Delocalization of excitons in a magnetic field

Abstract

Brief Reports are accounts of completed research which, while meeting the usual Physical Review standards of scientific quality, do not warrant regular articles. A Brief Report may be no longer than four printed pages and must be accompanied by an abstract. The same publication schedule as for regular articles is followed, and page proofs are sent to authors.The two-body effects for a Mott-Wannier exciton in a magnetic field are investigated. For excitons with nonvanishing pseudomomentum there exists an outer potential well which contains a class of weakly bound and delocalized quantum states. The spectrum and eigenfunctions in this potential we11 are calculated in a harmonic approximation.The behavior of matter in strong magnetic fields became in the past two decades a subject of great interest. The numerous investigations in different branches of physics like, for example, atomic, molecular, and solidstate physics, have shown that the properties of matter in strong external fields are very different from those of the field-free case and we, therefore, encounter a variety of new phenomena due to the presence of the strong field. The term "strong field" has no absolute meaning but rather indicates that the forces due to the field are comparable to or even larger than the interaction forces of the system. This can happen for different states of the same physical system on different scales of the absolute field strength. In particular, it is possible to investigate the strong field regime of, for example, the hydrogen atom by studying its highly excited Rydberg states at laboratory magnetic-field strengths. ' In solid-state physics, the analog of such a "simple" system like the hydrogen atom would be an elementary excitation like, for example, an exciton. Let us assume that the distance of the particle and hole is much larger than the lattice spacing, i.e. , we consider a Mott-Wannier exciton. For this kind of exciton all effects due to the presence of the lattice can be included in a simple way in the excitonic Hamiltonian model. ' This Hamiltonian model is a phenomenological approach which neglects many residual interactions. However, it represents under certain circumstances a good zeroth-order approximation to the exact excitonic Hamiltonian.Excitons, excitonic molecules, as well as excitonic matter, have been studied extensively in the literature. They are common phenomena occuring in insulator and semiconductor physics. Since the dielectricity constant can become large and since the effective masses of the particle and hole are very often small compared to the proton and electron mass, the corresponding excitonic Rydberg (binding energy of the exciton) can be much H= (K -eBXr) + 1 2 1 2M 2p p -e~A p 2 2where @=[m mh/(mhm )] (we assume mh )m ). mh and m are the mass of the hole and particle, respectively. p = (m~m& /M), M, 8, and e are the reduced and total mass, magnetic field vector, and dielectricity constant, re-smaller than the hydrogenic one. This has drastic consequences if we turn on a magnetic field: ...

Physical properties of elongated inorganic nanoparticles

“…An exciton is a bound system, composed of an electron (e) and a hole (h) that experience a mutual Coulomb interaction. Here, we will be dealing with a particular type of exciton, the ''Wannier-Mott'' exciton, in which the e-h distance is much larger than the lattice constant of the crystal in which it is formed [86]. One key parameter associated with the exciton is its binding energy, which is defined as:…”

Hydrogen atom moving across a strong magnetic field: analytical approximations

“…In particular, socalled decentred states (with the electron localized mostly in the "magnetic well" aside from the Coulomb centre) are likely to be populated. These exotic states have been predicted by Burkova et al (1976) and studied by Ipatova et al (1984), Baye et al (1992), Dzyaloshinskii (1992) and Schmelcher (1993). As well as the usual "centred" states, the decentred states have an infinite discrete energy spectrum (Potekhin 1994, hereafter Paper I).…”

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“…It has also been found that a velocity-dependent, Coriolis-like force in Newton's equations causes the ionization of the electron to exhibit chaotic scattering [MW92,UF95,JFU99]. All these phenomena, as well as renewed interest in the motional Stark effect [JHY83,F94], make the crossed-fields problem an experimental accessible paradigm for a wide variety of outstanding issues in atomic and molecular physics, solid-state physics [DS92,Schm93], nuclear physics [BM75], astrophysics [Ma89], and celestial mechanics [Mi82].…”