Quantum Confined Fano Interference

Abstract

We study the transition from a dense continuum to a sparse quasicontinuum in the Fano problem. Transmission measurements on epitaxial layers of GaAs in a high magnetic field and calculations of the optical absorption show how the Fano interference disappears as quantum confinement discretizes the continuum states. The transition between quasi-one-dimensional and quasi-zero-dimensional systems occurs at length scales which are unusually large for optical experiments. [S0031-9007(97)02443-5] PACS numbers: 78.66.Fd, 32.80.Dz, 73.20.Dx Quantum size effects have been thoroughly investigated since advances in material synthesis made possible the growth of semiconductor heterostructures with atomic monolayer accuracy. They become apparent in a physical phenomenon when at least one dimension of the sample becomes comparable to or smaller than the length scale that governs the quantum mechanics of that phenomenon. In the optical domain the exciton Bohr radius a o is usually the relevant length scale, and quantum confinement dominates the optical properties of semiconductor structures of size L # a o [1,2]. In the case of transport the carrier de Broglie wavelength l B determines the length scale at which quantum transport effects are observed [3]. In this Letter we present a new example of quantum size effects, apparent in the line shape of an optical resonance involving the quantum mechanical coupling between a localized, discrete state and a quasicontinuum. As shown below, the size effect is a direct consequence of the energy quantization due to the finite sample thickness. Remarkably, it appears for length scales L . 15a o that are unusually large for the optical domain.Quantum mechanical interference between a discrete state and a quasicontinuum is a fundamental problem in physics. It is one of a few exactly solvable models in many-body theory [4], and as such it gives insight into other many-particle phenomena. This problem was simultaneously formulated by Anderson and Fano. Anderson applied it to the mixing of localized impurity orbitals and extended conduction band states in solid state physics [5]. Fano used it to describe the interference of electronic transitions in atomic spectra [6]. The coupling of the discrete state to the quasicontinuum in the Fano-Anderson model is, furthermore, a prototype of irreversible decay [7,8]. It can represent various fundamental relaxation mechanisms, such as spontaneous emission, nuclear decay, the autoionization of excited atoms originally discussed by Fano [6], intramolecular relaxation, and coupling to a phonon bath [9]. The quantum interference manifests itself as a resonance in the optical absorption spectrum with a characteristic asymmetric line shape. Very close to its peak, a pronounced minimum occurs at an energy where the transition amplitudes of the discrete state and the continuum interfere destructively. It has been observed in a variety of atomic, molecular, and semiconductor systems [10], and recently in the optical absorption of bulk semiconductors in high mag...

Quantum mirages in scanning tunneling spectroscopy of Kondo adsorbates: Vibrational signatures

“…45 A related effect is expected for processes in mesoscopic systems such as excitonic or impurity optical absorption in quantum dots as a function of the dot size. 46 It should be pointed out that there is a meaningful connection between the Fano-like line shapes obtained here ͓as represented by Eq. ͑15͔͒ for resonant STM processes involving scattering from a boundary wall or defect ͑such as the elliptical coral͒ and the closely related ͑but distinctly different͒ ones that characterize direct processes such as those in single, uncorraled atom systems.…”

Structural control of Fano resonances in semiconductor heterostructures

“…Some experimental evidence for structurally induced Fano resonances in intersubband transitions of semiconductor heterostructures has been presented [28][29][30][31]. Many more studies have been devoted to Fano resonances associated with interband transitions, such as [32][33][34][35][36] and references therein. Moreover, Fano resonances in semiconductors have been reported within other physical context, such as an excited state of EL2 and Raman spectra [37,38].…”

Simple model of a Feshbach resonance in the strong-coupling regime

“…(2) We assume that the open channel potential U0(r) vanishes as |r| -» oo, i.e., the open channel asymptote defines the zero of potential energy. The closed channel potential Uc(r) tends asymptotically to a positive constant v > 0.…”