Exact derivative interband dielectric function at Van Hove singularities |
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Authors: | S Rabii JE Fischer |
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Institution: | The Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19174, USA |
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Abstract: | Interpretations of derivative spectra obtained by wavelength or thermal modulation have been based on universal lineshape functions that include only the resonant term, , obtained from differentiating ε(ω) with respect to ω or ωg, and that neglect the (ω + iη)?2 prefactor. We find the following differences between the approximate universal lineshape functions and the exact results obtained by including the nonresonant terms. dε/dω and dε2/dω are no longer simply related to each other; two entirely different functions are obtained. Wavelength and temperature modulation no longer have identical lineshapes. Either dε1/dω or dε2/dω has a resonant derivative lineshape according to whether j is even or odd, respectively, in contrast to the approximate universal function, which has no zeros, dε1/dω for a pure M1 singularity has positive and negative peaks of approximately equal strength, which would agree with the experimental results without invoking hyperbolic excitons (admixtures of Mj and mj+1 lineshapes). On the other hand, the nonexcitonic exact result fails to reproduce other experimental features. At the very least, our results call into question the extraction of numbers from detailed curve fits to the approximate functions. |
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