Optical Properties of Correlated Electrons
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Optical spectra provide a versatile tool for studying the electronic properties of matter. In addition, the absolute spectral weight of an optical spectrum reveals optical sum-rules, which are one of the most powerful tools of experimental and theoretical physics providing access to deeply rooted quantities such as the effective mass of the charge carriers and their kinetic energy. The formalism for the optical conductivity of correlated electrons is presented in this chapter for general values of the inverse wavelength \(q\) and general band dispersion \(\epsilon _k\) of the electrons. The corresponding sumrule is found to have a characteristic \(q\)-dependence for the nearest-neighbour tight binding model, causing in this case a vanishing of spectral weight for \(q\) at the Brillouin-zone boundary, i.e. for \(qa=\pi \). These findings are of possible importance for \(k\)-resolved infrared spectroscopy, a technique which is in full development at the moment.
KeywordsVector Potential Current Operator Optical Conductivity Electron Energy Loss Spectroscopy Regular Part
It is a pleasure to thank Adrian Kantian, Christophe Berthod, Alexey Kuzmenko and Gianni Blatter for their comments. This work was supported by the SNSF through Grants No. 200020-140761 and 200020-135085, and the National Center of Competence in Research (NCCR) Materials with Novel Electronic PropertiesMaNEP.
- 4.J. Chen, M. Badioli, p Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A.Z. Elorza, N. Camara, F. Javier Garca de Abajo, R. Hillenbrand, F.H.L. Koppens, Nature 487, 77 (2012)Google Scholar
- 6.C.F. Klingshirn, Semiconductor Optics (Springer, Berlin, 1995)Google Scholar
- 7.D. Pines, P. Nozières, The Theory of Quantum Liquids, Part I (Benjamin, New York, 1966)Google Scholar
- 10.A. Millis, in Strong Interactions in Low Dimensions, Physics and Chemistry of Materials with Low-Dimensions, Vol. 25, (Springer, Dordrecht, 2004)Google Scholar
- 11.D. van der Marel, in Strong Interactions in Low Dimensions, Physics and Chemistry of Materials with Low-Dimensions, Vol. 25, (Springer, Dordrecht, 2004)Google Scholar
- 12.E. van Heumen, D. van der Marel, in Lectures on the Physics of Strongly Correlated Systems XI, ed. by A. Avella, F. Manzini, (American Institute of Physics, New York, 2007)Google Scholar
- 14.C.N. Presura, Ph.D. thesis, Rijksuniversiteit Groningen, 2003Google Scholar
- 15.S. Nakai, N. Nuecker, H. Romberg, M. Alexander, J. Fink, Phys. Scripta 41, 596 (1990)Google Scholar
- 16.F.P. Mena, J.F. DiTusa, D. van der Marel, G. Aeppli, D.P. Young, A. Damascelli, J.A. Mydosh, Phys. Rev. B 73, 085205 (2006)Google Scholar
- 17.S. I. Mirzaei, D. Stricker, J. N. Hancock, C. Berthod, A. Georges, E. van Heumen, M. K. Chan, X. Zhao, Y. Li, M. Greven, N. Barisic, D. van der Marel, Proc. Natl. Acad. Sci. USA 110, 5774 (2013)Google Scholar