Nonanalytic enhancement of the charge transfer from adatom to one-dimensional semiconductor superlattice and optical absorption spectrum

Tanaka, Satoshi; Garmon, Savannah; Petrosky, Tomio

doi:10.1103/physrevb.73.115340

Cited by 49 publications

(100 citation statements)

References 25 publications

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“…Note, that the denominator is just the product η + (ǫ q )η − (ǫ q ) which is strictly positive along the integration path in (A1) but in general has four roots on the complex plane 26 . Introducing the variable z = e iq the integration is now taken along an arc of the complex unit circle which can be written as the sum of the two contours shown in Fig.…”

Section: Appendix A: Asymptotic Form Of the Correlationsmentioning

confidence: 99%

Fano resonances and entanglement entropy

Eisler

Garmon

2010

Phys. Rev. B

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We study the entanglement in the ground state of a chain of free spinless fermions with a single side-coupled impurity. We find a logarithmic scaling for the entanglement entropy of a segment neighboring the impurity. The prefactor of the logarithm varies continuously and contains an impurity contribution described by a one-parameter function, while the contribution of the unmodified boundary enters additively. The coefficient is found explicitly by pointing out similarities with other models involving interface defects. The proposed formula gives excellent agreement with our numerical data. If the segment has an open boundary, one finds a rapidly oscillating subleading term in the entropy that persists in the limit of large block sizes. The particle number fluctuation inside the subsystem is also reported. It is analogous with the expression for the entropy scaling, however with a simpler functional form for the coefficient.

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Section: Appendix A: Asymptotic Form Of the Correlationsmentioning

confidence: 99%

Fano resonances and entanglement entropy

Eisler

Garmon

2010

Phys. Rev. B

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“…In the present system, the latter yields oscillations in Σ + (z) with energy as shown in Fig.2 in Ref. [24], in contrast to the infinite chain case [33]. In fact, with the change of variables z = − cos θ, the self-energy is written by…”

Section: Complex Eigenvalue Problemmentioning

confidence: 60%

“…[33], in terms of the resonant state representation. For the unbounded chain, the Hamiltonian is represented bŷ…”

Section: Discussionmentioning

confidence: 99%

“…reduces to a fourth order polynomial equation, yielding a resonance state and an anti-resonance state in addition to the two bound states that are called as Persistent Bound States: PBS [25,33]. 4 We show in Fig.6 the trajectory of the resonance state by the dotted line and the solutions for E d = −0.9 and E d = −0.6, by filled circle and filled square, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…Using the first order time-dependent perturbation method for the interaction between light and matter, the absorption spectrum is given by [32,33] …”

Section: Modelmentioning

confidence: 99%

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Fano absorption spectrum with the complex spectral analysis

et al. 2017

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A new aspect of understanding a Fano absorption spectrum is presented in terms of the complex spectral analysis. The absorption spectrum of an impurity embedded in semi-infinite superlattice is investigated. The boundary condition on the continuum causes a large energy dependence of the self-energy, enhances the nonlinearity of the eigenvalue problem of the effective Hamiltonian, yielding several nonanalytic resonance states. The overall spectral features is perfectly reproduced by the direct transitions to these discrete resonance states. Even with a single optical transition path the spectrum exhibits an asymmetric Fano profile, which is enhanced for the transition to the nonanalytic resonance states. Since this is the genuine eigenstates of the total Hamiltonian, there is no ambiguity in the interpretation of the absorption spectrum, avoiding the arbitrary interpretation based on the quantum interference. The spectral change around the exceptional point is well understood when we extract the resonant state component.

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Amplification of non‐Markovian decay due to bound state absorption into continuum

Garmon

Petrosky

Simine

et al. 2012

Fortschritte der Physik

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Key words non-Markovian decay, power law decay, bound stateIt is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time 'near zone' and long time 'far zone.' In the near zone the survival probability falls off according to a t −1 power law, and in the far zone it falls off as t −3 . We show that the timescale TQ separating these two regions is inversely related to the gap between the discrete bound state energy and the continuum threshold. In the case that the bound state is absorbed into the continuum and vanishes, then the time scale TQ diverges and the survival probability follows the t −1 power law even on asymptotic scales. Conversely, one could study the case of an anti-bound state approaching the threshold before being ejected from the continuum to form a bound state. Again the t −1 power law dominates precisely at the point of ejection.

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Nonanalytic enhancement of the charge transfer from adatom to one-dimensional semiconductor superlattice and optical absorption spectrum

Cited by 49 publications

References 25 publications

Fano resonances and entanglement entropy

Fano resonances and entanglement entropy

Fano absorption spectrum with the complex spectral analysis

Amplification of non‐Markovian decay due to bound state absorption into continuum

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