fano profile. This effect leads to the best chance of detecting the QBIC by scanning tunneling microscopy probe.

• OSTI ID: 21294341
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 80, Issue 11; Other Information: DOI: 10.1103/PhysRevB.80.115318; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
AMPLIFICATION
ASYMMETRY
BOUND STATE
COMPUTERIZED SIMULATION
COUPLING CONSTANTS
DECAY
DENSITY
DISTURBANCES
EIGENVALUES
ELECTRONS
ENERGY SPECTRA
EXPANSION
FANO FACTOR
IMPURITIES
INTERFERENCE
PERTURBATION THEORY
PHOTOEMISSION
POLARIZATION
QUANTUM WIRES
QUASIBOUND STATE
SCANNING TUNNELING MICROSCOPY
SINGULARITY
SPIN