In this Letter we discuss various properties of the local density of states (DOS) for a superconductor-ferromagnet hybrid system. The DOS is modified at small energies on both sides of the interface. Due to the interplay of superconductivity and ferromagnetism, the local DOS depends on the spin direction. The spin polarization effects extend over a long distance from the interface both in the superconductor and in the ferromagnet. If the ferromagnet is of finite lenght, the DOS shows a (spin dependent) gap.PACS numbers: 74.80. Fp,72.50.Bg, 74.50.+r Typeset using REVT E X 1 When a normal metal is in contact with a superconductor, pairing correlations appear on the normal side. The proximity effect is intimately related to the microscopic mechanism which governs the transport through SN interfaces. An incoming electron from N is reflected at the interface as a quasi-hole, and a Cooper pair is injected into the superconductor. Physical consequences of the proximity effect have been investigated since the early days of superconductivity 1 . Nevertheless, thanks to the development of nanofabrication technology, there has been a tremendous interest in exploring mesoscopic effects in hybrid Superconductor-Normal metal (SN) hybrid structures 2 . This activity lead to the discovery of new phenomena as the magnetoresistance oscillations in SN system 3 and the reentrant effect 4,5 .Due to the proximity effect, there is a modification of the local density of states (DOS)as it was recently shown both experimentally 6 and theoretically 7,8 . The local DOS in SN systems depends on the position relative to the interface. In the normal metal the DOS is suppressed at low energies whereas in the superconductor new states appear below the BCS gap. Properties of level statistics in hybrid system have been studied in Refs. 9,10.The proximity effect is very sensitive to the presence of a strong electron-electron interaction, as in the case of nanostructures 11 , and to pair-breaking effects. In this Letter we focus on this last aspect by considering the case in which the metal is an itinerant ferromagnet. An experiment which measures the local DOS in an FS system similarly to that of Ref. 6 seems to be feasable and it may lead, in our opinion, to further understanding of proximity in ferromagnetic materials. In this Letter we therefore study this problem by solving selfconsistently the Usadel equations for an FS interface. We will show that the combined effects of superconductivity (which introduces an energy dependence in the DOS) and ferromagnetism (which results in a finite momentum for the Cooper pairs entering the ferromagnet) leads to a rich structure in the DOS. The effects discussed in this Letter occur when the exchange energy is of the order of the superconducting gap. There is also a magnetic proximity effect which, for instance, induces a spin dependent DOS also on the superconducting side.Zeeman splitting of the DOS of magnetic materials and superconductors has been intesively investigated 20 . Most of the a...
This paper describes the economic phenomenon of price spiking in electric power markets and introduces an alternative way to model it. A stochastic FitzHugh-Nagumo dynamics in a special regime is proposed as a basic model for the power market, and an extension of the FitzHugh-Nagumo system is introduced to improve the statistical features of the basic model. Ideas from stochastic and coherence resonance are used to discuss the models.
The density, current, and spin response functions are investigated above the critical temperature for a system of three-dimensional fermions interacting via an attractive short-range potential, as the strength of this potential is varied from weak to strong coupling. In the strong-coupling (bosonic) limit, we identify the dominant diagrammatic contributions for a "dilute" system of composite bosons which form as bound-fermion pairs, by giving appropriate prescriptions for mapping bosonic onto fermionic diagrams. We then extrapolate these contributions to the weak-coupling limit and compare them with the ordinary (Aslamazov-Larkin, Maki-Thompson, and density-of-states) terms occurring in the theory of superconducting fluctuations for a clean system above the critical temperature. Specifically, we show that in the strong-coupling limit, at the zeroth order in the diluteness parameter for the composite bosons, the Aslamazov-Larkin term represents formally the dominant contribution to the density and current response functions, while the Maki-Thompson and densityof-states terms are strongly suppressed. Corrections to the Aslamazov-Larkin term are further identified via the above mapping prescriptions at the next order in the diluteness parameter for the composite bosons, where the residual mutual interaction appears explicitly. The spin response function is also examined, and it is found to be correctly suppressed in the strong-coupling limit only when appropriate sets of diagrams are considered simultaneously, thus providing a criterion for grouping diagrammatic contributions to the response functions.
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